{"id":339,"date":"2025-08-17T14:57:37","date_gmt":"2025-08-17T05:57:37","guid":{"rendered":"https:\/\/www.iso-g.com\/?p=339"},"modified":"2026-02-26T20:46:54","modified_gmt":"2026-02-26T11:46:54","slug":"%e5%b9%b3%e5%9d%87%e8%a8%88%e7%ae%97%e9%87%8f%e3%81%af%ef%bc%9f%e3%82%af%e3%82%a4%e3%83%83%e3%82%af%e3%82%bd%e3%83%bc%e3%83%88%e5%85%a5%e9%96%80","status":"publish","type":"post","link":"https:\/\/www.iso-g.com\/index.php\/2025\/08\/17\/%e5%b9%b3%e5%9d%87%e8%a8%88%e7%ae%97%e9%87%8f%e3%81%af%ef%bc%9f%e3%82%af%e3%82%a4%e3%83%83%e3%82%af%e3%82%bd%e3%83%bc%e3%83%88%e5%85%a5%e9%96%80\/","title":{"rendered":"\u5e73\u5747\u8a08\u7b97\u91cf\u306f\uff1f\u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8\u5165\u9580"},"content":{"rendered":"<h2>1. \u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8\u306e\u6982\u8981\uff08\u5b9a\u7fa9\u30fb\u4ed5\u7d44\u307f\uff09<\/h2>\n<h3>1-1. \u5206\u5272\u7d71\u6cbb\u6cd5\u306e\u8003\u3048\u65b9\u3068\u76f4\u611f\u7684\u7406\u89e3<\/h3>\n<h3>\u5206\u5272\u7d71\u6cbb\u6cd5\u306e\u8003\u3048\u65b9\u3068\u76f4\u611f\u7684\u7406\u89e3<\/h3>\n<h3>\u7d50\u8ad6<\/h3>\n<p>\u5206\u5272\u7d71\u6cbb\u6cd5\uff08Divide &amp; Conquer\uff09\u306f\u3001<strong>\u554f\u984c\u3092\u5c0f\u3055\u304f\u5206\u5272\u2192\u5404\u5c0f\u554f\u984c\u3092\u72ec\u7acb\u306b\u89e3\u304f\u2192\u7d50\u679c\u3092\u7d50\u5408<\/strong>\u3068\u3044\u30463\u30b9\u30c6\u30c3\u30d7\u3067\u89e3\u304f\u8a2d\u8a08\u30d1\u30bf\u30fc\u30f3\u3067\u3059\u3002<\/p>\n<p>\u5206\u5272\u5f8c\u306e\u5c0f\u554f\u984c\u304c\u201c\u5143\u306e\u554f\u984c\u3068\u540c\u578b\u201d\u3067\u3001\u7d50\u5408\u30b3\u30b9\u30c8\u304c\u6291\u3048\u3089\u308c\u308b\u3068\u304d\u306b\u7279\u306b\u5f37\u529b\u3067\u3001\u8a08\u7b97\u91cf\u306f\u3057\u3070\u3057\u3070 <strong>O(n log n)<\/strong> \u306b\u53ce\u307e\u308a\u307e\u3059\uff08\u4f8b\uff1a\u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8\u30fb\u30de\u30fc\u30b8\u30bd\u30fc\u30c8\uff09\u3002<\/p>\n<p>\u3053\u306e\u632f\u308b\u821e\u3044\u306f\u518d\u5e30\u95a2\u4fc2\u5f0f\u3092<strong>\u30de\u30b9\u30bf\u30fc\u5b9a\u7406<\/strong>\u3067\u89e3\u6790\u3059\u308b\u3053\u3068\u3067\u7406\u8ad6\u7684\u306b\u88cf\u3065\u3051\u3089\u308c\u307e\u3059\u3002<\/p>\n<hr \/>\n<h3>\u7406\u7531\u3084\u6839\u62e0<\/h3>\n<ul>\n<li><strong>\u7406\u8ad6\u7684\u88cf\u3065\u3051\uff08\u30de\u30b9\u30bf\u30fc\u5b9a\u7406\uff09<\/strong><br \/>\n\u5206\u5272\u7d71\u6cbb\u306e\u5b9f\u884c\u6642\u9593\u306f\u4e00\u822c\u306b<br \/>\n<strong>T(n) = a\u00b7T(n\/b) + f(n)<\/strong>\uff08a\u500b\u306e\u90e8\u5206\u554f\u984c\u3001\u5404\u30b5\u30a4\u30ban\/b\u3001\u7d50\u5408\u30b3\u30b9\u30c8f(n)\uff09<br \/>\n\u3068\u8868\u305b\u3001\u30de\u30b9\u30bf\u30fc\u5b9a\u7406\u306b\u3088\u308a\u53b3\u5bc6\u306b\u8a55\u4fa1\u3067\u304d\u307e\u3059\u3002\u4f8b\u3048\u3070 <strong>a=2, b=2, f(n)=\u0398(n)<\/strong>\uff08\u300c\u534a\u5206\u306b\u5206\u3051\u3066\u4e8c\u56de\u547c\u3073\u3001\u7dda\u5f62\u306b\u7d50\u5408\u300d\uff09\u306a\u3089 <strong>T(n)=\u0398(n log n)<\/strong>\u3002\u30b9\u30bf\u30f3\u30d5\u30a9\u30fc\u30c9\u5927\u5b66\u306e\u8b1b\u7fa9\u8cc7\u6599\u306f\u3053\u306e\u8003\u3048\u65b9\u3068\u5177\u4f53\u4f8b\uff08\u6574\u6570\u4e57\u7b97\u3001\u6700\u5927\u5024\u63a2\u7d22\u306a\u3069\uff09\u3092\u4f53\u7cfb\u7684\u306b\u793a\u3057\u3066\u3044\u307e\u3059\u3002<\/li>\n<li><strong>\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u5b9f\u4f8b\u306e\u78ba\u7acb<\/strong><br \/>\n\u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8\u306f\u201c\u30d4\u30dc\u30c3\u30c8\u3067\u5206\u5272\u2192\u5de6\u53f3\u3092\u518d\u5e30\u201d\u3068\u3044\u3046\u5178\u578b\u7684\u306a\u5206\u5272\u7d71\u6cbb\u3067\u3001<strong>\u5e73\u5747O(n log n)\u3001\u6700\u60aaO(n\u00b2)<\/strong> \u304c\u77e5\u3089\u308c\u3066\u3044\u307e\u3059\u3002\u5b66\u8853\u30fb\u6559\u80b2\u30b5\u30a4\u30c8\u3067\u3082\u540c\u69d8\u306e\u5b9a\u7fa9\u3068\u8a08\u7b97\u91cf\u304c\u6574\u7406\u3055\u308c\u3066\u3044\u307e\u3059\u3002<\/li>\n<li><strong>\u516c\u7684\u6559\u80b2\u6a5f\u95a2\u306e\u6559\u6750<\/strong><br \/>\nMIT OpenCourseWare \u3067\u306f\u3001\u5206\u5272\u7d71\u6cbb\u3092\u57fa\u790e\u3068\u3057\u3066 <strong>Strassen\u306e\u884c\u5217\u7a4d<\/strong>\u3084<strong>FFT<\/strong>\u306e\u8b1b\u7fa9\u304c\u516c\u958b\u3055\u308c\u3001\u5f93\u6765\u306e\u624b\u6cd5\u3088\u308a\u826f\u3044\u8a08\u7b97\u91cf\u306b\u5230\u9054\u3059\u308b\u300c\u5206\u5272\u2192\u7d50\u5408\u300d\u306e\u5a01\u529b\u304c\u89e3\u8aac\u3055\u308c\u3066\u3044\u307e\u3059\u3002\u3053\u308c\u306f\u5927\u5b66\u30ec\u30d9\u30eb\u306e\u516c\u958b\u6559\u6750\u3068\u3057\u3066\u4fe1\u983c\u3067\u304d\u308b\u4e00\u6b21\u8cc7\u6599\u3067\u3059\u3002<\/li>\n<li><strong>\u76f4\u611f\u306e\u88dc\u5f37\uff08\u53ef\u8996\u5316\uff09<\/strong><br \/>\n\u53ef\u8996\u5316\u30c4\u30fc\u30eb\uff08VisuAlgo\u7b49\uff09\u3067\u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8\/\u30de\u30fc\u30b8\u30bd\u30fc\u30c8\u306e\u300c\u5206\u5272\u2192\u7d50\u5408\u300d\u3092\u89b3\u5bdf\u3059\u308b\u3068\u3001<strong>\u518d\u5e30\u6728\u306e\u5404\u30ec\u30d9\u30eb\u3067\u6271\u3046\u8981\u7d20\u6570\u304c\u307b\u307cn\u306b\u4fdd\u305f\u308c\u3001\u6df1\u3055\u304clog n<\/strong> \u3067\u3042\u308b\u3053\u3068\u304c\u8996\u899a\u7684\u306b\u7406\u89e3\u3067\u304d\u307e\u3059\u3002<\/li>\n<\/ul>\n<hr \/>\n<h3>\u5b9f\u4f8b<\/h3>\n<h3>1) \u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8\uff08Divide: \u30d4\u30dc\u30c3\u30c8\u3067\u5de6\u53f3\/ Conquer: \u518d\u5e30 \/ Combine: \u307b\u307c\u4e0d\u8981\uff09<\/h3>\n<ul>\n<li><strong>\u6d41\u308c<\/strong>\uff1a\u914d\u5217\u304b\u3089\u30d4\u30dc\u30c3\u30c8\u3092\u9078\u3073\u3001<strong>\u5c0f\u3055\u3044\u5074<\/strong>\u3068<strong>\u5927\u304d\u3044\u5074<\/strong>\u306b\u5206\u3051\u308b \u2192 \u5404\u5074\u3092\u518d\u5e30\u7684\u306b\u6574\u5217 \u2192 \u9023\u7d50\u3002<\/li>\n<li><strong>\u76f4\u611f<\/strong>\uff1a\u6bce\u56de\u201c\u307b\u307c\u534a\u5206\u201d\u306b\u5272\u308c\u3066\u3044\u3051\u3070\u3001\u518d\u5e30\u306e<strong>\u6df1\u3055\u306f\u7d04log n<\/strong>\u3001\u5404\u30ec\u30d9\u30eb\u3067\u89e6\u308b\u8981\u7d20\u306f\u5408\u8a08<strong>\u7d04n<\/strong> \u2192 \u5408\u8a08 <strong>n log n<\/strong>\u3002<\/li>\n<li><strong>\u8a08\u7b97\u91cf<\/strong>\uff1a\u5e73\u5747 O(n log n)\u3001\u6700\u60aa O(n\u00b2)\uff08\u6975\u7aef\u306b\u504f\u3063\u305f\u5206\u5272\uff09\u3002\u30d4\u30dc\u30c3\u30c8\u6226\u7565\uff08\u30e9\u30f3\u30c0\u30e0\u5316\u3084\u4e09\u70b9\u4e2d\u592e\u5024\uff09\u3067\u6700\u60aa\u3092\u907f\u3051\u3084\u3059\u304f\u3057\u307e\u3059\u3002<\/li>\n<\/ul>\n<h3>2) \u30de\u30fc\u30b8\u30bd\u30fc\u30c8\uff08Divide: \u534a\u5206\u5272 \/ Conquer: \u518d\u5e30 \/ Combine: \u30de\u30fc\u30b8\uff09<\/h3>\n<ul>\n<li><strong>\u6d41\u308c<\/strong>\uff1a\u914d\u5217\u3092\u534a\u5206\u306b\u5206\u5272 \u2192 \u5404\u534a\u5206\u3092\u6574\u5217 \u2192 <strong>\u7dda\u5f62\u6642\u9593\u306e\u30de\u30fc\u30b8<\/strong>\u3067\u7d50\u5408\u3002<\/li>\n<li><strong>\u76f4\u611f<\/strong>\uff1a\u5e38\u306b\u4e8c\u5206\u5272\u306a\u306e\u3067<strong>\u6df1\u3055log n<\/strong>\u3001\u5404\u30ec\u30d9\u30eb\u306e\u30de\u30fc\u30b8\u306f<strong>\u5408\u8a08n<\/strong> \u2192 <strong>n log n<\/strong>\u3002\u53ef\u8996\u5316\u3092\u901a\u3058\u3066\u7d50\u5408\u5de5\u7a0b\u306e\u30b3\u30b9\u30c8\u304c\u898b\u3048\u308b\u306e\u304c\u5b66\u7fd2\u306b\u52b9\u679c\u7684\u3002<\/li>\n<\/ul>\n<h3>3) \u9ad8\u5ea6\u306a\u5fdc\u7528\uff08Strassen\u306e\u884c\u5217\u7a4d\u3001FFT\uff09<\/h3>\n<ul>\n<li><strong>Strassen<\/strong>\uff1a\u884c\u5217\u7a4d\u3092\u300c8\u500b\u306e\u90e8\u5206\u554f\u984c\u300d\u304b\u3089\u300c7\u500b\u300d\u306b\u6e1b\u3089\u3059\u5de5\u592b\u3067\u3001\u5f93\u6765\u306eO(n\u00b3)\u3088\u308a\u3082\u9ad8\u901f\uff08<strong>O(n^{log\u20827}) \u2248 O(n^{2.81})<\/strong>\uff09\u3002<\/li>\n<li><strong>FFT<\/strong>\uff1a\u96e2\u6563\u30d5\u30fc\u30ea\u30a8\u5909\u63db\u3092\u5206\u5272\u7d71\u6cbb\u3067**O(n log n)**\u306b\u77ed\u7e2e\u3002<br \/>\n\u3044\u305a\u308c\u3082\u5927\u5b66\u306e\u516c\u5f0f\u8b1b\u7fa9\u8cc7\u6599\u306b\u57fa\u3065\u304f\u6a19\u6e96\u7684\u306a\u7d50\u679c\u3067\u3059\u3002<\/li>\n<\/ul>\n<hr \/>\n<h3>\u76f4\u611f\u3092\u63b4\u3080\u305f\u3081\u306e\u6700\u77ed\u30e1\u30e2<\/h3>\n<div class=\"s_table\"><table>\n<thead>\n<tr>\n<th>\u30b9\u30c6\u30c3\u30d7<\/th>\n<th>\u4f55\u3092\u3059\u308b\u304b<\/th>\n<th>\u30b3\u30b9\u30c8\u306e\u5178\u578b<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>Divide<\/td>\n<td>\u554f\u984c\u3092\u540c\u578b\u306e\u5c0f\u554f\u984c\u306b\u5272\u308b<\/td>\n<td>\u5c0f\u3055\u3044\uff08\u307b\u307c\u30bc\u30ed\u301cn\uff09<\/td>\n<\/tr>\n<tr>\n<td>Conquer<\/td>\n<td>\u5404\u5c0f\u554f\u984c\u3092\u518d\u5e30\u3067\u89e3\u304f\uff08a\u500b\uff09<\/td>\n<td>a\u00b7T(n\/b)<\/td>\n<\/tr>\n<tr>\n<td>Combine<\/td>\n<td>\u5c0f\u554f\u984c\u306e\u89e3\u3092\u7d50\u5408\u3059\u308b<\/td>\n<td>f(n)\uff08\u4f8b\uff1an\u3067\u30de\u30fc\u30b8\uff09<\/td>\n<\/tr>\n<\/tbody>\n<\/table><\/div>\n<ul>\n<li><strong>\u518d\u5e30\u6728\u306e\u30a4\u30e1\u30fc\u30b8<\/strong>\uff1a<br \/>\n\u300c<strong>\u6a2a\uff08\u5404\u30ec\u30d9\u30eb\u306e\u5408\u8a08\u4ed5\u4e8b\u91cf\uff09\u2248 n<\/strong>\u300d\u00d7\u300c<strong>\u7e26\uff08\u30ec\u30d9\u30eb\u6570\uff09\u2248 log n<\/strong>\u300d\uff1d <strong>n log n<\/strong>\u3002\u3053\u3053\u304b\u3089\u3001\u5206\u5272\u7d71\u6cbb\u304c\u201c\u901f\u304f\u306a\u308a\u3084\u3059\u3044\u201d\u76f4\u611f\u304c\u63b4\u3081\u307e\u3059\u3002<\/li>\n<\/ul>\n<hr \/>\n<h3>\u7d50\u8ad6\uff08\u307e\u3068\u3081\uff09<\/h3>\n<p>\u5206\u5272\u7d71\u6cbb\u6cd5\u306f\u3001<strong>\u540c\u578b\u306e\u5c0f\u554f\u984c\u306b\u5206\u3051\u3089\u308c\u308b<\/strong>\u30fb<strong>\u7d50\u5408\u30b3\u30b9\u30c8\u304c\u5236\u5fa1\u3067\u304d\u308b<\/strong>\u3068\u3044\u3046\u6761\u4ef6\u304c\u305d\u308d\u3046\u3068\u3001\u7406\u8ad6\uff08\u30de\u30b9\u30bf\u30fc\u5b9a\u7406\uff09\u3068\u5b9f\u52d9\uff08\u30bd\u30fc\u30c8\u3001FFT\u306a\u3069\uff09\u306e\u4e21\u9762\u3067<strong>n log n\u7d1a<\/strong>\u306e\u6027\u80fd\u3092\u3082\u305f\u3089\u3057\u307e\u3059\u3002<\/p>\n<p>\u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8\u3067\u306f\u3001<strong>\u826f\u3044\u5206\u5272\u3092\u751f\u3080\u30d4\u30dc\u30c3\u30c8\u6226\u7565<\/strong>\u304c\u9375\u3002<\/p>\n<p>\u53ef\u8996\u5316\u3067\u201c\u5404\u30ec\u30d9\u30eb\u5408\u8a08n \u00d7 \u6df1\u3055log n\u201d\u306e\u69cb\u9020\u3092\u4f53\u5f97\u3057\u3001\u5fc5\u8981\u306b\u5fdc\u3058\u3066\u30de\u30fc\u30b8\u30bd\u30fc\u30c8\u7b49\u306e\u4ed6\u624b\u6cd5\u3068\u4f7f\u3044\u5206\u3051\u308b\u306e\u304c\u30d7\u30ed\u306e\u8a2d\u8a08\u5224\u65ad\u3067\u3059\u3002<\/p>\n<p><img decoding=\"async\" class=\"alignnone size-medium wp-image-340\" src=\"https:\/\/www.iso-g.com\/wp-content\/uploads\/2025\/08\/woman-8119716_640-300x240.jpg\" alt=\"\" width=\"300\" height=\"240\" srcset=\"https:\/\/www.iso-g.com\/wp-content\/uploads\/2025\/08\/woman-8119716_640-300x240.jpg 300w, https:\/\/www.iso-g.com\/wp-content\/uploads\/2025\/08\/woman-8119716_640.jpg 640w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p class=\"spacer\">&nbsp;<\/p>\n<h3>1-2. \u7528\u8a9e\u3068\u524d\u63d0\uff08\u914d\u5217\/\u6bd4\u8f03\u30bd\u30fc\u30c8\/\u30a4\u30f3\u30d7\u30ec\u30fc\u30b9\uff09<\/h3>\n<h3>\u7528\u8a9e\u3068\u524d\u63d0\uff08\u914d\u5217 \/ \u6bd4\u8f03\u30bd\u30fc\u30c8 \/ \u30a4\u30f3\u30d7\u30ec\u30fc\u30b9\uff09<\/h3>\n<h3>\u7d50\u8ad6<\/h3>\n<p>\u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8\u3092\u6b63\u3057\u304f\u7406\u89e3\u30fb\u8a55\u4fa1\u3059\u308b\u306b\u306f\u3001\u6b21\u306e\u524d\u63d0\u7528\u8a9e\u3092\u62bc\u3055\u3048\u308b\u306e\u304c\u8fd1\u9053\u3067\u3059\u3002<\/p>\n<ul>\n<li><strong>\u914d\u5217\uff08Array\uff09<\/strong>\uff1a\u6574\u6570\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3067<strong>\u30e9\u30f3\u30c0\u30e0\u30a2\u30af\u30bb\u30b9<\/strong>\u3067\u304d\u308b\u9023\u7d9a\u9818\u57df\u306e\u30b3\u30ec\u30af\u30b7\u30e7\u30f3\u3002\u591a\u304f\u306e\u5b9a\u7fa9\u3067\u300c\u6574\u6570\u6dfb\u5b57\u3067\u76f4\u63a5\u30a2\u30af\u30bb\u30b9\u3067\u304d\u308b\u3053\u3068\u300d\u304c\u672c\u8cea\u3067\u3059\u3002<\/li>\n<li><strong>\u6bd4\u8f03\u30bd\u30fc\u30c8\uff08Comparison sort\uff09<\/strong>\uff1a\u8981\u7d20\u9593\u306e<strong>\u5927\u5c0f\u6bd4\u8f03\u3060\u3051<\/strong>\u3092\u624b\u639b\u304b\u308a\u306b\u9806\u5e8f\u4ed8\u3051\u308b\u30bd\u30fc\u30c8\u7fa4\uff08\u4f8b\uff1a\u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8\u3001\u633f\u5165\u30bd\u30fc\u30c8\uff09\u3002<\/li>\n<li><strong>\u30a4\u30f3\u30d7\u30ec\u30fc\u30b9\uff08in-place\uff09<\/strong>\uff1a\u5165\u529b\u3068<strong>\u540c\u3058\u8a18\u61b6\u9818\u57df\u5185<\/strong>\u3067\u4e26\u3079\u66ff\u3048\u3092\u5b8c\u7d50\u3059\u308b\u5b9f\u88c5\u65b9\u91dd\u3002\u88dc\u52a9\u9818\u57df\u306f <strong>o(n)<\/strong>\uff08\u5178\u578b\u7684\u306b\u306f\u4e00\u5b9a\u500b\u6570\u306e\u4e00\u6642\u5909\u6570\u3068\u547c\u3073\u51fa\u3057\u30d5\u30ec\u30fc\u30e0\uff09\u306b\u5236\u9650\u3055\u308c\u307e\u3059\u3002<\/li>\n<\/ul>\n<p>\u3053\u308c\u3089\u3092\u524d\u63d0\u306b\u3059\u308b\u3068\u3001\u6bd4\u8f03\u30bd\u30fc\u30c8\u306b\u306f<strong>\u7406\u8ad6\u7684\u306a\u4e0b\u9650<\/strong>\uff08\u03a9(n log n)\uff09\u304c\u3042\u308a\u3001\u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8\u3092\u914d\u5217\u4e0a\u3067<strong>\u30a4\u30f3\u30d7\u30ec\u30fc\u30b9<\/strong>\u306b\u5b9f\u88c5\u3059\u308b\u72d9\u3044\uff08\u9ad8\u901f\u304b\u3064\u7701\u30e1\u30e2\u30ea\uff09\u3092\u6b63\u3057\u304f\u4f4d\u7f6e\u3065\u3051\u3089\u308c\u307e\u3059\u3002<\/p>\n<hr \/>\n<h3>\u7406\u7531\u3084\u6839\u62e0<\/h3>\n<ul>\n<li><strong>\u516c\u7684\u6a5f\u95a2\u306e\u5b9a\u7fa9\u3067\u78ba\u8a8d\u3067\u304d\u308b\u3053\u3068<\/strong>\n<ul>\n<li><strong>\u914d\u5217<\/strong>\uff1aNIST DADS \u306f\u300c\u6574\u6570\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3067\u30e9\u30f3\u30c0\u30e0\u30a2\u30af\u30bb\u30b9\u3067\u304d\u308b\u9805\u76ee\u306e\u96c6\u5408\u300d\u3068\u5b9a\u7fa9\u3002CSRC \u3067\u3082\u300c\u6574\u6570\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3067\u8981\u7d20\u3092\u8b58\u5225\u3059\u308b\u30c7\u30fc\u30bf\u69cb\u9020\u300d\u3068\u8aac\u660e\u304c\u3042\u308a\u307e\u3059\u3002\u914d\u5217\u3092\u524d\u63d0\u306b\u3059\u308b\u3068\u3001\u30d1\u30fc\u30c6\u30a3\u30b7\u30e7\u30f3\u64cd\u4f5c\u3092<strong>\u5b9a\u6570\u6642\u9593\u306e\u6dfb\u5b57\u64cd\u4f5c<\/strong>\u3067\u8a18\u8ff0\u3067\u304d\u307e\u3059\u3002<\/li>\n<li><strong>\u6bd4\u8f03\u30bd\u30fc\u30c8<\/strong>\uff1aNIST DADS \u306f\u300c\u30ad\u30fc\u306e<strong>\u6bd4\u8f03\u306e\u307f<\/strong>\u3067\u9806\u5e8f\u4ed8\u3051\u308b\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u300d\u3068\u5b9a\u7fa9\u3002\u5f93\u3063\u3066\u30ad\u30fc\u306e\u5206\u5e03\u3084\u7bc4\u56f2\u306b\u4f9d\u5b58\u3059\u308b\u300c\u8a08\u6570\u30bd\u30fc\u30c8\u300d\u7b49\u306f\u5225\u7cfb\u7d71\uff08<strong>restricted-universe sort<\/strong>\uff09\u306b\u306a\u308a\u307e\u3059\u3002<\/li>\n<li><strong>\u30a4\u30f3\u30d7\u30ec\u30fc\u30b9<\/strong>\uff1aNIST DADS \u306f\u300c\u4e26\u3079\u66ff\u3048\u5f8c\u3082<strong>\u540c\u3058\u30b9\u30c8\u30ec\u30fc\u30b8<\/strong>\u3092\u5360\u6709\u3057\u3001\u4efb\u610f\u6642\u70b9\u3067\u88dc\u52a9\u30e1\u30e2\u30ea\u306b\u4fdd\u6301\u3059\u308b\u9805\u76ee\u6570\u306f<strong>\u5b9a\u6570\u500b<\/strong>\u300d\u3068\u5b9a\u7fa9\u3002\u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8\u306f\u5178\u578b\u7684\u306b\u3053\u306e\u8981\u4ef6\u3092\u6e80\u305f\u3057\u307e\u3059\uff08\u518d\u5e30\u30b9\u30bf\u30c3\u30af\u306f\u8981\u7d20\u500b\u6570\u3067\u306f\u306a\u304f<strong>\u30d5\u30ec\u30fc\u30e0<\/strong>\u3067\u5897\u3048\u308b\uff09\u3002<\/li>\n<\/ul>\n<\/li>\n<li><strong>\u7406\u8ad6\u7684\u80cc\u666f\uff08\u6bd4\u8f03\u30e2\u30c7\u30eb\u306e\u4e0b\u9650\uff09<\/strong><br \/>\n\u6bd4\u8f03\u30bd\u30fc\u30c8\u306f<strong>\u6c7a\u5b9a\u6728<\/strong>\u3068\u3057\u3066\u6349\u3048\u3089\u308c\u3001n \u8981\u7d20\u306e\u5168\u9806\u5e8f\uff08n! \u3068\u304a\u308a\uff09\u3092\u8b58\u5225\u3059\u308b\u306b\u306f\u9ad8\u3055\u304c <strong>\u03a9(log(n!)) = \u03a9(n log n)<\/strong> \u5fc5\u8981\u2014\u3057\u305f\u304c\u3063\u3066<strong>\u3069\u3093\u306a\u6bd4\u8f03\u30bd\u30fc\u30c8\u3067\u3082<\/strong>\u6700\u60aa\u8a08\u7b97\u91cf\u306f <strong>\u03a9(n log n)<\/strong> \u3092\u4e0b\u56de\u308c\u307e\u305b\u3093\uff08MIT \u306e\u8b1b\u7fa9\u8cc7\u6599\uff09\u3002<\/li>\n<\/ul>\n<hr \/>\n<h3>\u5b9f\u4f8b<\/h3>\n<p><strong>\u7528\u8a9e\u3068\u524d\u63d0\u304c\u5b9f\u88c5\u3084\u9078\u5b9a\u306b\u3069\u3046\u52b9\u304f\u304b<\/strong>\u3092\u3001\u958b\u767a\u306e\u73fe\u5834\u76ee\u7dda\u3067\u5177\u4f53\u5316\u3057\u307e\u3059\u3002<\/p>\n<div class=\"s_table\"><table>\n<thead>\n<tr>\n<th>\u89b3\u70b9<\/th>\n<th>\u4f8b\u30fb\u72b6\u6cc1<\/th>\n<th>\u3069\u3046\u52b9\u304f\u304b<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>\u914d\u5217\uff08\u30e9\u30f3\u30c0\u30e0\u30a2\u30af\u30bb\u30b9\uff09<\/td>\n<td><code>A[i]<\/code> \u3068 <code>A[j]<\/code> \u3092\u4ea4\u63db\u3057\u306a\u304c\u3089\u5de6\u53f3\u306b\u30dd\u30a4\u30f3\u30bf\u3092\u9032\u3081\u308b\u30d1\u30fc\u30c6\u30a3\u30b7\u30e7\u30f3<\/td>\n<td><strong>\u5b9a\u6570\u6642\u9593\u306e\u6dfb\u5b57\u64cd\u4f5c<\/strong>\u3067\u30a4\u30f3\u30d7\u30ec\u30fc\u30b9\u5206\u5272\u304c\u53ef\u80fd\uff08\u914d\u5217\u304c\u524d\u63d0\uff09 \u3002<\/td>\n<\/tr>\n<tr>\n<td>\u6bd4\u8f03\u30bd\u30fc\u30c8<\/td>\n<td>\u30ad\u30fc\u304c\u5de8\u5927\uff0f\u6bd4\u8f03\u95a2\u6570\u304c\u9ad8\u30b3\u30b9\u30c8\u306a\u5834\u5408<\/td>\n<td><strong>\u6bd4\u8f03\u56de\u6570\u304c\u30dc\u30c8\u30eb\u30cd\u30c3\u30af<\/strong>\u3002\u5e73\u5747 O(n log n) \u3067\u3082\u5b9a\u6570\u56e0\u5b50\u306e\u6700\u9069\u5316\uff08\u30d4\u30dc\u30c3\u30c8\u6226\u7565\u7b49\uff09\u304c\u52b9\u304f\u3002\u4e0b\u9650\u306f<strong>\u7406\u8ad6\u7684\u306b<\/strong> \u03a9(n log n)\u3002<\/td>\n<\/tr>\n<tr>\n<td>\u975e\u6bd4\u8f03\u7cfb\u3068\u306e\u4f7f\u3044\u5206\u3051<\/td>\n<td>\u30ad\u30fc\u304c 0\u2026k \u306e\u6709\u9650\u7bc4\u56f2\u306b\u53ce\u307e\u308b\uff08ID\u3001\u6210\u7e3e\u306a\u3069\uff09<\/td>\n<td>\u8a08\u6570\u30bd\u30fc\u30c8\u7b49\uff08restricted-universe\uff09\u304c\u9078\u629e\u80a2\u3002<strong>\u6bd4\u8f03\u4e0b\u9650\u306e\u675f\u7e1b\u3092\u53d7\u3051\u306a\u3044<\/strong>\u305f\u3081 <strong>O(n + k)<\/strong> \u304c\u72d9\u3048\u308b\u3002<\/td>\n<\/tr>\n<tr>\n<td>\u30a4\u30f3\u30d7\u30ec\u30fc\u30b9<\/td>\n<td>\u914d\u5217\u30b5\u30a4\u30ba\u304c\u5927\u304d\u3044\u304c<strong>\u8ffd\u52a0\u30e1\u30e2\u30ea\u3092\u6291\u3048\u305f\u3044<\/strong><\/td>\n<td>\u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8\u306f<strong>\u5165\u529b\u9818\u57df\u3067\u5b8c\u7d50<\/strong>\uff08\u88dc\u52a9\u306f\u5b9a\u6570\uff0b\u518d\u5e30\u30d5\u30ec\u30fc\u30e0\uff09\u3002\u30e1\u30e2\u30ea\u5236\u7d04\u74b0\u5883\u3067\u6709\u5229\u3002<\/td>\n<\/tr>\n<\/tbody>\n<\/table><\/div>\n<blockquote><p>\u88dc\u8db3\uff08\u30b9\u30bf\u30c3\u30af\u4f7f\u7528\u91cf\u306e\u76f4\u611f\uff09<br \/>\n\u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8\u306f\u300c\u8981\u7d20\u3092\u30b3\u30d4\u30fc\u3059\u308b<strong>\u5927\u304d\u306a\u88dc\u52a9\u914d\u5217<\/strong>\u300d\u306f\u4f7f\u308f\u305a\u30a4\u30f3\u30d7\u30ec\u30fc\u30b9\u3067\u3059\u304c\u3001\u518d\u5e30\u306b\u4f34\u3044<strong>\u547c\u3073\u51fa\u3057\u30d5\u30ec\u30fc\u30e0<\/strong>\u306f\u5897\u3048\u307e\u3059\u3002\u5747\u7b49\u5206\u5272\u304c\u7d9a\u304f\u5e73\u5747\u7684\u306a\u72b6\u6cc1\u3067\u306f\u518d\u5e30\u306e\u9ad8\u3055\u306f <strong>O(log n)<\/strong>\uff08\uff1d\u30b9\u30bf\u30c3\u30af\u3082\u6982\u306d O(log n)\uff09\u3002\u3053\u308c\u306f\u6bd4\u8f03\u30e2\u30c7\u30eb\u306e\u4e0b\u9650\u3068\u306f\u5225\u306e\u3001<strong>\u5b9f\u88c5\u4e0a\u306e\u30e1\u30e2\u30ea\u6319\u52d5<\/strong>\u3067\u3059\u3002<\/p><\/blockquote>\n<hr \/>\n<h3>\u7d50\u8ad6\uff08\u307e\u3068\u3081\uff09<\/h3>\n<ul>\n<li><strong>\u914d\u5217<\/strong>\uff1d\u6574\u6570\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3067\u30e9\u30f3\u30c0\u30e0\u30a2\u30af\u30bb\u30b9\u3067\u304d\u308b\u571f\u53f0\u3001<strong>\u6bd4\u8f03\u30bd\u30fc\u30c8<\/strong>\uff1d\u6bd4\u8f03\u3060\u3051\u3067\u9806\u5e8f\u4ed8\u3051\u308b\u67a0\u7d44\u307f\u3001<strong>\u30a4\u30f3\u30d7\u30ec\u30fc\u30b9<\/strong>\uff1d\u540c\u4e00\u9818\u57df\u5185\u3067\u4e26\u3079\u66ff\u3048\u308b\u5b9f\u88c5\u65b9\u91dd\u3002\u3044\u305a\u308c\u3082<strong>NIST\uff08\u7c73\u56fd\u6a19\u6e96\u6280\u8853\u7814\u7a76\u6240\uff09\u306e\u5b9a\u7fa9<\/strong>\u3067\u88cf\u3065\u3051\u3089\u308c\u307e\u3059\u3002<\/li>\n<li>\u3053\u306e\u524d\u63d0\u306b\u7acb\u3066\u3070\u3001\u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8\u306f\u300c<strong>\u914d\u5217\u4e0a\u3067\u306e\u30a4\u30f3\u30d7\u30ec\u30fc\u30b9\u306a\u6bd4\u8f03\u30bd\u30fc\u30c8<\/strong>\u300d\u3068\u3057\u3066\u8a2d\u8a08\u610f\u56f3\u304c\u660e\u78ba\u306b\u306a\u308a\u3001\u6bd4\u8f03\u30e2\u30c7\u30eb\u306e<strong>\u7406\u8ad6\u4e0b\u9650 \u03a9(n log n)<\/strong> \u3092\u8e0f\u307e\u3048\u305f\u6027\u80fd\u8a55\u4fa1\u30fb\u4ed6\u624b\u6cd5\uff08\u8a08\u6570\u30bd\u30fc\u30c8\u7b49\uff09\u3068\u306e<strong>\u9069\u6750\u9069\u6240<\/strong>\u304c\u5224\u65ad\u3057\u3084\u3059\u304f\u306a\u308a\u307e\u3059\u3002<\/li>\n<\/ul>\n<p>\u5fc5\u8981\u306a\u3089\u3001\u3053\u306e\u7bc0\u306b\u7d9a\u3051\u3066\u300c\u30d4\u30dc\u30c3\u30c8\u6226\u7565\u300d\u300c\u30d1\u30fc\u30c6\u30a3\u30b7\u30e7\u30f3\u6cd5\uff08Hoare\/Lomuto\uff09\u300d\u306e\u9078\u3073\u65b9\u3068\u53ef\u8996\u5316\u30ea\u30f3\u30af\u96c6\u3082\u7528\u610f\u3057\u307e\u3059\u3002<\/p>\n<p><script async src=\"https:\/\/pagead2.googlesyndication.com\/pagead\/js\/adsbygoogle.js?client=ca-pub-5641494373062258\" crossorigin=\"anonymous\"><\/script><br \/>\n<!-- \u8a18\u4e8b\u5185\u5e83\u544a\u30b9\u30af\u30a8\u30a2 --><br \/>\n<ins class=\"adsbygoogle\" style=\"display: block;\" data-ad-client=\"ca-pub-5641494373062258\" data-ad-slot=\"6864483099\" data-ad-format=\"auto\" data-full-width-responsive=\"true\"><\/ins><br \/>\n<script>\n     (adsbygoogle = window.adsbygoogle || []).push({});\n<\/script><\/p>\n<p class=\"spacer\">&nbsp;<\/p>\n<h2>2. \u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8\u304c\u6210\u7acb\u3059\u308b\u6761\u4ef6\uff08\u30c7\u30fc\u30bf\u306e\u5206\u5272\u30fb\u57fa\u6e96\u5024\u30fb\u9806\u5e8f\u95a2\u4fc2\uff09<\/h2>\n<h3>2-1. \u57fa\u6e96\u5024\uff08\u30d4\u30dc\u30c3\u30c8\uff09\u306e\u9078\u3073\u65b9<\/h3>\n<h3>\u57fa\u6e96\u5024\uff08\u30d4\u30dc\u30c3\u30c8\uff09\u306e\u9078\u3073\u65b9<\/h3>\n<h3>\u7d50\u8ad6<\/h3>\n<p>\u5b9f\u52d9\u3068\u5b66\u7fd2\u306e\u4e21\u9762\u3067\u5931\u6557\u3057\u306b\u304f\u3044\u65b9\u91dd\u306f\u6b21\u306e\u7d44\u307f\u5408\u308f\u305b\u3067\u3059\u3002<\/p>\n<ol>\n<li>**\u4e71\u629e\uff08randomized\uff09**\u3067\u30d4\u30dc\u30c3\u30c8\u3092\u9078\u3076\uff08\u672a\u77e5\/\u504f\u308a\u306b\u5f37\u3044\uff09<\/li>\n<li><strong>\u4e2d\u592e\u5024\u8fd1\u4f3c<\/strong>\uff08<em>median-of-3<\/em>\u3001\u5fc5\u8981\u306a\u3089 <em>Tukey\u2019s ninther<\/em>\uff09\u3067\u5206\u5272\u306e\u504f\u308a\u3092\u6e1b\u3089\u3059<\/li>\n<li>**\u91cd\u8907\u304c\u591a\u3044\u914d\u5217\u306f3\u5206\u5272\uff083-way\uff09**\u3067\u51e6\u7406\u3059\u308b<\/li>\n<li>\u6700\u60aa\u30b1\u30fc\u30b9\u5bfe\u7b56\u3068\u3057\u3066**Introsort\uff08\u6df1\u3055\u76e3\u8996\u2192Heapsort\u3078\u30d5\u30a9\u30fc\u30eb\u30d0\u30c3\u30af\uff09**\u3092\u7528\u610f\u3059\u308b<\/li>\n<li>\u5b9f\u88c5\u3067\u306f<strong>\u5c0f\u533a\u9593\u306f\u633f\u5165\u30bd\u30fc\u30c8\u3078\u5207\u308a\u66ff\u3048<\/strong>\uff08\u4f8b\uff1a\u226410\u301c20\u8981\u7d20\uff09<br \/>\n\u3053\u306e\u65b9\u91dd\u306f\u3001\u7406\u8ad6\u7684\u306b\u671f\u5f85\u8a08\u7b97\u91cf <strong>O(n log n)<\/strong> \u3092\u4fdd\u3061\u306a\u304c\u3089\u3001\u5b9f\u88c5\u306e\u5b9a\u6570\u56e0\u5b50\u3068\u6700\u60aa\u6642\u306e\u9000\u907f\u7b56\u307e\u3067\u30ab\u30d0\u30fc\u3057\u307e\u3059\u3002<\/li>\n<\/ol>\n<hr \/>\n<h3>\u7406\u7531\u3084\u6839\u62e0<\/h3>\n<ul>\n<li><strong>\u4e71\u629e\u30d4\u30dc\u30c3\u30c8\u306f\u671f\u5f85 O(n log n)<\/strong><br \/>\n\u5927\u5b66\u306e\u8b1b\u7fa9\u8cc7\u6599\uff08MIT OCW\uff09\u3067\u306f\u3001\u5404\u518d\u5e30\u3067\u30d4\u30dc\u30c3\u30c8\u3092\u4e71\u629e\u3059\u308b\u3068<strong>\u3059\u3079\u3066\u306e\u5165\u529b<\/strong>\u306b\u5bfe\u3057\u3066\u671f\u5f85\u8a08\u7b97\u91cf\u304c <strong>O(n log n)<\/strong> \u306b\u53ce\u307e\u308b\u3053\u3068\u304c\u793a\u3055\u308c\u3066\u3044\u307e\u3059\u3002\u6c7a\u5b9a\u8ad6\u7684\u306a\u201c\u7aef\u306e\u8981\u7d20\u3092\u5e38\u306b\u9078\u3076\u201d\u65b9\u5f0f\u306e\u3088\u3046\u306b\u6574\u5217\u6e08\u307f\u5165\u529b\u3067\u7834\u7dbb\u3057\u306b\u304f\u3044\u306e\u304c\u5229\u70b9\u3067\u3059\u3002<\/li>\n<li><strong>\u4e2d\u592e\u5024\u8fd1\u4f3c\uff08median-of-3 \/ ninther\uff09\u306f\u5206\u5272\u306e\u504f\u308a\u3092\u6291\u3048\u308b\u73fe\u5b9f\u7684\u306a\u59a5\u5354\u6848<\/strong><br \/>\nBentley &amp; McIlroy \u306f\u5b9f\u52d9\u7684\u30bd\u30fc\u30c8\u95a2\u6570\u306e\u201c\u5de5\u5b66\u201d\u3068\u3057\u3066\u3001**median-of-3\uff08\u5148\u982d\u30fb\u4e2d\u592e\u30fb\u672b\u5c3e\uff09**\u3084\u3088\u308a\u5f37\u529b\u306a <strong>Tukey\u2019s ninther<\/strong>\uff083\u3064\u306emedian-of-3\u306e\u4e2d\u592e\u5024\uff09\u3092\u63a8\u5968\u3057\u3001\u6bd4\u8f03\u56de\u6570\u3068\u5206\u5272\u306e\u30d0\u30e9\u30f3\u30b9\u3092\u6539\u5584\u3059\u308b\u65b9\u91dd\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002Princeton\u306e\u8b1b\u7fa9\u8cc7\u6599\u3067\u3082\u3001<strong>\u30ab\u30c3\u30c8\u30aa\u30d5\u2192\u633f\u5165\u30bd\u30fc\u30c8 \/ median-of-3 or ninther \/ 3-way\u5206\u5272<\/strong>\u3068\u3044\u3046\u5b9f\u88c5\u6307\u91dd\u304c\u6574\u7406\u3055\u308c\u3066\u3044\u307e\u3059\u3002<\/li>\n<li><strong>\u91cd\u8907\u30ad\u30fc\u306b\u306f3-way\u5206\u5272\u304c\u6709\u52b9<\/strong><br \/>\nSedgewick\u2013Bentley\u7cfb\u306e\u8cc7\u6599\u306f\u3001\u91cd\u8907\u304c\u591a\u3044\u3068\u304d\u306b<strong>3-way\u5206\u5272<\/strong>\uff08&lt;, =, &gt;\uff09\u3092\u63a1\u7528\u3059\u308b\u3068\u3001\u7121\u99c4\u306a\u6bd4\u8f03\u30fb\u4ea4\u63db\u304c\u6e1b\u308a\u201c\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc\u6700\u9069\u201d\u306b\u8fd1\u3044\u6319\u52d5\u306b\u306a\u308b\u3053\u3068\u3092\u793a\u3057\u307e\u3059\u3002<\/li>\n<li><strong>\u6700\u60aa\u30b1\u30fc\u30b9\u3092\u907f\u3051\u308b\u4fdd\u967a\uff1aIntrosort<\/strong><br \/>\nMusser \u306e <strong>Introsort<\/strong> \u306f\u3001\u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8\u306e\u518d\u5e30\u6df1\u3055\u304c\u3057\u304d\u3044\u5024\u3092\u8d85\u3048\u305f\u3089 <strong>Heapsort<\/strong> \u306b\u5207\u66ff\u3048\u308b\u3053\u3068\u3067\u3001<strong>\u5e38\u306b O(n log n)<\/strong> \u3092\u4fdd\u8a3c\u3057\u307e\u3059\u3002median-of-3 \u3067\u3082\u4f5c\u308c\u308b\u201c\u30ad\u30e9\u30fc\u5165\u529b\u201d\u306b\u5bfe\u3057\u3066\u3082\u30d5\u30a9\u30fc\u30eb\u30d0\u30c3\u30af\u3067\u5b88\u308b\u8a2d\u8a08\u3067\u3059\u3002<\/li>\n<li><strong>\u6a19\u6e96\u30e9\u30a4\u30d6\u30e9\u30ea\u306e\u5b9f\u4f8b\uff1aDual-Pivot Quicksort<\/strong><br \/>\nJava\uff08<code>Arrays.sort<\/code>\uff09\u306f\u30d7\u30ea\u30df\u30c6\u30a3\u30d6\u914d\u5217\u3067 <strong>Yaroslavskiy \u306e Dual-Pivot Quicksort<\/strong> \u3092\u63a1\u7528\u3057\u3001\u9ad8\u901f\u5316\u3092\u5831\u544a\u3002\u5b66\u8853\u89e3\u6790\u3067\u3082\u5e73\u5747\u6319\u52d5\u306e\u6709\u5229\u3055\u304c\u7814\u7a76\u3055\u308c\u3066\u3044\u307e\u3059\uff08Wild &amp; Nebel\uff09\u3002\u30d4\u30dc\u30c3\u30c8\u30922\u3064\u53d6\u308b\u6d41\u6d3e\u3082\u5b9f\u52d9\u3067\u9078\u629e\u80a2\u306b\u306a\u3063\u3066\u3044\u307e\u3059\u3002<\/li>\n<\/ul>\n<hr \/>\n<h3>\u5b9f\u4f8b\uff08\u72b6\u6cc1\u5225\u306e\u30d4\u30dc\u30c3\u30c8\u65b9\u91dd\uff09<\/h3>\n<div class=\"s_table\"><table>\n<thead>\n<tr>\n<th>\u72b6\u6cc1<\/th>\n<th>\u63a8\u5968\u30d4\u30dc\u30c3\u30c8\uff0f\u5206\u5272<\/th>\n<th>\u306d\u3089\u3044\u30fb\u30dd\u30a4\u30f3\u30c8<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>\u5165\u529b\u5206\u5e03\u304c\u4e0d\u660e\u30fb\u5bfe adversarial<\/td>\n<td><strong>\u4e71\u629e\u30d4\u30dc\u30c3\u30c8<\/strong> + <strong>\u5c0f\u533a\u9593\u30ab\u30c3\u30c8\u30aa\u30d5\uff08\u633f\u5165\u30bd\u30fc\u30c8\uff09<\/strong><\/td>\n<td>\u671f\u5f85 <strong>O(n log n)<\/strong> \u3092\u78ba\u4fdd\u3057\u3064\u3064\u5b9a\u6570\u56e0\u5b50\u3092\u6291\u3048\u308b\u3002<\/td>\n<\/tr>\n<tr>\n<td>\u307b\u307c\u6574\u5217\/\u9006\u9806\u30fb\u7de9\u3084\u304b\u306a\u504f\u308a<\/td>\n<td><strong>median-of-3<\/strong>\uff08\u5148\u982d\/\u4e2d\u592e\/\u672b\u5c3e\uff09 or <strong>ninther<\/strong><\/td>\n<td>\u504f\u3063\u305f\u5206\u5272\u3092\u7de9\u548c\u3057\u3001\u4ea4\u63db\u30fb\u518d\u5e30\u306e\u904e\u5270\u5897\u52a0\u3092\u56de\u907f\u3002<\/td>\n<\/tr>\n<tr>\n<td>\u91cd\u8907\u30ad\u30fc\u304c\u591a\u3044<\/td>\n<td><strong>\u4efb\u610f\u306e\u30d4\u30dc\u30c3\u30c8<\/strong> + <strong>3-way\u5206\u5272\uff08DNF\uff09<\/strong><\/td>\n<td>\u201c= \u30d4\u30dc\u30c3\u30c8\u201d\u9818\u57df\u3092\u307e\u3068\u3081\u3066\u7e2e\u5c0f\u3001\u63a2\u7d22\u6728\u306e\u6df1\u3055\u3092\u6291\u3048\u308b\u3002<\/td>\n<\/tr>\n<tr>\n<td>\u6700\u60aa\u8a08\u7b97\u91cf\u3092\u78ba\u5b9f\u306b\u907f\u3051\u305f\u3044<\/td>\n<td><strong>Introsort<\/strong>\uff08\u6df1\u3055\u76e3\u8996\u2192Heapsort\uff09<\/td>\n<td>\u3069\u3093\u306a\u5165\u529b\u3067\u3082 <strong>O(n log n)<\/strong> \u3092\u4fdd\u8a3c\u3002<\/td>\n<\/tr>\n<tr>\n<td>Java\u306e\u30d7\u30ea\u30df\u30c6\u30a3\u30d6\u914d\u5217<\/td>\n<td><strong>Dual-Pivot Quicksort<\/strong>\uff08\u5b9f\u88c5\u6e08\u307f\uff09<\/td>\n<td>2\u30d4\u30dc\u30c3\u30c8\u3067\u5b9f\u7528\u4e0a\u9ad8\u901f\u3002\u5e73\u5747\u6319\u52d5\u306f\u7814\u7a76\u3067\u88cf\u3065\u3051\u3002<\/td>\n<\/tr>\n<\/tbody>\n<\/table><\/div>\n<blockquote><p>\u53c2\u8003\uff1aMIT\u306e\u8b1b\u7fa9\u3067\u306f\u300c\u771f\u306e\u4e2d\u592e\u5024\u300d\u3092\u7dda\u5f62\u6642\u9593\u3067\u9078\u3076\u3053\u3068\u3082\u7406\u8ad6\u4e0a\u306f\u53ef\u80fd\u3067\u3059\u304c\uff08\u9078\u629e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u5229\u7528\uff09\u3001<strong>\u5b9f\u88c5\u30b3\u30b9\u30c8\u304c\u5927\u304d\u304f\u5b9f\u7528\u3067\u306f\u8ca0\u3051\u3084\u3059\u3044<\/strong>\u305f\u3081\u3001\u4e71\u629e\u3084\u5c0f\u6a19\u672c\u306e\u4e2d\u592e\u5024\u304c\u73fe\u5b9f\u89e3\u3068\u3055\u308c\u3066\u3044\u307e\u3059\u3002<\/p><\/blockquote>\n<hr \/>\n<h3>\u30b3\u30fc\u30c9\u8a2d\u8a08\u30e1\u30e2\uff08\u5b9f\u88c5\u30c1\u30a7\u30c3\u30af\u30ea\u30b9\u30c8\uff09<\/h3>\n<ul>\n<li>\u4e71\u629e or median-of-3\uff08\u5fc5\u8981\u306a\u3089 ninther\uff09\u3067\u30d4\u30dc\u30c3\u30c8\u9078\u629e<\/li>\n<li><strong>3-way\u5206\u5272<\/strong>\uff08\u91cd\u8907\u5bfe\u7b56\uff09<\/li>\n<li><strong>\u5c0f\u533a\u9593\u306f\u633f\u5165\u30bd\u30fc\u30c8<\/strong>\u3078\uff08\u3057\u304d\u3044\u5024\u306f\u74b0\u5883\u4f9d\u5b58\uff09<\/li>\n<li><strong>\u5c3e\u518d\u5e30\u306e\u9664\u53bb<\/strong>\uff08\u5927\u5074\u306f\u30eb\u30fc\u30d7\u3078\uff09<\/li>\n<li><strong>Introsort\u306e\u30ac\u30fc\u30c9<\/strong>\uff08<code>maxDepth = 2 * floor(log2(n))<\/code> \u306a\u3069\uff09<br \/>\n\u3053\u308c\u3089\u306f\u5927\u5b66\u8b1b\u7fa9\u30fb\u5b9f\u88c5\u8cc7\u6599\u306b\u6cbf\u3063\u305f\u201c\u5b9a\u756a\u306e\u9ad8\u901f\u5316\u30fb\u5b89\u5168\u7b56\u201d\u3067\u3059\u3002<\/li>\n<\/ul>\n<hr \/>\n<h3>\u7d50\u8ad6\uff08\u307e\u3068\u3081\uff09<\/h3>\n<ul>\n<li><strong>\u307e\u305a\u4e71\u629e<\/strong>\u3001<strong>\u504f\u308a\u304c\u6016\u3051\u308c\u3070 median-of-3 \/ ninther<\/strong>\u3001<strong>\u91cd\u8907\u306f3-way<\/strong>\u3001<strong>\u4fdd\u967a\u306b Introsort<\/strong>\u3002\u3053\u306e\u30bb\u30c3\u30c8\u3067\u3001\u5e73\u5747\u6027\u80fd\u30fb\u5b9a\u6570\u56e0\u5b50\u30fb\u6700\u60aa\u6642\u306e\u5b89\u5168\u6027\u3092\u30d0\u30e9\u30f3\u30b9\u826f\u304f\u9054\u6210\u3067\u304d\u307e\u3059\u3002<\/li>\n<li>\u3053\u308c\u306f MIT\/Princeton \u306e\u8b1b\u7fa9\u8cc7\u6599\u3084 Bentley &amp; McIlroy \u306e\u5b9f\u52d9\u7814\u7a76\u3001Java \u306e\u5b9f\u88c5\u5b9f\u7e3e\uff08Dual-Pivot\uff09\u3068\u3044\u3063\u305f<strong>\u4fe1\u983c\u6027\u306e\u9ad8\u3044\u4e00\u6b21\u60c5\u5831<\/strong>\u3067\u88cf\u3065\u3051\u3089\u308c\u305f\u5b9f\u6226\u7684\u306a\u6307\u91dd\u3067\u3059\u3002<\/li>\n<\/ul>\n<h3>2-2. \u5206\u5272\uff08\u30d1\u30fc\u30c6\u30a3\u30b7\u30e7\u30f3\uff09\u306e\u65b9\u6cd5<\/h3>\n<h3>\u5206\u5272\uff08\u30d1\u30fc\u30c6\u30a3\u30b7\u30e7\u30f3\uff09\u306e\u65b9\u6cd5<\/h3>\n<h3>\u7d50\u8ad6<\/h3>\n<p>\u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8\u306e\u901f\u5ea6\u3068\u5b89\u5b9a\u611f\u306f<strong>\u30d1\u30fc\u30c6\u30a3\u30b7\u30e7\u30f3\u306e\u3084\u308a\u65b9<\/strong>\u3067\u5927\u304d\u304f\u5909\u308f\u308a\u307e\u3059\u3002\u5b9f\u52d9\u3067\u306f\u6b21\u304c\u5b9a\u756a\u3067\u3059\u3002<\/p>\n<ul>\n<li><strong>\u91cd\u8907\u304c\u591a\u3044\u914d\u5217<\/strong>\u2192 <strong>3-way\uff08Dutch National Flag\uff09\u5206\u5272<\/strong>\uff1a\u91cd\u8907\u3092\u201c= \u9818\u57df\u201d\u306b\u307e\u3068\u3081\u3001\u5e83\u3044\u7bc4\u56f2\u3067\u307b\u307c\u7dda\u5f62\u6642\u9593\u306b\u8fd1\u3065\u3051\u3089\u308c\u307e\u3059\u3002<\/li>\n<li><strong>\u4e00\u822c\u7684\u306a\u914d\u5217<\/strong>\u2192 <strong>Hoare \u65b9\u5f0f<\/strong>\u307e\u305f\u306f<strong>median-of-3 \u7b49\u306e\u30d4\u30dc\u30c3\u30c8 + 3-way<\/strong>\uff1a\u4ea4\u63db\u56de\u6570\u3092\u6291\u3048\u3064\u3064\u30d0\u30e9\u30f3\u30b9\u826f\u304f\u9ad8\u901f\u3002<\/li>\n<li><strong>Java \u306e\u30d7\u30ea\u30df\u30c6\u30a3\u30d6\u914d\u5217<\/strong>\u2192 <strong>\u30c7\u30e5\u30a2\u30eb\u30d4\u30dc\u30c3\u30c8\uff08Yaroslavskiy\uff09<\/strong>\uff1a\u30e1\u30e2\u30ea\u968e\u5c64\u306e\u89b3\u70b9\uff08\u8d70\u67fb\u8981\u7d20\u6570\uff09\u3067\u6709\u5229\u306b\u306a\u308b\u8a2d\u8a08\u3002\u6a19\u6e96\u30e9\u30a4\u30d6\u30e9\u30ea\uff08Java 7 \u4ee5\u964d\uff09\u3067\u3082\u63a1\u7528\u5b9f\u7e3e\u304c\u3042\u308a\u307e\u3059\u3002<\/li>\n<\/ul>\n<hr \/>\n<h3>\u7406\u7531\u3084\u6839\u62e0<\/h3>\n<ul>\n<li><strong>\u516c\u7684\u30fb\u5927\u5b66\u306e\u4e00\u6b21\u8cc7\u6599\u3067\u78ba\u8a8d\u3067\u304d\u308b\u4e8b\u5b9f<\/strong>\n<ul>\n<li><strong>NIST\uff08\u7c73\u56fd\u6a19\u6e96\u6280\u8853\u7814\u7a76\u6240\uff09DADS<\/strong>\u306f\u3001\u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8\u3092\u300c\u30d4\u30dc\u30c3\u30c8\u3067<strong>\u5206\u5272<\/strong>\u3057\u3066\u518d\u5e30\u7684\u306b\u6574\u5217\u300d\u3068\u5b9a\u7fa9\u3057\u3001<strong>2 \u30d4\u30dc\u30c3\u30c8\u7248<\/strong>\uff08\u30c7\u30e5\u30a2\u30eb\u30d4\u30dc\u30c3\u30c8\uff09\u3084<strong>Dutch National Flag<\/strong>\u306e\u6587\u732e\u3082\u6574\u7406\u3057\u3066\u3044\u307e\u3059\u3002\u30d1\u30fc\u30c6\u30a3\u30b7\u30e7\u30f3\u304c\u4e2d\u5fc3\u6982\u5ff5\u3067\u3042\u308b\u3053\u3068\u304c\u516c\u7684\u8f9e\u66f8\u30ec\u30d9\u30eb\u3067\u660e\u793a\u3055\u308c\u3066\u3044\u307e\u3059\u3002<\/li>\n<li><strong>MIT OpenCourseWare<\/strong>\u306f\u30e9\u30f3\u30c0\u30e0\u5316\u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8\u3068\u305d\u306e\u89e3\u6790\uff08\u671f\u5f85 <strong>O(n log n)<\/strong>\uff09\u3092\u8b1b\u7fa9\u3057\u3001\u504f\u308a\u5165\u529b\u306b\u5bfe\u3059\u308b\u30e9\u30f3\u30c0\u30e0\u5316\u3084\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u306e\u6709\u52b9\u6027\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002\u30d1\u30fc\u30c6\u30a3\u30b7\u30e7\u30f3\u304c\u60aa\u5316\u3057\u306a\u3044\u8a2d\u8a08\u304c\u809d\u3067\u3059\u3002<\/li>\n<\/ul>\n<\/li>\n<li><strong>\u91cd\u8907\u5bfe\u7b56\u3068\u3057\u3066\u306e 3-way \u5206\u5272\u306e\u52b9\u679c<\/strong>\n<ul>\n<li>\u30d7\u30ea\u30f3\u30b9\u30c8\u30f3\u5927\u5b66\u306e\u8b1b\u7fa9\u30b9\u30e9\u30a4\u30c9\u306f\u3001<strong>3-way \u5206\u5272<\/strong>\u304c\u91cd\u8907\u306e\u591a\u3044\u30b1\u30fc\u30b9\u3067<strong>\u4e0b\u9650\uff08\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc\uff09\u306b\u8fd1\u3044\u6bd4\u8f03\u56de\u6570<\/strong>\u3092\u9054\u6210\u3057\u3001\u5e83\u3044\u72b6\u6cc1\u3067\u5b9f\u884c\u6642\u9593\u3092<strong>\u7dda\u5f62\u7d1a<\/strong>\u306b\u5f15\u304d\u4e0b\u3052\u3046\u308b\u3053\u3068\u3092\u89e3\u8aac\u3057\u3066\u3044\u307e\u3059\uff08\u53ef\u8996\u5316\u30fb\u64ec\u4f3c\u30b3\u30fc\u30c9\u4ed8\u304d\uff09\u3002<\/li>\n<\/ul>\n<\/li>\n<li><strong>\u30ad\u30e3\u30c3\u30b7\u30e5\u30fb\u30e1\u30e2\u30ea\u30a2\u30af\u30bb\u30b9\u307e\u3067\u8e0f\u307f\u8fbc\u3093\u3060\u5de5\u5b66\u7684\u6839\u62e0<\/strong>\n<ul>\n<li>\u540c\u30b9\u30e9\u30a4\u30c9\u306f<strong>\u6bd4\u8f03\u56de\u6570\u30fb\u4ea4\u63db\u56de\u6570\u30fb\u201c\u8d70\u67fb\u8981\u7d20\u6570\u201d\u3092\u5b9a\u91cf\u6bd4\u8f03\u3057\u3001\u30c7\u30e5\u30a2\u30eb\u30d4\u30dc\u30c3\u30c8\u304c\u8d70\u67fb\u8981\u7d20\u6570<\/strong>\u3067\u6709\u5229\uff1d\u30ad\u30e3\u30c3\u30b7\u30e5\u52b9\u7387\u304c\u826f\u3044\u3053\u3068\u3092\u793a\u3057\u307e\u3059\uff08\u8fd1\u5e74\u306e\u5b9f\u884c\u901f\u5ea6\u5dee\u306e\u4e3b\u8981\u56e0\uff09\u3002<\/li>\n<li>\u3055\u3089\u306b\u5b66\u8853\u8ad6\u6587\uff08Wild &amp; Nebel\uff09\u306f\u3001\u30c7\u30e5\u30a2\u30eb\u30d4\u30dc\u30c3\u30c8\u306e<strong>\u5e73\u5747\u6027\u80fd<\/strong>\u3092\u89e3\u6790\u3057\u3001\u300c\u5358\u7d14\u306a\u6bd4\u8f03\u56de\u6570\u306e\u5c11\u306a\u3055\u300d\u3067\u306f\u8aac\u660e\u3057\u304d\u308c\u306a\u3044\u304c<strong>\u30e1\u30e2\u30ea\u968e\u5c64<\/strong>\u3092\u53cd\u6620\u3057\u305f\u6307\u6a19\uff08\u8d70\u67fb\u8981\u7d20\u7b49\uff09\u3067\u512a\u4f4d\u6027\u304c\u8aac\u660e\u3067\u304d\u308b\u3068\u5831\u544a\u3057\u3066\u3044\u307e\u3059\u3002<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<hr \/>\n<h3>\u5b9f\u4f8b\uff08\u65b9\u5f0f\u3054\u3068\u306e\u8981\u70b9\u3068\u4f7f\u3044\u3069\u3053\u308d\uff09<\/h3>\n<div class=\"s_table\"><table>\n<thead>\n<tr>\n<th>\u5206\u5272\u65b9\u5f0f<\/th>\n<th>\u4ed5\u7d44\u307f\uff08\u8981\u7d04\uff09<\/th>\n<th>\u9577\u6240<\/th>\n<th>\u6ce8\u610f\u70b9 \/ \u5411\u304b\u306a\u3044\u4f8b<\/th>\n<th>\u5178\u578b\u7528\u9014<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td><strong>Lomuto<\/strong>\uff081 \u672c\u5883\u754c\uff09<\/td>\n<td>\u5de6\u304b\u3089\u8d70\u67fb\u3057\u300c&lt; pivot \u9818\u57df\u300d\u306e\u5883\u754c\u30921 \u672c\u3067\u5e83\u3052\u308b<\/td>\n<td>\u5b9f\u88c5\u304c\u7c21\u5358<\/td>\n<td>\u4ea4\u63db\u304c\u5897\u3048\u304c\u3061\u3002\u7b49\u5024\u591a\u6570\u30fb\u7aef\u8981\u7d20\u30d4\u30dc\u30c3\u30c8\u3067\u6700\u60aa\u5316\u3057\u3084\u3059\u3044<\/td>\n<td>\u5b66\u7fd2\u30fb\u691c\u8a3c\u7528\u306e\u6700\u5c0f\u5b9f\u88c5<\/td>\n<\/tr>\n<tr>\n<td><strong>Hoare<\/strong>\uff08\u4e21\u7aef\u30dd\u30a4\u30f3\u30bf\uff09<\/td>\n<td>\u5de6\u53f3\u304b\u3089\u5185\u5411\u304d\u306b\u8d70\u67fb\u3057\u4e0d\u4e00\u81f4\u3092\u4ea4\u63db\u3001\u30dd\u30a4\u30f3\u30bf\u4ea4\u5dee\u3067\u505c\u6b62<\/td>\n<td><strong>\u4ea4\u63db\u5c11\u306a\u3081\u3067\u9ad8\u901f<\/strong>\u306b\u306a\u308a\u3084\u3059\u3044<\/td>\n<td>\u30d4\u30dc\u30c3\u30c8\u306e\u78ba\u5b9a\u4f4d\u7f6e\u306b\u6ce8\u610f\uff08\u518d\u5e30\u7bc4\u56f2\u306e\u53d6\u308a\u65b9\u304c Lomuto \u3068\u7570\u306a\u308b\uff09<\/td>\n<td>\u4e00\u822c\u7528\u9014\u306e\u30d9\u30fc\u30b9\u5b9f\u88c5<\/td>\n<\/tr>\n<tr>\n<td><strong>3-way\uff08DNF\uff09<\/strong><\/td>\n<td>&lt;, =, &gt; \u306e<strong>3 \u9818\u57df<\/strong>\u3092\u4e00\u5ea6\u306e\u8d70\u67fb\u3067\u4f5c\u308b<\/td>\n<td><strong>\u91cd\u8907\u306b\u5f37\u3044<\/strong>\u3002\u91cd\u8907\u304c\u591a\u3044\u3068<strong>\u7dda\u5f62\u7d1a<\/strong>\u306b\u8fd1\u3065\u304f<\/td>\n<td>\u5b9f\u88c5\u306f 2-way \u3088\u308a\u8907\u96d1<\/td>\n<td>\u6587\u5b57\u5217\u30fb\u30ab\u30c6\u30b4\u30ea\u591a\u91cd\u51fa\u73fe\u306a\u3069\u91cd\u8907\u304c\u591a\u3044\u30c7\u30fc\u30bf<\/td>\n<\/tr>\n<tr>\n<td><strong>\u30c7\u30e5\u30a2\u30eb\u30d4\u30dc\u30c3\u30c8<\/strong>\uff08Yaroslavskiy\uff09<\/td>\n<td><strong>2 \u3064\u306e\u30d4\u30dc\u30c3\u30c8<\/strong>\u3067 &lt; p1 \/ p1..p2 \/ &gt; p2 \u306e3 \u533a\u9593\u306b\u5206\u3051\u308b<\/td>\n<td><strong>\u8d70\u67fb\u8981\u7d20\u6570\u304c\u5c11\u306a\u3081<\/strong>\uff1d\u30ad\u30e3\u30c3\u30b7\u30e5\u306b\u4e57\u308a\u3084\u3059\u3044\u3002Java 7 \u4ee5\u964d\u3067\u63a1\u7528<\/td>\n<td>\u5b9f\u88c5\u304c\u8907\u96d1\u3001\u7406\u8ad6\u6bd4\u8f03\u56de\u6570\u3060\u3051\u3067\u306f\u512a\u4f4d\u304c\u898b\u3048\u306b\u304f\u3044<\/td>\n<td><strong>\u5927\u898f\u6a21\u914d\u5217\u30fb\u30d7\u30ea\u30df\u30c6\u30a3\u30d6\u578b<\/strong>\uff08Java \u6a19\u6e96\u306b\u8fd1\u3044\u69cb\u6210\uff09<\/td>\n<\/tr>\n<\/tbody>\n<\/table><\/div>\n<ul>\n<li>3-way \u5206\u5272\u306e\u624b\u9806\uff08Dijkstra \u306e DNF\uff09\uff1a<strong>lt \/ i \/ gt<\/strong> \u306e 3 \u30dd\u30a4\u30f3\u30bf\u3067 1 \u30d1\u30b9\u306b &lt;,=,&gt; \u3092\u4f5c\u308b\uff08N \u56de\u306e\u691c\u67fb\u3068\u9ad8\u3005 N \u56de\u306e\u4ea4\u63db\u3067\u6e08\u3080\u76ee\u6a19\uff09\u3002\u5927\u5b66\u8b1b\u7fa9\u8cc7\u6599\u306b\u30b3\u30fc\u30c9\u30fb\u56f3\u89e3\u304c\u63b2\u8f09\u3002<\/li>\n<li>\u30c7\u30e5\u30a2\u30eb\u30d4\u30dc\u30c3\u30c8\uff1aJava 7 \u4ee5\u964d\u306e <code>Arrays.sort<\/code>\uff08\u30d7\u30ea\u30df\u30c6\u30a3\u30d6\uff09\u3067\u63a1\u7528\u3002Wild\u2013Nebel \u3089\u306f\u3001<strong>\u6bd4\u8f03\u56de\u6570<\/strong>\u3067\u306f\u5358\u4e00\u30d4\u30dc\u30c3\u30c8\u3088\u308a\u6709\u5229\u3068\u65ad\u8a00\u3067\u304d\u306a\u3044\u304c\u3001<strong>\u8981\u7d20\u8d70\u67fb<\/strong>\u30fb<strong>\u30d0\u30a4\u30c8\u30b3\u30fc\u30c9<\/strong>\u306a\u3069\u8907\u5408\u6307\u6a19\u3067\u5e73\u5747\u6319\u52d5\u306e\u512a\u4f4d\u3092\u89e3\u6790\u3002<\/li>\n<\/ul>\n<hr \/>\n<h3>\u30b1\u30fc\u30b9\u5225\u306e\u8a2d\u8a08\u6307\u91dd\uff08\u30d7\u30ed\u306e\u73fe\u5834\u611f\uff09<\/h3>\n<ol>\n<li><strong>\u91cd\u8907\u304c\u591a\u3044\uff08\u4f8b\uff1a\u591a\u304f\u304c\u540c\u3058\u30ad\u30fc\uff09<\/strong><br \/>\n\u2192 <strong>3-way \u5206\u5272<\/strong>\u3092\u7b2c\u4e00\u9078\u629e\u3002\u91cd\u8907\u3092\u201c= \u9818\u57df\u201d\u3078\u5438\u53ce\u3057\u3001\u518d\u5e30\u306e\u6df1\u3055\u3068\u7121\u99c4\u306a\u4ea4\u63db\u3092\u6291\u3048\u308b\u3002\u7406\u8ad6\u7684\u306b\u3082<strong>\u7dda\u5f62\u7d1a<\/strong>\u306b\u8fd1\u3044\u6bd4\u8f03\u56de\u6570\u307e\u3067\u4e0b\u3052\u3089\u308c\u308b\u3002<\/li>\n<li><strong>\u5165\u529b\u5206\u5e03\u304c\u672a\u77e5\u30fb\u30d0\u30e9\u30c4\u30ad\u5927<\/strong><br \/>\n\u2192 <strong>Hoare \u65b9\u5f0f + \u30e9\u30f3\u30c0\u30e0\u5316 or median-of-3<\/strong>\u3067<strong>\u504f\u308a\u5206\u5272<\/strong>\u3092\u907f\u3051\u308b\u3002\u30e9\u30f3\u30c0\u30e0\u5316\u306f<strong>\u671f\u5f85 O(n log n)<\/strong> \u3092\u4fdd\u8a3c\uff08MIT OCW\uff09\u3002\u91cd\u8907\u304c\u6c17\u306b\u306a\u308c\u3070 3-way \u3078\u5207\u66ff\u3002<\/li>\n<li><strong>Java \u306e\u30d7\u30ea\u30df\u30c6\u30a3\u30d6\u914d\u5217\u3092\u9ad8\u901f\u306b<\/strong><br \/>\n\u2192 <strong>\u30c7\u30e5\u30a2\u30eb\u30d4\u30dc\u30c3\u30c8<\/strong>\uff08JDK7 \u4ee5\u964d\u306e\u5b9f\u88c5\u601d\u60f3\uff09\u3002<strong>\u8d70\u67fb\u8981\u7d20\u6570<\/strong>\u306e\u6e1b\u5c11\uff1d\u30ad\u30e3\u30c3\u30b7\u30e5\u52b9\u7387\u6539\u5584\u3067\u5e73\u5747\u7684\u306b\u6709\u5229\u3002<\/li>\n<\/ol>\n<hr \/>\n<h3>\u30df\u30cb\u30c1\u30e5\u30fc\u30c8\u30ea\u30a2\u30eb\uff1a\u4f55\u3092\u6bd4\u8f03\u3059\u3079\u304d\uff1f<\/h3>\n<ul>\n<li><strong>\u6bd4\u8f03\u56de\u6570<\/strong>\u3060\u3051\u3067\u306a\u304f\u3001<strong>\u4ea4\u63db\u56de\u6570<\/strong>\u3084<strong>\u8d70\u67fb\u8981\u7d20\u6570<\/strong>\uff08= \u30e1\u30e2\u30ea\u30a2\u30af\u30bb\u30b9\u91cf\u306e\u8fd1\u4f3c\uff09\u3092\u898b\u308b\u3068\u3001\u8fd1\u4ee3\u7684\u306a\u6700\u9069\u5316\uff083-way\u3001\u30c7\u30e5\u30a2\u30eb\u30d4\u30dc\u30c3\u30c8\u7b49\uff09\u306e\u826f\u3055\u304c\u8aac\u660e\u3067\u304d\u307e\u3059\uff08Princeton \u30b9\u30e9\u30a4\u30c9\u306e\u6bd4\u8f03\u8868\uff09\u3002<\/li>\n<li><strong>\u5b9a\u756a\u6700\u9069\u5316<\/strong>\uff1a\u5c0f\u533a\u9593\u306f\u633f\u5165\u30bd\u30fc\u30c8\u3078\u5207\u66ff\uff0f\u5c3e\u518d\u5e30\u306e\u9664\u53bb\uff0f\uff08\u5fc5\u8981\u306a\u3089\uff09\u6df1\u3055\u76e3\u8996\u3067\u30d2\u30fc\u30d7\u30bd\u30fc\u30c8\u3078\u30d5\u30a9\u30fc\u30eb\u30d0\u30c3\u30af\uff08Introsort \u7684\uff09\u3002\u3053\u308c\u3089\u306f<strong>\u60aa\u5316\u30b1\u30fc\u30b9<\/strong>\u3092\u6291\u3048\u308b\u5b9f\u88c5\u30c6\u30af\u3067\u3059\u3002<\/li>\n<\/ul>\n<hr \/>\n<h3>\u7d50\u8ad6\uff08\u307e\u3068\u3081\uff09<\/h3>\n<ul>\n<li><strong>\u9078\u3073\u65b9\u306e\u8ef8\u306f\u300c\u91cd\u8907\u300d\u300c\u504f\u308a\u300d\u300c\u30e1\u30e2\u30ea\u30a2\u30af\u30bb\u30b9\u300d<\/strong>\u3002\n<ul>\n<li>\u91cd\u8907\u304c\u591a\u3044 \u2192 <strong>3-way<\/strong>\u3002<\/li>\n<li>\u4e00\u822c\u7528\u9014 \u2192 <strong>Hoare +\uff08\u4e71\u629e or median-of-3\uff09<\/strong>, \u91cd\u8907\u304c\u5897\u3048\u305f\u3089 3-way\u3002<\/li>\n<li>Java \u30d7\u30ea\u30df\u30c6\u30a3\u30d6 \u2192 <strong>\u30c7\u30e5\u30a2\u30eb\u30d4\u30dc\u30c3\u30c8<\/strong>\u3067<strong>\u8d70\u67fb\u8981\u7d20\u6570<\/strong>\u3092\u6291\u3048\u5e73\u5747\u6027\u80fd\u3092\u7a3c\u3050\u3002<\/li>\n<\/ul>\n<\/li>\n<li>\u3053\u308c\u3089\u306f <strong>NIST DADS<\/strong> \u306e\u5b9a\u7fa9\u30fb<strong>MIT\/Princeton<\/strong> \u306e\u8b1b\u7fa9\u8cc7\u6599\u30fb<strong>Java 7<\/strong> \u306e\u5b9f\u88c5\u3068<strong>\u5b66\u8853\u89e3\u6790<\/strong>\u3067\u88cf\u3065\u3051\u3089\u308c\u305f\u5b9f\u6226\u7684\u30ac\u30a4\u30c9\u30e9\u30a4\u30f3\u3067\u3059\u3002<\/li>\n<\/ul>\n<p><script async src=\"https:\/\/pagead2.googlesyndication.com\/pagead\/js\/adsbygoogle.js?client=ca-pub-5641494373062258\" crossorigin=\"anonymous\"><\/script><br \/>\n<!-- \u8a18\u4e8b\u5185\u5e83\u544a\u30b9\u30af\u30a8\u30a2 --><br \/>\n<ins class=\"adsbygoogle\" style=\"display: block;\" data-ad-client=\"ca-pub-5641494373062258\" data-ad-slot=\"6864483099\" data-ad-format=\"auto\" data-full-width-responsive=\"true\"><\/ins><br \/>\n<script>\n     (adsbygoogle = window.adsbygoogle || []).push({});\n<\/script><\/p>\n<h2>3. \u4ed6\u306e\u30bd\u30fc\u30c8\u3068\u306e\u9055\u3044\u30fb\u9577\u6240\u77ed\u6240\uff08\u5e73\u5747\u8a08\u7b97\u91cf\/\u5b89\u5b9a\u6027\/\u30e1\u30e2\u30ea\uff09<\/h2>\n<p class=\"spacer\">&nbsp;<\/p>\n<h3>3-1. \u5e73\u5747\u8a08\u7b97\u91cf\u3068\u6700\u60aa\u8a08\u7b97\u91cf\u306e\u6bd4\u8f03<\/h3>\n<h3>\u5e73\u5747\u8a08\u7b97\u91cf\u3068\u6700\u60aa\u8a08\u7b97\u91cf\u306e\u6bd4\u8f03<\/h3>\n<h3>\u7d50\u8ad6<\/h3>\n<ul>\n<li>\u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8\u306e<strong>\u5e73\u5747\u8a08\u7b97\u91cf\u306f O(n log n)<\/strong>\u3001<strong>\u6700\u60aa\u8a08\u7b97\u91cf\u306f \u0398(n\u00b2)<\/strong>\u3002\u5e73\u5747\u3067\u306f\u5b9f\u7528\u4e0a\u304d\u308f\u3081\u3066\u9ad8\u901f\u3060\u304c\u3001\u5206\u5272\u304c\u504f\u308b\u3068\u4e8c\u4e57\u6642\u9593\u306b\u60aa\u5316\u3059\u308b\u3002\u4e71\u629e\uff08randomized\uff09\u3084\u9069\u5207\u306a\u30d4\u30dc\u30c3\u30c8\u6226\u7565\u3067\u5e73\u5747\u6319\u52d5\u3092\u5b89\u5b9a\u5316\u3067\u304d\u308b\u3002<\/li>\n<\/ul>\n<hr \/>\n<h3>\u7406\u7531\u3084\u6839\u62e0<\/h3>\n<ul>\n<li><strong>\u516c\u7684\u6a5f\u95a2\uff08NIST\uff09<\/strong><br \/>\nNIST\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u8f9e\u66f8\u306f\u3001\u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8\u306e\u6700\u60aa\u304c <strong>\u0398(n\u00b2)<\/strong>\u3001\u5178\u578b\u306f <strong>O(n log n)<\/strong> \u3068\u660e\u8a18\u3002\u3088\u304f\u8abf\u6574\u3055\u308c\u305f\u5b9f\u88c5\u306f\u4ed6\u30bd\u30fc\u30c8\u3088\u308a\u5b9f\u52d9\u3067\u901f\u3044\u3053\u3068\u3001\u9078\u629e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3067\u5e38\u306b\u826f\u3044\u30d4\u30dc\u30c3\u30c8\u3092\u9078\u3079\u3070<strong>\u6700\u60aa O(n log n)<\/strong> \u306e\u6d3e\u751f\u3082\u53ef\u80fd\u3068\u89e3\u8aac\u3002<\/li>\n<li><strong>\u5927\u5b66\u8b1b\u7fa9\uff08MIT OCW\uff09<\/strong><br \/>\n\u4e71\u629e\u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8\u306f<strong>\u3042\u3089\u3086\u308b\u5165\u529b<\/strong>\u306b\u5bfe\u3057\u3066<strong>\u671f\u5f85\u8a08\u7b97\u91cf O(n log n)<\/strong> \u3092\u6e80\u305f\u3059\u3053\u3068\u3092\u8b1b\u7fa9\u30ce\u30fc\u30c8\u3067\u793a\u3059\uff08\u89e3\u6790\u306fCLRS\u53c2\u7167\uff09\u3002\u504f\u308a\u5206\u5272\u3092\u78ba\u7387\u7684\u306b\u907f\u3051\u3089\u308c\u308b\u306e\u304c\u8981\u70b9\u3002<\/li>\n<li><strong>\u5927\u5b66\u8b1b\u7fa9\uff08Princeton\uff09<\/strong><br \/>\n\u5e73\u5747\u306e\u6bd4\u8f03\u56de\u6570\u306f <strong>\u7d04 2n ln n<\/strong>\u3001\u6700\u60aa\u306e\u6bd4\u8f03\u56de\u6570\u306f <strong>\u7d04 \u00bd n\u00b2<\/strong> \u3068\u89e3\u6790\uff08\u81ea\u7136\u5bfe\u6570\uff09\u3002\u7406\u8ad6\u5f0f\u304c\u5177\u4f53\u7684\u306a\u5b9a\u6570\u56e0\u5b50\u307e\u3067\u793a\u3059\u3002<\/li>\n<li><strong>\u6bd4\u8f03\u30bd\u30fc\u30c8\u306e\u4e0b\u9650\uff08\u7406\u8ad6\uff09<\/strong><br \/>\n\u6bd4\u8f03\u30e2\u30c7\u30eb\u3067\u306f<strong>\u3069\u3093\u306a\u6bd4\u8f03\u30bd\u30fc\u30c8\u3067\u3082<\/strong>\u4e0b\u9650\u304c <strong>\u03a9(n log n)<\/strong>\uff08\u6700\u60aa\u30fb\u5e73\u5747\u306b\u95a2\u3059\u308b\u62e1\u5f35\u3082\uff09\u306b\u306a\u308b\u2014\u3057\u305f\u304c\u3063\u3066\u201c\u5e73\u5747 O(n log n)\u201d\u306f\u6700\u9069\u7d1a\u3067\u3042\u308b\u3002<\/li>\n<\/ul>\n<hr \/>\n<h3>\u5b9f\u4f8b<\/h3>\n<h4>1) \u5165\u529b\u3068\u30d4\u30dc\u30c3\u30c8\u3067\u3069\u3046\u5909\u308f\u308b\uff1f<\/h4>\n<div class=\"s_table\"><table>\n<thead>\n<tr>\n<th>\u5178\u578b\u30b1\u30fc\u30b9<\/th>\n<th>\u30d4\u30dc\u30c3\u30c8\u306e\u53d6\u308a\u65b9<\/th>\n<th>\u5206\u5272\u306e\u69d8\u5b50<\/th>\n<th>\u6642\u9593\u8a08\u7b97\u91cf\u306e\u5e30\u7d50<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>\u30e9\u30f3\u30c0\u30e0 or \u672a\u77e5\u306e\u5165\u529b<\/td>\n<td><strong>\u4e71\u629e<\/strong>\uff08\u5404\u518d\u5e30\u3067\u30e9\u30f3\u30c0\u30e0\u8981\u7d20\uff09<\/td>\n<td>\u671f\u5f85\u7684\u306b\u201c\u307b\u307c\u5747\u7b49\u201d<\/td>\n<td><strong>\u671f\u5f85 O(n log n)<\/strong>\uff08\u5168\u5165\u529b\u306b\u5bfe\u3057\uff09<\/td>\n<\/tr>\n<tr>\n<td>\u307b\u307c\u6574\u5217\/\u9006\u9806<\/td>\n<td>\u5148\u982d\u3084\u672b\u5c3e\u3092\u5e38\u306b\u30d4\u30dc\u30c3\u30c8<\/td>\n<td>\u6bce\u56de\u304d\u308f\u3081\u3066\u504f\u308b<\/td>\n<td><strong>\u0398(n\u00b2)<\/strong>\uff08\u30ef\u30fc\u30b9\u30c8\uff09<\/td>\n<\/tr>\n<tr>\n<td>\u4e00\u822c\u5165\u529b<\/td>\n<td>\u4e2d\u592e\u30fb\u5148\u982d\u30fb\u672b\u5c3e\u304b\u3089 <strong>median-of-3<\/strong><\/td>\n<td>\u504f\u308a\u3092\u6291\u3048\u3084\u3059\u3044<\/td>\n<td>\u5b9f\u52d9\u3067\u9ad8\u901f\uff08\u5e73\u5747 O(n log n) \u3092\u4fdd\u3061\u3084\u3059\u3044\uff09<\/td>\n<\/tr>\n<\/tbody>\n<\/table><\/div>\n<h4>2) \u898f\u6a21\u611f\u306e\u6bd4\u8f03\uff08\u6bd4\u8f03\u56de\u6570\u306e\u6982\u7b97\uff09<\/h4>\n<p>Princeton\u306e\u5f0f\u3092\u7528\u3044\u305f\u6982\u7b97\uff08\u81ea\u7136\u5bfe\u6570\uff09\u3002<\/p>\n<div class=\"s_table\"><table>\n<thead>\n<tr>\n<th align=\"right\" style=\"width: 533px;\">n<\/th>\n<th align=\"right\" style=\"width: 238px;\">\u5e73\u5747\u6bd4\u8f03\u56de\u6570 \u2248 <strong>2n ln n<\/strong><\/th>\n<th align=\"right\" style=\"width: 218px;\">\u6700\u60aa\u6bd4\u8f03\u56de\u6570 \u2248 <strong>\u00bd n\u00b2<\/strong><\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td align=\"right\" style=\"width: 533px;\">1,000<\/td>\n<td align=\"right\" style=\"width: 238px;\">\u7d04 <strong>13,816<\/strong><\/td>\n<td align=\"right\" style=\"width: 218px;\">\u7d04 <strong>500,000<\/strong><\/td>\n<\/tr>\n<tr>\n<td align=\"right\" style=\"width: 533px;\">10,000<\/td>\n<td align=\"right\" style=\"width: 238px;\">\u7d04 <strong>184,207<\/strong><\/td>\n<td align=\"right\" style=\"width: 218px;\">\u7d04 <strong>50,000,000<\/strong><\/td>\n<\/tr>\n<tr>\n<td align=\"right\" style=\"width: 533px;\">100,000<\/td>\n<td align=\"right\" style=\"width: 238px;\">\u7d04 <strong>2,302,585<\/strong><\/td>\n<td align=\"right\" style=\"width: 218px;\">\u7d04 <strong>5,000,000,000<\/strong><\/td>\n<\/tr>\n<tr>\n<td align=\"right\" style=\"width: 533px;\">\uff08\u5e73\u5747\u306f <strong>O(n log n)<\/strong>\u3001\u6700\u60aa\u306f <strong>\u0398(n\u00b2)<\/strong> \u306b\u6cbf\u3063\u305f\u4f38\u3073\u65b9\u3092\u793a\u3059\u3002\uff09<\/td>\n<td align=\"right\" style=\"width: 238px;\"><\/td>\n<td align=\"right\" style=\"width: 218px;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table><\/div>\n<h4>3) \u3069\u3046\u9632\u3050\uff1f\uff08\u5b9f\u88c5\u306e\u5b88\u308a\uff09<\/h4>\n<ul>\n<li><strong>\u4e71\u629e\u30d4\u30dc\u30c3\u30c8<\/strong>\uff1a\u5165\u529b\u4f9d\u5b58\u306e\u504f\u308a\u3092\u78ba\u7387\u7684\u306b\u56de\u907f\u3057\u3001\u671f\u5f85 <strong>O(n log n)<\/strong> \u3092\u78ba\u4fdd\u3002<\/li>\n<li><strong>Introsort \u306a\u3069\u306e\u30d5\u30a9\u30fc\u30eb\u30d0\u30c3\u30af<\/strong>\uff1a\u518d\u5e30\u304c\u6df1\u304f\u306a\u3063\u305f\u3089Heapsort\u3078\u5207\u66ff\u3048\u3001<strong>\u6700\u60aa O(n log n)<\/strong> \u3092\u4fdd\u8a3c\uff08NIST\u3082\u201c\u9078\u629e\u3067\u826f\u30d4\u30dc\u30c3\u30c8\u3092\u5e38\u306b\u53d6\u308c\u3070\u6700\u60aa O(n log n)\u201d\u306e\u6d3e\u751f\u306b\u89e6\u308c\u308b\uff09\u3002<\/li>\n<\/ul>\n<hr \/>\n<h3>\u7d50\u8ad6\uff08\u307e\u3068\u3081\uff09<\/h3>\n<ul>\n<li><strong>\u5e73\u5747<\/strong>\uff1a\u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8\u306f<strong>O(n log n)<\/strong> \u3068\u7406\u8ad6\u7684\u306b\u6700\u9069\u7d1a\u3002\u5b9f\u88c5\u6700\u9069\u5316\uff08\u4e71\u629e\u30fbmedian-of-3 \u7b49\uff09\u3067\u3055\u3089\u306b\u5b89\u5b9a\u30fb\u9ad8\u901f\u5316\u3067\u304d\u308b\u3002<\/li>\n<li><strong>\u6700\u60aa<\/strong>\uff1a\u504f\u308a\u5206\u5272\u3067 <strong>\u0398(n\u00b2)<\/strong>\u3002\u5bfe\u7b56\u3068\u3057\u3066<strong>\u4e71\u629e<\/strong>\u3084**\u30d5\u30a9\u30fc\u30eb\u30d0\u30c3\u30af\uff08Introsort\u7cfb\uff09**\u3092\u7528\u610f\u3059\u308c\u3070\u3001\u5b9f\u52d9\u3067\u306e\u201c\u4e8c\u4e57\u843d\u3061\u201d\u30ea\u30b9\u30af\u3092\u5927\u5e45\u306b\u6291\u3048\u3089\u308c\u308b\u3002<\/li>\n<li><strong>\u7406\u8ad6\u7684\u80cc\u666f<\/strong>\uff1a\u6bd4\u8f03\u30e2\u30c7\u30eb\u3067\u306f<strong>\u03a9(n log n)<\/strong> \u304c\u4e0b\u9650\u3002\u3057\u305f\u304c\u3063\u3066\u300c\u5e73\u5747 O(n log n)\u300d\u3092\u5f97\u3089\u308c\u308b\u8a2d\u8a08\u306f<strong>\u5230\u9054\u53ef\u80fd\u306a\u4e0a\u9650\u306b\u8fd1\u3044<\/strong>\u3002<\/li>\n<\/ul>\n<p>\u5fc5\u8981\u306a\u3089\u3001\u3042\u306a\u305f\u306e\u30c7\u30fc\u30bf\u7279\u6027\uff08\u91cd\u8907\u306e\u591a\u3055\u3001\u307b\u307c\u6574\u5217\u304b\u3001\u30ad\u30fc\u6bd4\u8f03\u30b3\u30b9\u30c8\u306a\u3069\uff09\u306b\u5408\u308f\u305b\u3066\u3001\u4e71\u629e\/median-of-3\/3-way\/Introsort \u306e\u5177\u4f53\u7684\u306a\u5b9f\u88c5\u30c6\u30f3\u30d7\u30ec\u3082\u7528\u610f\u3057\u307e\u3059\u3002<\/p>\n<p class=\"spacer\">&nbsp;<\/p>\n<h3>3-2. \u5b89\u5b9a\u6027\u30fb\u30e1\u30e2\u30ea\u4f7f\u7528\u91cf\uff08\u30a4\u30f3\u30d7\u30ec\u30fc\u30b9\u6027\uff09<\/h3>\n<h3>\u5b89\u5b9a\u6027\u30fb\u30e1\u30e2\u30ea\u4f7f\u7528\u91cf\uff08\u30a4\u30f3\u30d7\u30ec\u30fc\u30b9\u6027\uff09<\/h3>\n<h3>\u7d50\u8ad6<\/h3>\n<ul>\n<li><strong>\u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8\u306f\u4e00\u822c\u306b\u201c\u5b89\u5b9a\u3067\u306f\u306a\u3044\u201d\u304c\u201c\u30a4\u30f3\u30d7\u30ec\u30fc\u30b9\u5bc4\u308a\uff08\u5c0f\u3055\u306a\u88dc\u52a9\u30b9\u30bf\u30c3\u30af\uff09\u201d\u3067\u52d5\u304f<\/strong>\u305f\u3081\u3001\u8ffd\u52a0\u30e1\u30e2\u30ea\u3092\u6291\u3048\u3064\u3064\u9ad8\u901f\u306b\u52d5\u4f5c\u3057\u3084\u3059\u3044\u3002\u5927\u91cf\u30c7\u30fc\u30bf\u3084\u30e1\u30e2\u30ea\u5236\u7d04\u4e0b\u3067\u6709\u5229\u3002<\/li>\n<li><strong>\u5b89\u5b9a\u6027\u304c\u5fc5\u8981\u306a\u3089\u201c\u5b89\u5b9a\u30bd\u30fc\u30c8\uff08\u4f8b\uff1a\u30de\u30fc\u30b8\u30bd\u30fc\u30c8\u7cfb\uff0fTimsort\uff09\u201d\u3092\u9078\u3076<\/strong>\u3002\u305f\u3060\u3057\u591a\u304f\u306e\u5b9f\u88c5\u306f<strong>\u8ffd\u52a0\u30e1\u30e2\u30ea O(n)<\/strong> \u3092\u8981\u3059\u308b\uff08Python\u306e\u7d44\u8fbc\u307f\u30bd\u30fc\u30c8\u306f\u5b89\u5b9a\u3002Java\u306f\u53c2\u7167\u578b\u306bTimsort\u7cfb\u30fb\u30d7\u30ea\u30df\u30c6\u30a3\u30d6\u306bDual-Pivot Quicksort\uff09\u3002<\/li>\n<li><strong>\u7528\u8a9e\u306e\u57fa\u6e96<\/strong>\uff1a\n<ul>\n<li>\u5b89\u5b9a\uff08stable\uff09= \u540c\u4e00\u30ad\u30fc\u8981\u7d20\u306e\u76f8\u5bfe\u9806\u5e8f\u304c\u4fdd\u5b58\u3055\u308c\u308b\u3002<\/li>\n<li>\u30a4\u30f3\u30d7\u30ec\u30fc\u30b9 = \u540c\u3058\u9818\u57df\u3067\u4e26\u3079\u66ff\u3048\u3001\u8ffd\u52a0\u30e1\u30e2\u30ea\u306f\u9ad8\u3005 o(n)\u3002<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<hr \/>\n<h3>\u7406\u7531\u3084\u6839\u62e0<\/h3>\n<ul>\n<li><strong>\u516c\u7684\u6a5f\u95a2\u306e\u5b9a\u7fa9<\/strong>\n<ul>\n<li>NIST\uff08\u7c73\u56fd\u6a19\u6e96\u6280\u8853\u7814\u7a76\u6240\uff09\u306e\u7528\u8a9e\u8f9e\u5178\u3067\u306f\u3001\u5b89\u5b9a\u30bd\u30fc\u30c8\u3068\u30a4\u30f3\u30d7\u30ec\u30fc\u30b9\u30bd\u30fc\u30c8\u3092\u4e0a\u8a18\u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3002\u5b9f\u88c5\u5224\u65ad\u306e\u524d\u63d0\u306b\u306a\u308b\u3002<\/li>\n<\/ul>\n<\/li>\n<li><strong>\u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8\u306e\u201c\u30a4\u30f3\u30d7\u30ec\u30fc\u30b9\u6027\u201d\u3068\u5e73\u5747\u7684\u3075\u308b\u307e\u3044<\/strong>\n<ul>\n<li>\u30d7\u30ea\u30f3\u30b9\u30c8\u30f3\u5927\u5b66\u306e\u8b1b\u7fa9\u8cc7\u6599\u306f\u3001\u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8\u3092\u300c<strong>in-place\uff08\u5c0f\u3055\u306a\u88dc\u52a9\u30b9\u30bf\u30c3\u30af\u306e\u307f\uff09<\/strong>\u30fb\u5e73\u5747 <strong>N log N<\/strong>\u300d\u3068\u660e\u793a\u3002\u5b9f\u52d9\u3067\u901f\u3044\u7406\u7531\u306e\u3072\u3068\u3064\u306f<strong>\u8ffd\u52a0\u30e1\u30e2\u30ea\u306e\u5c0f\u3055\u3055<\/strong>\u3002<\/li>\n<li>NIST\u306e\u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8\u9805\u76ee\u3082\u3001\u6d3e\u751f\uff08Dual-Pivot\uff09\u3067\u306f**\u300c\u3088\u308a\u5c11\u306a\u3044\u30e1\u30e2\u30ea\u30a2\u30af\u30bb\u30b9\u300d**\u304c\u9ad8\u901f\u5316\u8981\u56e0\u306b\u306a\u308b\u3068\u89e3\u8aac\u3002\u30e1\u30e2\u30ea\u968e\u5c64\u3092\u610f\u8b58\u3057\u305f\u5b9f\u88c5\u3067\u6709\u5229\u306b\u306a\u308a\u3084\u3059\u3044\u3002<\/li>\n<\/ul>\n<\/li>\n<li><strong>\u5b89\u5b9a\u30bd\u30fc\u30c8\u306e\u30e1\u30e2\u30ea\u4e8b\u60c5<\/strong>\n<ul>\n<li>\u30de\u30fc\u30b8\u30bd\u30fc\u30c8\u306f<strong>\u88dc\u52a9\u914d\u5217\u304c\u5fc5\u8981\u3067 O(n) \u8ffd\u52a0\u30e1\u30e2\u30ea<\/strong>\uff08\u5927\u5b66\u306e\u8b1b\u7fa9\u8cc7\u6599\u306e\u547d\u984c\u3068\u3057\u3066\u660e\u8a18\uff09\u3002<\/li>\n<li>Python\u306e <code>list.sort<\/code> \u306f<strong>\u5b89\u5b9a<\/strong>\uff08Timsort\u7cfb\uff09\u3002\u516c\u5f0f\u30cf\u30a6\u30c4\u30fc\u3067\u3082\u5b89\u5b9a\u6027\u3092\u660e\u793a\u3002<\/li>\n<li>Java\u306e\u6a19\u6e96\u30e9\u30a4\u30d6\u30e9\u30ea\u306f<strong>\u53c2\u7167\u578b\uff08Object[]\uff09\u306b\u5b89\u5b9a\u306a\u5b9f\u88c5<\/strong>\u3001<strong>\u30d7\u30ea\u30df\u30c6\u30a3\u30d6\u914d\u5217\u306bDual-Pivot Quicksort<\/strong>\u3092\u63a1\u7528\uff08\u5b9f\u88c5\u30ce\u30fc\u30c8\uff09\u3002<\/li>\n<\/ul>\n<\/li>\n<li><strong>\u201c\u5b89\u5b9a\u3067\u306f\u306a\u3044\u201d\u4ee3\u8868\u4f8b\u3068\u3057\u3066\u306e\u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8<\/strong>\n<ul>\n<li>\u4e00\u822c\u5b9f\u88c5\u306e\u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8\u306f<strong>\u4e0d\u5b89\u5b9a<\/strong>\u3067\u3042\u308b\u3053\u3068\u304c\u5e83\u304f\u77e5\u3089\u308c\u3066\u304a\u308a\u3001\u767e\u79d1\u4e8b\u5178\u7684\u306a\u307e\u3068\u3081\u3067\u3082\u660e\u8a18\u3002<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<hr \/>\n<h3>\u5b9f\u4f8b\uff08\u8a2d\u8a08\u5224\u65ad\u306b\u4f7f\u3048\u308b\u6bd4\u8f03\u8868\uff09<\/h3>\n<div class=\"s_table\"><table>\n<thead>\n<tr>\n<th>\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0<\/th>\n<th>\u5b89\u5b9a\u6027<\/th>\n<th>\u8ffd\u52a0\u30e1\u30e2\u30ea\uff08\u5178\u578b\uff09<\/th>\n<th>\u4ee3\u8868\u7684\u306a\u6839\u62e0\/\u5099\u8003<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td><strong>\u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8<\/strong><\/td>\n<td><strong>\u4e0d\u5b89\u5b9a<\/strong><\/td>\n<td><strong>\u5c0f<\/strong>\uff1a\u518d\u5e30\u30b9\u30bf\u30c3\u30af\u4e2d\u5fc3\uff08\u5e73\u5747\u306f\u5c0f\u3001\u5b9f\u88c5\u306f\u201cin-place\uff08\u5c0f\u3055\u306a\u88dc\u52a9\u30b9\u30bf\u30c3\u30af\uff09\u201d\u3068\u8aac\u660e\uff09<\/td>\n<td>\u30d7\u30ea\u30f3\u30b9\u30c8\u30f3\u8cc7\u6599\u300cin-place\uff08\u5c0f\u3055\u306a\u88dc\u52a9\u30b9\u30bf\u30c3\u30af\uff09\u300d\u3001NIST\u306e\u5b9a\u7fa9\u30fb\u89e3\u8aac\u3002<\/td>\n<\/tr>\n<tr>\n<td><strong>\u30de\u30fc\u30b8\u30bd\u30fc\u30c8\uff08\u914d\u5217\u7248\uff09<\/strong><\/td>\n<td><strong>\u5b89\u5b9a\uff08\u5b9f\u88c5\u6b21\u7b2c\uff09<\/strong><\/td>\n<td><strong>\u5927<\/strong>\uff1a<strong>O(n)<\/strong> \u306e\u88dc\u52a9\u914d\u5217<\/td>\n<td>\u30d7\u30ea\u30f3\u30b9\u30c8\u30f3\u8cc7\u6599\u306b\u300c\u88dc\u52a9\u914d\u5217\u306f\u9577\u3055 N \u304c\u5fc5\u8981\u300d\u3002<\/td>\n<\/tr>\n<tr>\n<td><strong>Timsort<\/strong>\uff08Python\/Java\u53c2\u7167\u578b\uff09<\/td>\n<td><strong>\u5b89\u5b9a<\/strong><\/td>\n<td><strong>\u4e2d\u301c\u5927<\/strong>\uff1a\u5165\u529b\u306e\u6574\u5217\u5ea6\u306b\u5fdc\u3058\u53ef\u5909\u3001<strong>\u6700\u60aa n\/2 \u53c2\u7167<\/strong>\u7a0b\u5ea6\u306e\u4e00\u6642\u9818\u57df\uff08Java\u306e\u5b9f\u88c5\u30ce\u30fc\u30c8\uff09<\/td>\n<td>Python\u516c\u5f0f\u306f\u5b89\u5b9a\u3092\u660e\u8a18\u3002Java\u306eList\/Arrays\u7cfb\u5b9f\u88c5\u30ce\u30fc\u30c8\u306b\u4e00\u6642\u9818\u57df\u306e\u4e0a\u9650\u50be\u5411\u3002<\/td>\n<\/tr>\n<tr>\n<td><strong>\u30d2\u30fc\u30d7\u30bd\u30fc\u30c8<\/strong><\/td>\n<td><strong>\u4e0d\u5b89\u5b9a<\/strong><\/td>\n<td><strong>\u5c0f<\/strong>\uff1a\u30a4\u30f3\u30d7\u30ec\u30fc\u30b9\u7cfb<\/td>\n<td>NIST\u3067 in-place \u306e\u4e00\u7a2e\u3068\u3057\u3066\u5206\u985e\u3002<\/td>\n<\/tr>\n<\/tbody>\n<\/table><\/div>\n<blockquote><p>\u88dc\u8db3\uff1aNIST\u306f\u300c<strong>\u4efb\u610f\u306e\u30bd\u30fc\u30c8\u3067\u3082<\/strong>\u5143\u306e\u4f4d\u7f6e\u3092\u201c\u30bf\u30a4\u30d6\u30ec\u30fc\u30af\u7528\u30ad\u30fc\u201d\u3068\u3057\u3066\u57cb\u3081\u8fbc\u3081\u3070<strong>\u5b89\u5b9a\u5316\u3067\u304d\u308b<\/strong>\u300d\u3068\u6ce8\u8a18\u3002\u8ffd\u52a0\u30e1\u30e2\u30ea\u3084\u51e6\u7406\u624b\u9806\u306e\u8907\u96d1\u5316\u3068\u30c8\u30ec\u30fc\u30c9\u30aa\u30d5\u3002<\/p><\/blockquote>\n<hr \/>\n<h3>\u5b9f\u52d9\u30b7\u30ca\u30ea\u30aa\u3067\u306e\u4f7f\u3044\u5206\u3051<\/h3>\n<ul>\n<li><strong>\u8907\u6570\u30ad\u30fc\u3067\u306e\u6bb5\u968e\u7684\u30bd\u30fc\u30c8\uff08\u90e8\u7f72\u2192\u7d66\u4e0e\u306a\u3069\uff09<\/strong><br \/>\n\u21d2 <strong>\u5b89\u5b9a\u6027\u304c\u5fc5\u8981<\/strong>\u3002Python\u306e <code>list.sort<\/code> \/ <code>sorted<\/code> \u306f<strong>\u5b89\u5b9a<\/strong>\u306a\u306e\u3067\u3001\u5148\u306b\u526f\u30ad\u30fc\u3001\u6b21\u306b\u4e3b\u30ad\u30fc\u306e\u9806\u306b\u547c\u3079\u3070\u610f\u56f3\u901a\u308a\u306e\u9806\u5e8f\u3092\u4fdd\u8a3c\u3067\u304d\u308b\u3002<\/li>\n<li><strong>\u5de8\u5927\u914d\u5217\u30fb\u30e1\u30e2\u30ea\u5236\u7d04\uff08\u7d44\u8fbc\u307f\u30fb\u30aa\u30f3\u30e1\u30e2\u30ea\u51e6\u7406\uff09<\/strong><br \/>\n\u21d2 <strong>\u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8\uff0f\u30d2\u30fc\u30d7\u30bd\u30fc\u30c8<\/strong>\u306a\u3069<strong>\u30a4\u30f3\u30d7\u30ec\u30fc\u30b9\u5bc4\u308a<\/strong>\u304c\u6709\u5229\u3002\u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8\u306f\u5c0f\u3055\u306a\u88dc\u52a9\u30b9\u30bf\u30c3\u30af\u3067\u5e73\u5747\u9ad8\u901f\u3002<\/li>\n<li><strong>Java\u3067\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\u914d\u5217\u3092\u5b89\u5b9a\u306b\u4e26\u3079\u305f\u3044<\/strong><br \/>\n\u21d2 <strong><code>Arrays.sort(Object[])<\/code> \u306f\u5b89\u5b9a\u5b9f\u88c5\u304c\u524d\u63d0<\/strong>\uff08Timsort\u7cfb\uff09\u3002<strong>\u30d7\u30ea\u30df\u30c6\u30a3\u30d6\u914d\u5217<\/strong>\u306f Dual-Pivot Quicksort\uff08\u4e0d\u5b89\u5b9a\uff09\u306a\u306e\u3067\u8981\u6ce8\u610f\u3002<\/li>\n<\/ul>\n<hr \/>\n<h3>\u7d50\u8ad6\uff08\u307e\u3068\u3081\uff09<\/h3>\n<ul>\n<li><strong>\u5b89\u5b9a\u6027\u304c\u6700\u512a\u5148\u306a\u3089<\/strong>\uff1aTimsort\uff0f\u30de\u30fc\u30b8\u30bd\u30fc\u30c8\u7cfb\uff08\u305f\u3060\u3057<strong>\u8ffd\u52a0\u30e1\u30e2\u30ea<\/strong>\u3092\u898b\u8fbc\u3080\uff09\u3002Python\/Java\u53c2\u7167\u578b\u306e\u6a19\u6e96\u30bd\u30fc\u30c8\u306f\u3053\u306e\u8a2d\u8a08\u3002<\/li>\n<li><strong>\u30e1\u30e2\u30ea\u52b9\u7387\u304c\u6700\u512a\u5148\u306a\u3089<\/strong>\uff1a\u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8\uff08\u5e73\u5747 O(n log n)\u30fb<strong>\u5c0f\u3055\u306a\u88dc\u52a9\u30b9\u30bf\u30c3\u30af<\/strong>\uff09\u3084\u30d2\u30fc\u30d7\u30bd\u30fc\u30c8\uff08\u30a4\u30f3\u30d7\u30ec\u30fc\u30b9\uff09\u3092\u8ef8\u306b\u3002\u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8\u306f\u4e00\u822c\u306b<strong>\u4e0d\u5b89\u5b9a<\/strong>\u306a\u306e\u3067\u3001\u5b89\u5b9a\u6027\u304c\u5fc5\u8981\u306a\u8981\u4ef6\u3067\u306f\u4e0d\u5411\u304d\u3002<\/li>\n<li><strong>\u6df7\u5408\u8981\u4ef6\u306a\u3089<\/strong>\uff1a\u307e\u305a\u8981\u4ef6\uff08\u5b89\u5b9a\u6027\uff0f\u30e1\u30e2\u30ea\uff09\u306b\u91cd\u307f\u3065\u3051\u3057\u3001**\u30c7\u30fc\u30bf\u7279\u6027\uff08\u91cd\u8907\u306e\u591a\u3055\u3001\u6574\u5217\u5ea6\uff09<strong>\u3068<\/strong>\u5b9f\u88c5\u306e\u5b9f\u60c5\uff08Python\/Java \u306e\u65e2\u5b9a\u52d5\u4f5c\uff09**\u3092\u8e0f\u307e\u3048\u305f\u9078\u629e\u304c\u6700\u77ed\u30eb\u30fc\u30c8\u3002\u5fc5\u8981\u306b\u5fdc\u3058\u3066\u201c\u5b89\u5b9a\u5316\u306e\u305f\u3081\u306e\u88dc\u52a9\u30ad\u30fc\u4ed8\u4e0e\u201d\u3068\u3044\u3046\u624b\u3082\u3042\u308b\u3002<\/li>\n<\/ul>\n<p>\u5fc5\u8981\u306a\u3089\u3001\u3042\u306a\u305f\u306e\u5b9f\u30c7\u30fc\u30bf\uff08\u4ef6\u6570\u30fb\u30ad\u30fc\u7279\u6027\u30fb\u30e1\u30e2\u30ea\u4e88\u7b97\uff09\u306b\u5408\u308f\u305b\u3066\u3001<strong>\u5b89\u5b9a\u6027\u3068\u30e1\u30e2\u30ea\u306e\u6700\u9069\u70b9<\/strong>\u3092\u72d9\u3046\u5b9f\u88c5\u30c6\u30f3\u30d7\u30ec\uff08Python\/Java\u7248\uff09\u3092\u63d0\u793a\u3057\u307e\u3059\u3002<\/p>\n<h3>3-3. \u30de\u30fc\u30b8\/\u30d2\u30fc\u30d7\/\u633f\u5165\/\u30b7\u30a7\u30eb\u3068\u306e\u6bd4\u8f03<\/h3>\n<h3>\u30de\u30fc\u30b8\/\u30d2\u30fc\u30d7\/\u633f\u5165\/\u30b7\u30a7\u30eb\u3068\u306e\u6bd4\u8f03<\/h3>\n<h3>\u7d50\u8ad6<\/h3>\n<ul>\n<li><strong>\u5e73\u5747\u7684\u306a\u901f\u3055\u3060\u3051\u306a\u3089<\/strong>\u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8\u2252\u30de\u30fc\u30b8\u30bd\u30fc\u30c8\u2252\u30d2\u30fc\u30d7\u30bd\u30fc\u30c8\u306f<strong>O(n log n)<\/strong>\u3002\u305f\u3060\u3057<strong>\u5b89\u5b9a\u6027\u304c\u5fc5\u8981\u306a\u3089\u30de\u30fc\u30b8\uff08\u3084Timsort\u7cfb\uff09<\/strong>\u3001<strong>\u30e1\u30e2\u30ea\u3092\u6291\u3048\u308b\u306a\u3089\u30af\u30a4\u30c3\u30af\/\u30d2\u30fc\u30d7<\/strong>\u304c\u672c\u547d\u3002\u633f\u5165\u30fb\u30b7\u30a7\u30eb\u306f<strong>\u5c0f\u898f\u6a21<\/strong>\u3084<strong>\u307b\u307c\u6574\u5217<\/strong>\u3067\u5f37\u3044\u201c\u73fe\u5834\u306e\u6b66\u5668\u201d\u3002<\/li>\n<\/ul>\n<hr \/>\n<h3>\u7406\u7531\u3084\u6839\u62e0\uff08\u8981\u70b9\uff09<\/h3>\n<ul>\n<li><strong>\u8a08\u7b97\u91cf\u306e\u571f\u53f0<\/strong>\n<ul>\n<li>\u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8\uff1a<strong>\u5178\u578b O(n log n)\u3001\u6700\u60aa \u0398(n\u00b2)<\/strong>\uff08\u4e71\u629e\u3084\u826f\u3044\u30d4\u30dc\u30c3\u30c8\u3067\u5e73\u5747\u6319\u52d5\u3092\u5b89\u5b9a\u5316\uff09\u3002<\/li>\n<li>\u30de\u30fc\u30b8\u30bd\u30fc\u30c8\uff1a<strong>\u0398(n log n)<\/strong>\u3002\u914d\u5217\u7248\u306f<strong>\u88dc\u52a9\u914d\u5217\u304c\u5fc5\u8981\uff1dO(n) \u8ffd\u52a0\u30e1\u30e2\u30ea<\/strong>\u3002<\/li>\n<li>\u30d2\u30fc\u30d7\u30bd\u30fc\u30c8\uff1a<strong>O(n log n)<\/strong>\u3001<strong>\u30a4\u30f3\u30d7\u30ec\u30fc\u30b9<\/strong>\u3001\u305f\u3060\u3057<strong>\u5b89\u5b9a\u3067\u306f\u306a\u3044<\/strong>\u3002<\/li>\n<li>\u633f\u5165\u30bd\u30fc\u30c8\uff1a<strong>\u6700\u60aa O(n\u00b2)<\/strong>\u3001<strong>\u5b89\u5b9a<\/strong>\u3001<strong>\u0398(1) \u8ffd\u52a0\u30e1\u30e2\u30ea<\/strong>\u3002\u90e8\u5206\u7684\u306b\u6574\u5217\u6e08\u307f\u306a\u3089\u901f\u3044\u3002<\/li>\n<li>\u30b7\u30a7\u30eb\u30bd\u30fc\u30c8\uff1a<strong>\u5897\u5206\u5217\u3067\u6319\u52d5\u304c\u5927\u304d\u304f\u5909\u5316<\/strong>\u3002Knuth\u5217\u306a\u3069\u306e\u5b9f\u88c5\u3067<strong>\u6700\u60aa \u0398(n^{3\/2})<\/strong>\u3001\u7406\u8ad6\u3067\u306f <strong>O(n log\u00b2 n)<\/strong> \u4e0a\u754c\u306e\u53e4\u5178\u7d50\u679c\u3082\u3002\u3044\u305a\u308c\u3082<strong>\u30a4\u30f3\u30d7\u30ec\u30fc\u30b9\uff0f\u975e\u5b89\u5b9a<\/strong>\u3002<\/li>\n<\/ul>\n<\/li>\n<li><strong>\u30e1\u30e2\u30ea\u30a2\u30af\u30bb\u30b9\u30fb\u5b9f\u88c5\u5b9f\u52d9<\/strong>\n<ul>\n<li>\u30de\u30fc\u30b8\u306f<strong>\u5b89\u5b9a<\/strong>\u3060\u304c<strong>\u88dc\u52a9\u914d\u5217 N<\/strong> \u304c\u5fc5\u8981\uff08in-place merge \u306f\u96e3\u984c\uff09\u3002<\/li>\n<li>\u30d2\u30fc\u30d7\u306f<strong>\u30ad\u30e3\u30c3\u30b7\u30e5\u52b9\u7387\u304c\u60aa\u304f<\/strong>\u5b9f\u6e2c\u3067\u30af\u30a4\u30c3\u30af\u306b\u52a3\u308b\u3053\u3068\u304c\u591a\u3044\uff08\u305f\u3060\u3057\u6700\u60aa O(n log n) \u4fdd\u969c\uff09\u3002<\/li>\n<li>\u30af\u30a4\u30c3\u30af\u306f<strong>\u30c1\u30e5\u30fc\u30cb\u30f3\u30b0\u6e08\u307f\u5b9f\u88c5\u304c\u5b9f\u52d9\u3067\u9ad8\u901f<\/strong>\u3068\u3044\u3046\u8a55\u4fa1\u304c\u516c\u7684\u8f9e\u5178\u306b\u3082\u8a18\u8f09\u3002<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<hr \/>\n<h3>\u6bd4\u8f03\u8868\uff08\u8981\u70b9\u30b5\u30de\u30ea\uff09<\/h3>\n<div class=\"s_table\"><table>\n<thead>\n<tr>\n<th>\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0<\/th>\n<th>\u5e73\u5747\u8a08\u7b97\u91cf<\/th>\n<th>\u6700\u60aa\u8a08\u7b97\u91cf<\/th>\n<th>\u5b89\u5b9a\u6027<\/th>\n<th>\u8ffd\u52a0\u30e1\u30e2\u30ea<\/th>\n<th>\u5b9f\u52d9\u3067\u306e\u8981\u70b9<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td><strong>\u30af\u30a4\u30c3\u30af<\/strong><\/td>\n<td>O(n log n)<\/td>\n<td>\u0398(n\u00b2)<\/td>\n<td>\u4e0d\u5b89\u5b9a<\/td>\n<td>\u5c0f\uff08\u30b9\u30bf\u30c3\u30af\u4e2d\u5fc3\uff09<\/td>\n<td>\u5b9f\u88c5\u6700\u9069\u5316\u3067\u5b9f\u52d9\u6700\u901f\u7d1a\u3002\u4e71\u629e\/median-of-3\/3-way\u3067\u5b89\u5b9a\u5316\u3002<\/td>\n<\/tr>\n<tr>\n<td><strong>\u30de\u30fc\u30b8<\/strong><\/td>\n<td>\u0398(n log n)<\/td>\n<td>\u0398(n log n)<\/td>\n<td><strong>\u5b89\u5b9a<\/strong><\/td>\n<td><strong>O(n)<\/strong><\/td>\n<td>\u5927\u898f\u6a21\u30fb\u5b89\u5b9a\u5fc5\u9808\u306b\u25ce\u3002\u914d\u5217\u7248\u306f\u88dc\u52a9\u914d\u5217\u304c\u524d\u63d0\u3002<\/td>\n<\/tr>\n<tr>\n<td><strong>\u30d2\u30fc\u30d7<\/strong><\/td>\n<td>O(n log n)<\/td>\n<td>O(n log n)<\/td>\n<td>\u4e0d\u5b89\u5b9a<\/td>\n<td><strong>\u0398(1)<\/strong><\/td>\n<td>\u30a4\u30f3\u30d7\u30ec\u30fc\u30b9\uff06\u6700\u60aa\u4fdd\u8a3c\u3002\u305f\u3060\u3057\u30ad\u30e3\u30c3\u30b7\u30e5\u52b9\u7387\u306f\u4f4e\u3081\u3002<\/td>\n<\/tr>\n<tr>\n<td><strong>\u633f\u5165<\/strong><\/td>\n<td>\u4f9d\u5b58\uff08\u90e8\u5206\u6574\u5217\u3067\u901f\u3044\uff09<\/td>\n<td>O(n\u00b2)<\/td>\n<td><strong>\u5b89\u5b9a<\/strong><\/td>\n<td><strong>\u0398(1)<\/strong><\/td>\n<td>\u5c0f\u914d\u5217\u3084<strong>\u307b\u307c\u6574\u5217<\/strong>\u306e\u30c7\u30fc\u30bf\u3067\u6700\u5f37\u3002\u30ab\u30c3\u30c8\u30aa\u30d5\u5148\u3068\u3057\u3066\u25ce\u3002<\/td>\n<\/tr>\n<tr>\n<td><strong>\u30b7\u30a7\u30eb<\/strong><\/td>\n<td>\u5b9f\u88c5\u4f9d\u5b58<\/td>\n<td>\u0398(n^{3\/2})\uff08Knuth\u5217\u5b9f\u88c5\u4f8b\uff09<\/td>\n<td>\u4e0d\u5b89\u5b9a<\/td>\n<td><strong>\u0398(1)<\/strong><\/td>\n<td>\u4e2d\u898f\u6a21\u3084\u90e8\u5206\u6574\u5217\u3067\u5f37\u3044\u3002\u5897\u5206\u5217\u9078\u5b9a\u304c\u30ab\u30ae\u3002<\/td>\n<\/tr>\n<\/tbody>\n<\/table><\/div>\n<blockquote><p>\u6ce8\uff1a\u30b7\u30a7\u30eb\u30bd\u30fc\u30c8\u306f\u5897\u5206\u5217\u306b\u3088\u308a\u7406\u8ad6\u7d50\u679c\u304c\u591a\u69d8\u3002Pratt\u578b\u3067\u306f<strong>O(n log\u00b2 n)<\/strong> \u306e\u53e4\u5178\u7684\u4e0a\u754c\u304c\u77e5\u3089\u308c\u307e\u3059\u3002\u5b9f\u88c5\u3067\u3088\u304f\u4f7f\u308f\u308c\u308bKnuth\u5217\u3067\u306f\u6700\u60aa <strong>\u0398(n^{3\/2})<\/strong> \u306e\u89e3\u6790\u304c\u63d0\u793a\u3055\u308c\u3066\u3044\u307e\u3059\u3002<\/p><\/blockquote>\n<hr \/>\n<h3>\u5b9f\u4f8b\uff08\u8981\u4ef6\u5225\u306e\u9078\u3073\u65b9\uff09<\/h3>\n<ul>\n<li><strong>\u8907\u6570\u30ad\u30fc\u306e\u6bb5\u968e\u30bd\u30fc\u30c8\uff08\u90e8\u7f72\u2192\u7d66\u4e0e\u306a\u3069\uff09\uff0f\u9806\u5e8f\u4fdd\u6301\u304c\u8981\u4ef6<\/strong><br \/>\n\u2192 <strong>\u30de\u30fc\u30b8\uff08Timsort\u7cfb\uff09<\/strong>\uff1a<strong>\u5b89\u5b9a<\/strong>\u3067\u6271\u3044\u3084\u3059\u3044\u3002\u914d\u5217\u7248\u306f\u88dc\u52a9\u914d\u5217 N \u3092\u78ba\u4fdd\u3002<\/li>\n<li><strong>\u30e1\u30e2\u30ea\u5236\u7d04\u304c\u53b3\u3057\u3044\uff0f\u5e38\u306b\u6700\u60aa\u3092\u907f\u3051\u305f\u3044<\/strong><br \/>\n\u2192 <strong>\u30d2\u30fc\u30d7<\/strong>\uff1a<strong>\u0398(1) \u8ffd\u52a0\u30e1\u30e2\u30ea + O(n log n) \u6700\u60aa\u4fdd\u8a3c<\/strong>\u3002\u305f\u3060\u3057\u5b9f\u6e2c\u3067\u306f\u30af\u30a4\u30c3\u30af\u306b\u52a3\u308b\u3053\u3068\u3082\u3002<\/li>\n<li><strong>\u4e00\u822c\u7684\u306a\u5927\u898f\u6a21\u914d\u5217\uff0f\u5e73\u5747\u6642\u9593\u3092\u6700\u91cd\u8996<\/strong><br \/>\n\u2192 <strong>\u30af\u30a4\u30c3\u30af<\/strong>\uff1a\u4e71\u629e\u3084median-of-3\u30013-way\u5206\u5272\u3067\u5e73\u5747<strong>O(n log n)<\/strong> \u3092\u5b89\u5b9a\u5316\u3002\u5b9f\u52d9\u3067\u9ad8\u901f\u3002\u6700\u60aa\u5bfe\u7b56\u306bIntrosort\u63a1\u7528\u3082\u3002<\/li>\n<li><strong>\u8981\u7d20\u6570\u304c\u5c0f\u3055\u3044\uff0f\u307b\u307c\u6574\u5217<\/strong><br \/>\n\u2192 <strong>\u633f\u5165<\/strong>\uff1a<strong>\u5b89\u5b9a\u30fb\u0398(1)\u30e1\u30e2\u30ea<\/strong>\u3002\u30af\u30a4\u30c3\u30af\u306e\u5c0f\u533a\u9593\u30ab\u30c3\u30c8\u30aa\u30d5\u3068\u3057\u3066\u3082\u6709\u52b9\u3002<\/li>\n<li><strong>\u4e2d\u898f\u6a21\u30fb\u90e8\u5206\u6574\u5217\uff0f\u5b89\u5b9a\u6027\u4e0d\u8981<\/strong><br \/>\n\u2192 <strong>\u30b7\u30a7\u30eb<\/strong>\uff1a\u30a4\u30f3\u30d7\u30ec\u30fc\u30b9\u3067\u6bd4\u8f03\u7684\u901f\u3044\u3002\u6700\u60aa\u306f\u6ce8\u610f\u3001\u5897\u5206\u5217\u8a2d\u8a08\u304c\u9375\u3002<\/li>\n<\/ul>\n<hr \/>\n<h3>\u7d50\u8ad6\uff08\u307e\u3068\u3081\uff09<\/h3>\n<ul>\n<li><strong>\u5b89\u5b9a\u6027\u304c\u6700\u512a\u5148<\/strong>\u306a\u3089\uff1a<strong>\u30de\u30fc\u30b8\uff08Timsort\u7cfb\uff09<\/strong>\u3002<\/li>\n<li><strong>\u30e1\u30e2\u30ea\u52b9\u7387\u30fb\u6700\u60aa\u4fdd\u8a3c<\/strong>\u306a\u3089\uff1a<strong>\u30d2\u30fc\u30d7<\/strong>\u3002<\/li>\n<li><strong>\u5e73\u5747\u6027\u80fd\/\u5b9f\u6e2c\u512a\u4f4d<\/strong>\u306a\u3089\uff1a<strong>\u30af\u30a4\u30c3\u30af\uff08\u4e71\u629e\uff0b3-way \u7b49\u3067\u5f37\u5316\uff09<\/strong>\u3002<\/li>\n<li><strong>\u5c0f\u914d\u5217\/\u90e8\u5206\u6574\u5217<\/strong>\u306a\u3089\uff1a<strong>\u633f\u5165<\/strong>\u3001<strong>\u4e2d\u898f\u6a21\u3067\u5b89\u5b9a\u4e0d\u8981<\/strong>\u306a\u3089\uff1a<strong>\u30b7\u30a7\u30eb<\/strong>\u3002<br \/>\n\u3053\u306e\u5224\u65ad\u306f\u3001<strong>NIST DADS<\/strong>\u306e\u5b9a\u7fa9\u30fb\u8a08\u7b97\u91cf\u3001<strong>Princeton<\/strong>\u8b1b\u7fa9\uff0f\u5b9f\u88c5\u8cc7\u6599\u306e\u30e1\u30e2\u30ea\u30fb\u5b89\u5b9a\u6027\u30fb\u7406\u8ad6\u89e3\u6790\u306b\u88cf\u3065\u3051\u3089\u308c\u305f\u3001\u5b9f\u52d9\u306b\u76f4\u7d50\u3059\u308b\u9078\u3073\u5206\u3051\u3067\u3059\u3002<\/li>\n<\/ul>\n<h3>3-4. \u6700\u60aa\u8a08\u7b97\u91cf\u306e\u56de\u907f\u7b56\uff08\u30e9\u30f3\u30c0\u30e0\u5316\/\u4e2d\u592e\u5024-of-three \u7b49\uff09<\/h3>\n<h3>\u6700\u60aa\u8a08\u7b97\u91cf\u306e\u56de\u907f\u7b56\uff08\u30e9\u30f3\u30c0\u30e0\u5316 \/ \u4e2d\u592e\u5024-of-three \u7b49\uff09<\/h3>\n<h3>\u7d50\u8ad6<\/h3>\n<p>\u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8\u306e<strong>\u6700\u60aa \u0398(n\u00b2)<\/strong> \u3092\u907f\u3051\u308b\u5b9f\u52d9\u7684\u30bb\u30c3\u30c8\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002<\/p>\n<ol>\n<li><strong>\u4e71\u629e\u30d4\u30dc\u30c3\u30c8<\/strong>\u3067\u671f\u5f85 <strong>O(n log n)<\/strong> \u3092\u4fdd\u8a3c\uff08\u3069\u3093\u306a\u5165\u529b\u3067\u3082\u300c\u5e73\u5747\u300d\u52a3\u5316\u3092\u9632\u3050\uff09<\/li>\n<li><strong>\u4e2d\u592e\u5024\u8fd1\u4f3c<\/strong>\uff1a<em>median-of-3<\/em>\uff08\u5fc5\u8981\u306b\u5fdc\u3058\u3066 <em>Tukey\u2019s ninther<\/em>\uff09\u3067\u504f\u308a\u5206\u5272\u3092\u6e1b\u3089\u3059<\/li>\n<li><strong>3-way \u5206\u5272<\/strong>\uff08&lt;, =, &gt;\uff09\u3067<strong>\u91cd\u8907\u30ad\u30fc<\/strong>\u7531\u6765\u306e\u9000\u5316\u3092\u56de\u907f\u3057\u3001\u5e83\u3044\u6761\u4ef6\u3067\u7dda\u5f62\u7d1a\u306b\u8fd1\u3065\u3051\u308b<\/li>\n<li><strong>Introsort<\/strong>\uff08\u6df1\u3055\u76e3\u8996\u2192Heapsort \u3078\u30d5\u30a9\u30fc\u30eb\u30d0\u30c3\u30af\uff09\u3067<strong>\u6700\u60aa\u3067\u3082 O(n log n)<\/strong> \u3092\u4fdd\u8a3c\u3059\u308b\u4fdd\u967a\u3092\u304b\u3051\u308b<\/li>\n<li>\u53c2\u8003\uff1a\u7406\u8ad6\u4e0a\u306f**Select\uff08\u4e2d\u592e\u5024\u9078\u629e\uff09**\u3067\u5e38\u306b\u826f\u3044\u30d4\u30dc\u30c3\u30c8\u3092\u9078\u3073\u3001\u6700\u60aa <strong>O(n log n)<\/strong> \u306b\u3067\u304d\u308b\u304c\u5b9f\u88c5\u30b3\u30b9\u30c8\u304c\u9ad8\u304f\u3001\u5b9f\u52d9\u3067\u306f\u4e0a\u8a18\u306e\u7d44\u5408\u305b\u304c\u4e3b\u6d41\u3002<\/li>\n<\/ol>\n<hr \/>\n<h3>\u7406\u7531\u3084\u6839\u62e0<\/h3>\n<ul>\n<li><strong>\u653f\u5e9c\u7cfb\u306e\u5b9a\u7fa9\u30fb\u8a55\u4fa1\uff08NIST\uff09<\/strong><br \/>\nNIST \u306f\u300c\u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8\u306f\u6700\u60aa \u0398(n\u00b2) \u3060\u304c\u3001\u901a\u5e38\u306f O(n log n)\u300d\u300cSelect \u3092\u4f7f\u3048\u3070\u6700\u60aa <strong>O(n log n)<\/strong> \u306e\u5909\u7a2e\u3082\u53ef\u80fd\u300d\u300c\u30e1\u30e2\u30ea\u30a2\u30af\u30bb\u30b9\u3092\u6e1b\u3089\u3059\u65b0\u7a2e\uff08Dual-Pivot\uff09\u306f\u5b9f\u7528\u3067\u901f\u3044\u300d\u3068\u6574\u7406\u3002\u6700\u60aa\u56de\u907f\u306b<strong>\u30d4\u30dc\u30c3\u30c8\u6226\u7565<\/strong>\u3084<strong>\u6d3e\u751f\u624b\u6cd5<\/strong>\u304c\u91cd\u8981\u3067\u3042\u308b\u3053\u3068\u3092\u793a\u3059\u4e00\u6b21\u60c5\u5831\u3067\u3059\u3002<\/li>\n<li><strong>\u4e71\u629e\u306e\u7406\u8ad6\u4fdd\u8a3c\uff08MIT OCW\uff09<\/strong><br \/>\n\u4e71\u629e\u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8\u306f<strong>\u3042\u3089\u3086\u308b\u5165\u529b\u306b\u5bfe\u3057\u3066<\/strong>\u671f\u5f85\u8a08\u7b97\u91cf <strong>O(n log n)<\/strong>\u3002\u504f\u308a\u5165\u529b\u3067\u3082\u5e73\u5747\u6319\u52d5\u3092\u5b89\u5b9a\u5316\u3067\u304d\u308b\u70b9\u304c\u516c\u5f0f\u8b1b\u7fa9\u8cc7\u6599\u3067\u8a3c\u660e\u3055\u308c\u3066\u3044\u307e\u3059\u3002<\/li>\n<li><strong>\u4e2d\u592e\u5024\u8fd1\u4f3c\u3068 3-way\uff08Princeton\uff09<\/strong><br \/>\n<em>median-of-3<\/em>\uff0f<em>ninther<\/em> \u306b\u3088\u308b<strong>\u504f\u308a\u7de9\u548c<\/strong>\u3001\u304a\u3088\u3073<strong>3-way \u5206\u5272<\/strong>\u304c\u91cd\u8907\u30ad\u30fc\u3067<strong>\u7dda\u5f62\u7d1a\u306b\u8fd1\u3065\u304f<\/strong>\u3053\u3068\u304c\u8b1b\u7fa9\u30b9\u30e9\u30a4\u30c9\u3084\u5b9f\u88c5\u8cc7\u6599\u3067\u5177\u4f53\u7684\u306b\u793a\u3055\u308c\u3066\u3044\u307e\u3059\u3002<\/li>\n<li><strong>\u5bfe\u7b56\u304c\u5fc5\u8981\u306a\u7406\u7531\uff08\u201c\u30ad\u30e9\u30fc\u5165\u529b\u201d\u306e\u5b58\u5728\uff09<\/strong><br \/>\nMcIlroy \u306e\u300c<strong>A Killer Adversary for Quicksort<\/strong>\u300d\u306f <em>median-of-3<\/em> \u3067\u3082<strong>\u610f\u56f3\u7684\u306b\u4e8c\u4e57\u6642\u9593\u3078\u8ffd\u3044\u8fbc\u3081\u308b<\/strong>\u5165\u529b\u304c\u4f5c\u308c\u308b\u3053\u3068\u3092\u793a\u3057\u3001**\u30d5\u30a9\u30fc\u30eb\u30d0\u30c3\u30af\uff08Introsort\uff09**\u306e\u5fc5\u8981\u6027\u3092\u88cf\u3065\u3051\u307e\u3059\u3002<\/li>\n<li><strong>\u30d5\u30a9\u30fc\u30eb\u30d0\u30c3\u30af\u306b\u3088\u308b\u6700\u60aa\u4fdd\u8a3c\uff08Introsort\uff09<\/strong><br \/>\nMusser \u306e Introsort \u306f<strong>\u518d\u5e30\u306e\u6df1\u3055\u304c\u95be\u5024\u8d85\u904e<\/strong>\u3067 Heapsort \u306b\u5207\u66ff\u3048\u3066<strong>\u5e38\u306b O(n log n)<\/strong> \u3092\u4fdd\u8a3c\u3002\u8fd1\u5e74\u306e\u691c\u8a3c\u8ad6\u6587\u3084\u89e3\u8aac\u3067\u3082\u3001libstdc++ \u306a\u3069\u3067\u63a1\u7528\u3055\u308c\u3066\u3044\u308b\u4e8b\u5b9f\u304c\u793a\u3055\u308c\u3066\u3044\u307e\u3059\u3002<\/li>\n<\/ul>\n<hr \/>\n<h3>\u5b9f\u4f8b\uff08\u72b6\u6cc1\u5225\u306e\u6700\u60aa\u56de\u907f\u30ab\u30bf\u30ed\u30b0\uff09<\/h3>\n<div class=\"s_table\"><table>\n<thead>\n<tr>\n<th>\u72b6\u6cc1<\/th>\n<th>\u63a8\u5968\u7b56<\/th>\n<th>\u671f\u5f85\u3067\u304d\u308b\u52b9\u679c \/ \u88dc\u8db3<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>\u5165\u529b\u5206\u5e03\u304c\u4e0d\u660e\u30fb\u30d0\u30e9\u3064\u304d\u5927<\/td>\n<td><strong>\u4e71\u629e\u30d4\u30dc\u30c3\u30c8<\/strong><\/td>\n<td>\u3069\u3093\u306a\u5165\u529b\u3067\u3082<strong>\u671f\u5f85 O(n log n)<\/strong>\u3002\u6574\u5217\/\u9006\u9806\u7b49\u306e\u504f\u308a\u306b\u5f37\u3044\u3002<\/td>\n<\/tr>\n<tr>\n<td>\u307b\u307c\u6574\u5217\/\u9006\u9806\u3067\u504f\u308a\u3084\u3059\u3044<\/td>\n<td><strong>median-of-3<\/strong>\uff08\u5fc5\u8981\u306a\u3089 <strong>ninther<\/strong>\uff09<\/td>\n<td>\u5206\u5272\u306e\u504f\u308a\u3092\u7de9\u548c\u3001\u4e8c\u4e57\u843d\u3061\u306e\u983b\u5ea6\u3092\u4f4e\u6e1b\u3002\u53ef\u8996\u5316\u30fb\u5b9f\u88c5\u4f8b\u304c\u8c4a\u5bcc\u3002<\/td>\n<\/tr>\n<tr>\n<td>\u91cd\u8907\u30ad\u30fc\u304c\u591a\u3044<\/td>\n<td><strong>3-way \u5206\u5272<\/strong><\/td>\n<td>\u201c=\u9818\u57df\u201d\u3092\u307e\u3068\u3081\u3001\u6bd4\u8f03\u3068\u518d\u5e30\u3092\u524a\u6e1b\u3002<strong>\u5e83\u7bc4\u306b\u7dda\u5f62\u7d1a<\/strong>\u3078\u8fd1\u3065\u304f\u3002<\/td>\n<\/tr>\n<tr>\n<td>\u60aa\u610f\u3042\u308b\u5165\u529b\u30fb\u6700\u60aa\u4fdd\u8a3c\u304c\u5fc5\u9808<\/td>\n<td><strong>Introsort<\/strong>\uff08\u6df1\u3055\u76e3\u8996\u2192Heapsort\uff09<\/td>\n<td><strong>\u4e0a\u9650 O(n log n)<\/strong> \u3092\u7406\u8ad6\u4fdd\u8a3c\u3002\u6a19\u6e96\u30e9\u30a4\u30d6\u30e9\u30ea\u5b9f\u88c5\u306b\u3082\u63a1\u7528\u3002<\/td>\n<\/tr>\n<tr>\n<td>\u7406\u8ad6\u4e0a\u306e\u6700\u60aa\u4fdd\u8a3c\u3092\u5358\u4f53\u3067\u9054\u6210<\/td>\n<td><strong>Select<\/strong>\u3067\u5e38\u306b\u826f\u3044\u30d4\u30dc\u30c3\u30c8<\/td>\n<td>\u5e38\u306b <strong>O(n log n)<\/strong> \u304c\u53ef\u80fd\u3060\u304c\u3001\u5b9f\u52d9\u3067\u306f\u30b3\u30b9\u30c8\u304c\u9ad8\u304f\u4e3b\u6d41\u3067\u306f\u306a\u3044\u3002<\/td>\n<\/tr>\n<\/tbody>\n<\/table><\/div>\n<blockquote><p>\u53c2\u8003\uff1aMcIlroy \u306e\u201c\u30ad\u30e9\u30fc\u5165\u529b\u201d\u306f\u3001<em>median-of-3<\/em> \u3067\u3082\u4e8c\u4e57\u3078\u8a98\u5c0e\u3067\u304d\u308b\u5177\u4f53\u4f8b\u3092\u793a\u3059\u2014<strong>\u4e71\u629e<\/strong>\u3084<strong>Introsort<\/strong>\u3092**\u201c\u30bb\u30c3\u30c8\u201d**\u3067\u7528\u3044\u308b\u52d5\u6a5f\u306b\u306a\u308a\u307e\u3059\u3002<\/p><\/blockquote>\n<hr \/>\n<h3>\u7d50\u8ad6\uff08\u307e\u3068\u3081\uff09<\/h3>\n<ul>\n<li><strong>\u5358\u767a\u306e\u30c6\u30af\u30cb\u30c3\u30af\u3067\u306f\u306a\u304f\u300c\u7d44\u5408\u305b\u300d\u3067\u5b88\u308b<\/strong>\u306e\u304c\u73fe\u5b9f\u89e3\u3002<br \/>\n<strong>\u4e71\u629e<\/strong>\u3067\u5e73\u5747\u6319\u52d5\u3092\u4fdd\u8a3c\u3057\u3001<strong>median-of-3 \/ ninther<\/strong>\u3067\u504f\u308a\u3092\u6291\u3048\u3001<strong>\u91cd\u8907\u306f 3-way<\/strong>\u3067\u6f70\u3057\u3001\u6700\u5f8c\u306f<strong>Introsort<\/strong>\u3067<strong>\u6700\u60aa O(n log n)<\/strong> \u3092\u4fdd\u8a3c\u3002<\/li>\n<li><strong>\u516c\u7684\u30fb\u5927\u5b66\u30bd\u30fc\u30b9\u306e\u88cf\u3065\u3051<\/strong>\uff1aNIST\uff08\u6700\u60aa \u0398(n\u00b2) \u3068\u5bfe\u7b56\u306e\u4f4d\u7f6e\u3065\u3051\uff09\u3001MIT\uff08\u4e71\u629e\u306e\u671f\u5f85 O(n log n) \u8a3c\u660e\uff09\u3001Princeton\uff08\u4e2d\u592e\u5024\u8fd1\u4f3c\u30fb3-way \u306e\u52b9\u679c\uff09\u3001Musser\uff08Introsort \u306e\u6700\u60aa\u4fdd\u8a3c\uff09\u3002\u3053\u308c\u3089\u3092\u6e80\u305f\u3059\u8a2d\u8a08\u304c\u3001\u5b9f\u52d9\u3067\u201c\u4e8c\u4e57\u843d\u3061\u201d\u3092\u73fe\u5b9f\u7684\u306b\u9632\u3050\u6700\u77ed\u30eb\u30fc\u30c8\u3067\u3059\u3002<\/li>\n<\/ul>\n<p>\u5fc5\u8981\u3067\u3042\u308c\u3070\u3001\u3042\u306a\u305f\u306e\u30c7\u30fc\u30bf\u7279\u6027\uff08\u30b5\u30a4\u30ba\u3001\u91cd\u8907\u7387\u3001\u6574\u5217\u5ea6\u3001\u4fe1\u983c\u3067\u304d\u308b\/\u3067\u304d\u306a\u3044\u5165\u529b\uff09\u306b\u5408\u308f\u305b\u305f<strong>\u4e71\u629e+3-way+Introsort<\/strong>\u306e\u5b9f\u88c5\u30c6\u30f3\u30d7\u30ec\u3068\u95be\u5024\uff08\u4f8b\uff1a<code>maxDepth = 2*floor(log2(n))<\/code>\u3001\u5c0f\u533a\u9593\u30ab\u30c3\u30c8\u30aa\u30d5\uff09\u3082\u7528\u610f\u3057\u307e\u3059\u3002<\/p>\n<h2>\u307e\u3068\u3081<\/h2>\n<h3>\u8981\u70b9\u306e\u6574\u7406\uff08\u4f7f\u3044\u3069\u3053\u308d\/\u6bd4\u8f03\uff09<\/h3>\n<h2>\u8981\u70b9\u306e\u6574\u7406\uff08\u4f7f\u3044\u3069\u3053\u308d\/\u6bd4\u8f03\uff09<\/h2>\n<h3>\u7d50\u8ad6<\/h3>\n<p>\u8981\u4ef6\u306f\u300c\u5b89\u5b9a\u6027\u300d\u300c\u30e1\u30e2\u30ea\u4e88\u7b97\u300d\u300c\u6700\u60aa\u6642\u306e\u4fdd\u8a3c\u300d\u300c\u30c7\u30fc\u30bf\u7279\u6027\uff08\u91cd\u8907\u30fb\u4e8b\u524d\u6574\u5217\u5ea6\uff09\u300d\u300c\u8a00\u8a9e\u6a19\u6e96\u306e\u5b9f\u88c5\u300d\u306e5\u8ef8\u3067\u5207\u308a\u5206\u3051\u308b\u306e\u304c\u6700\u77ed\u3067\u3059\u3002\u5b9f\u52d9\u3067\u306f<\/p>\n<ul>\n<li><strong>\u5e73\u5747\u6027\u80fd\u91cd\u8996<\/strong>\uff1d<strong>\u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8<\/strong>\uff08\u4e71\u629e\uff0b3-way \u306a\u3069\uff09<\/li>\n<li><strong>\u5b89\u5b9a\u6027\u5fc5\u9808<\/strong>\uff1d<strong>\u30de\u30fc\u30b8\/Timsort<\/strong><\/li>\n<li><strong>\u30e1\u30e2\u30ea\u6700\u5c0f\uff06\u6700\u60aa\u4fdd\u8a3c<\/strong>\uff1d<strong>\u30d2\u30fc\u30d7\u30bd\u30fc\u30c8<\/strong><\/li>\n<li><strong>\u5c0f\u914d\u5217\/\u307b\u307c\u6574\u5217<\/strong>\uff1d<strong>\u633f\u5165\u30bd\u30fc\u30c8 or Timsort<\/strong><br \/>\n\u3092\u57fa\u672c\u6307\u91dd\u306b\u3059\u308c\u3070\u5916\u3057\u306b\u304f\u3044\u3067\u3059\u3002NIST\u30fbMIT\u30fbPrinceton\u30fb\u516c\u5f0f\u30c9\u30ad\u30e5\u30e1\u30f3\u30c8\u304c\u3053\u306e\u9078\u3073\u5206\u3051\u3092\u88cf\u3065\u3051\u3066\u3044\u307e\u3059\u3002<\/li>\n<\/ul>\n<hr \/>\n<h3>\u7406\u7531\u3084\u6839\u62e0<\/h3>\n<ul>\n<li><strong>\u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8<\/strong>\u306f\u901a\u5e38<strong>O(n log n)<\/strong>\u3001\u6700\u60aa<strong>\u0398(n\u00b2)<\/strong>\u3002\u4e71\u629e\u3067<strong>\u5168\u5165\u529b\u306b\u5bfe\u3057\u671f\u5f85O(n log n)<\/strong> \u3092\u4fdd\u8a3c\u3067\u304d\u30013-way\u5206\u5272\u306f\u91cd\u8907\u304c\u591a\u3044\u3068<strong>\u7dda\u5f62\u7d1a<\/strong>\u306b\u8fd1\u3065\u304f\u305f\u3081\u73fe\u5834\u3067\u901f\u3044\u5834\u9762\u304c\u591a\u3044\u3002NIST\u306f\u5b9f\u52d9\u3067\u306e\u512a\u4f4d\u6027\u3084\u30c7\u30e5\u30a2\u30eb\u30d4\u30dc\u30c3\u30c8\uff08\u30e1\u30e2\u30ea\u30a2\u30af\u30bb\u30b9\u6e1b\uff09\u306b\u3082\u8a00\u53ca\u3002<\/li>\n<li><strong>\u30de\u30fc\u30b8\u30bd\u30fc\u30c8<\/strong>\u306f<strong>\u5b89\u5b9a\u30fb\u0398(n log n)<\/strong> \u3060\u304c<strong>\u914d\u5217\u7248\u306f\u88dc\u52a9\u914d\u5217N<\/strong>\u304c\u5fc5\u8981\uff08\uff1d\u30e1\u30e2\u30ea\u591a\u3081\uff09\u3002Princeton\u306e\u8b1b\u7fa9\u8cc7\u6599\u306f\u300caux\u914d\u5217\u304c\u9577\u3055N\u5fc5\u8981\u300d\u3068\u660e\u793a\u3002<\/li>\n<li><strong>Timsort<\/strong>\uff08Python\u6a19\u6e96\u30fbJava\u306e\u53c2\u7167\u578b\u3067\u7cfb\u7d71\u63a1\u7528\uff09\u306f<strong>\u5b89\u5b9a<\/strong>\u3067\u3001<strong>\u65e2\u5b58\u306e\u6574\u5217\u5ea6\u3092\u6d3b\u7528<\/strong>\u3057\u3066\u5b9f\u7528\u4e0a\u3068\u3066\u3082\u5f37\u3044\uff08\u90e8\u5206\u6574\u5217\u30c7\u30fc\u30bf\u306b\u6700\u9069\uff09\u3002<\/li>\n<li><strong>\u30d2\u30fc\u30d7\u30bd\u30fc\u30c8<\/strong>\u306f<strong>O(1)\u88dc\u52a9\u30e1\u30e2\u30ea<\/strong>\u3067<strong>\u6700\u60aaO(n log n)<\/strong> \u3092\u4fdd\u8a3c\u3059\u308b\u30a4\u30f3\u30d7\u30ec\u30fc\u30b9\u6bd4\u8f03\u30bd\u30fc\u30c8\u3002\u5b89\u5b9a\u3067\u306f\u306a\u3044\u304c\u3001\u30e1\u30e2\u30ea\u5236\u7d04\u3084\u30ef\u30fc\u30b9\u30c8\u4fdd\u8a3c\u304c\u5fc5\u8981\u306a\u5834\u9762\u3067\u6709\u52b9\u3002<\/li>\n<li><strong>\u8a00\u8a9e\u6a19\u6e96\u306e\u5b9f\u88c5<\/strong>\uff1aJava \u306e <code>Arrays.sort<\/code> \u306f<strong>\u30d7\u30ea\u30df\u30c6\u30a3\u30d6\u914d\u5217\u306b\u30c7\u30e5\u30a2\u30eb\u30d4\u30dc\u30c3\u30c8QS<\/strong>\u3001<strong>Object[] \u306f\u5b89\u5b9a\u30bd\u30fc\u30c8<\/strong>\uff08\u5b9f\u88c5\u306f\u5b89\u5b9a\u3067\u3042\u308b\u3053\u3068\u304c\u4ed5\u69d8\u8981\u4ef6\uff09\u3002Python \u306e <code>list.sort<\/code>\/<code>sorted<\/code> \u306f<strong>Timsort\uff08\u5b89\u5b9a\uff09<\/strong>\u3002\u9078\u5b9a\u6642\u306f\u201c\u65e2\u5b9a\u306e\u7279\u6027\u201d\u3092\u524d\u63d0\u306b\u3059\u308b\u306e\u304c\u5b89\u5168\u3067\u3059\u3002<\/li>\n<\/ul>\n<hr \/>\n<h3>\u5b9f\u4f8b\uff08\u4f7f\u3044\u3069\u3053\u308d\u30de\u30c8\u30ea\u30af\u30b9\uff09<\/h3>\n<div class=\"s_table\"><table>\n<thead>\n<tr>\n<th>\u8981\u4ef6\/\u72b6\u6cc1<\/th>\n<th>\u63a8\u5968<\/th>\n<th>\u6839\u62e0\u30fb\u306d\u3089\u3044<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td><strong>\u5e73\u5747\u901f\u5ea6\u304c\u6700\u91cd\u8981<\/strong>\uff08\u4e00\u822c\u7684\u306a\u5927\u898f\u6a21\u914d\u5217\uff09<\/td>\n<td><strong>\u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8<\/strong>\uff08\u4e71\u629e\uff0b3-way\uff09<\/td>\n<td>\u671f\u5f85 <strong>O(n log n)<\/strong>\u3002\u91cd\u8907\u304c\u591a\u3044\u30683-way\u3067<strong>\u7dda\u5f62\u7d1a\u306b\u8fd1\u3065\u304f<\/strong>\u2192\u5b9f\u6e2c\u3067\u901f\u3044\u3053\u3068\u304c\u591a\u3044\u3002<\/td>\n<\/tr>\n<tr>\n<td><strong>\u5b89\u5b9a\u6027\u304c\u5fc5\u9808<\/strong>\uff08\u8907\u6570\u30ad\u30fc\u306e\u6bb5\u968e\u30bd\u30fc\u30c8\u7b49\uff09<\/td>\n<td><strong>\u30de\u30fc\u30b8\/Timsort<\/strong><\/td>\n<td>\u30de\u30fc\u30b8\u306f\u5b89\u5b9a\u3067 <strong>\u0398(n log n)<\/strong>\u3002Timsort\u306f<strong>\u5b89\u5b9a<\/strong>\u304b\u3064<strong>\u65e2\u5b58\u306e\u6574\u5217\u5ea6\u6d3b\u7528<\/strong>\u306b\u5f37\u3044\u3002<\/td>\n<\/tr>\n<tr>\n<td><strong>\u30e1\u30e2\u30ea\u3092\u6975\u5c0f\u306b<\/strong>\u3001\u304b\u3064<strong>\u6700\u60aa\u4fdd\u8a3c<\/strong>\u304c\u6b32\u3057\u3044<\/td>\n<td><strong>\u30d2\u30fc\u30d7\u30bd\u30fc\u30c8<\/strong><\/td>\n<td><strong>O(1)\u88dc\u52a9\u30e1\u30e2\u30ea<\/strong>\u3067<strong>\u6700\u60aaO(n log n)<\/strong>\u3002\u30a4\u30f3\u30d7\u30ec\u30fc\u30b9\u52d5\u4f5c\u3002<\/td>\n<\/tr>\n<tr>\n<td><strong>\u91cd\u8907\u30ad\u30fc\u304c\u975e\u5e38\u306b\u591a\u3044<\/strong><\/td>\n<td><strong>\u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8\uff083-way\uff09<\/strong><\/td>\n<td>3-way\u306f\u91cd\u8907\u3092\u201c=\u9818\u57df\u201d\u306b\u96c6\u7d04\u3057\u3001\u6bd4\u8f03\u30fb\u518d\u5e30\u3092\u524a\u6e1b\u3002<\/td>\n<\/tr>\n<tr>\n<td><strong>\u90e8\u5206\u7684\u306b\u6574\u5217\u6e08\u307f\/\u5c0f\u914d\u5217\u304c\u591a\u3044<\/strong><\/td>\n<td><strong>\u633f\u5165\u30bd\u30fc\u30c8 or Timsort<\/strong><\/td>\n<td>Timsort\u306f\u65e2\u5b58\u30e9\u30f3\uff08\u9023\u7d9a\u6574\u5217\u533a\u9593\uff09\u3092\u6d3b\u304b\u305b\u308b\u3002\u633f\u5165\u306f\u5c0f\u533a\u9593\u3067\u9ad8\u901f\u3002<\/td>\n<\/tr>\n<tr>\n<td><strong>Java \u6a19\u6e96\u306b\u5408\u308f\u305b\u305f\u3044<\/strong><\/td>\n<td><strong>\u30d7\u30ea\u30df\u30c6\u30a3\u30d6\uff1dDual-Pivot QS<\/strong>\uff0f<strong>Object[]=\u5b89\u5b9a<\/strong><\/td>\n<td>Oracle\u516c\u5f0f\u306e\u5b9f\u88c5\u30ce\u30fc\u30c8\u3069\u304a\u308a\u3002\u8a2d\u8a08\u306e\u524d\u63d0\u306b\u3002<\/td>\n<\/tr>\n<\/tbody>\n<\/table><\/div>\n<hr \/>\n<h3>\u88dc\u52a9\u306e\u6bd4\u8f03\u8868\uff08\u4e3b\u8981\u30dd\u30a4\u30f3\u30c8\u3060\u3051\uff09<\/h3>\n<div class=\"s_table\"><table>\n<thead>\n<tr>\n<th>\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0<\/th>\n<th>\u5e73\u5747<\/th>\n<th>\u6700\u60aa<\/th>\n<th>\u5b89\u5b9a<\/th>\n<th>\u8ffd\u52a0\u30e1\u30e2\u30ea<\/th>\n<th>\u5099\u8003<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>\u30af\u30a4\u30c3\u30af\uff08\u4e71\u629e\/3-way\uff09<\/td>\n<td>O(n log n)<\/td>\n<td>\u0398(n\u00b2)<\/td>\n<td>\u3075\u3064\u3046\u4e0d\u5b89\u5b9a<\/td>\n<td>\u5c0f\uff08\u30b9\u30bf\u30c3\u30af\u4e2d\u5fc3\uff09<\/td>\n<td>3-way\u3067\u91cd\u8907\u306b\u5f37\u3044\u3001\u4e71\u629e\u3067\u671f\u5f85\u6027\u80fd\u4fdd\u8a3c\u3002<\/td>\n<\/tr>\n<tr>\n<td>\u30de\u30fc\u30b8<\/td>\n<td>\u0398(n log n)<\/td>\n<td>\u0398(n log n)<\/td>\n<td><strong>\u5b89\u5b9a<\/strong><\/td>\n<td><strong>O(n)<\/strong><\/td>\n<td>\u914d\u5217\u7248\u306f\u88dc\u52a9\u914d\u5217N\u304c\u5fc5\u8981\u3002<\/td>\n<\/tr>\n<tr>\n<td>\u30d2\u30fc\u30d7<\/td>\n<td>O(n log n)<\/td>\n<td>O(n log n)<\/td>\n<td>\u4e0d\u5b89\u5b9a<\/td>\n<td><strong>O(1)<\/strong><\/td>\n<td>\u30a4\u30f3\u30d7\u30ec\u30fc\u30b9\u30fb\u6700\u60aa\u4fdd\u8a3c\u3002<\/td>\n<\/tr>\n<tr>\n<td>Timsort<\/td>\n<td>\u0398(n log n)\uff08\u826f\u30c7\u30fc\u30bf\u3067\u3088\u308a\u901f\u3044\uff09<\/td>\n<td>\u0398(n log n)<\/td>\n<td><strong>\u5b89\u5b9a<\/strong><\/td>\n<td>\u53ef\u5909<\/td>\n<td>Python\u6a19\u6e96\u3002\u65e2\u5b58\u306e\u6574\u5217\u5ea6\u3092\u6d3b\u7528\u3002<\/td>\n<\/tr>\n<\/tbody>\n<\/table><\/div>\n<hr \/>\n<h3>\u7d50\u8ad6\uff08\u307e\u3068\u3081\uff09<\/h3>\n<ul>\n<li><strong>\u8ff7\u3063\u305f\u3089<\/strong>\uff1a\u4e00\u822c\u7528\u9014\u306f<strong>\u30af\u30a4\u30c3\u30af<\/strong>\u3001<strong>\u5b89\u5b9a\u6027\u304c\u5fc5\u8981\u306a\u3089\u30de\u30fc\u30b8\/Timsort<\/strong>\u3001<strong>\u30e1\u30e2\u30ea\u3084\u6700\u60aa\u4fdd\u8a3c\u306a\u3089\u30d2\u30fc\u30d7<\/strong>\u3002\u3053\u306e\u4e09\u629e\u304c\u57fa\u672c\u7dda\u3002<\/li>\n<li><strong>\u74b0\u5883\u524d\u63d0\u3082\u6d3b\u7528<\/strong>\uff1a<strong>Python \u306f Timsort\uff08\u5b89\u5b9a\uff09<\/strong>\u3001<strong>Java \u306f\u30d7\u30ea\u30df\u30c6\u30a3\u30d6=Dual-Pivot QS\uff0fObject[]=\u5b89\u5b9a<\/strong>\u3002\u30d7\u30e9\u30c3\u30c8\u30d5\u30a9\u30fc\u30e0\u306e\u65e2\u5b9a\u6319\u52d5\u306b\u5408\u308f\u305b\u308b\u3068\u5b9f\u88c5\u304c\u30b7\u30f3\u30d7\u30eb\u3067\u3001\u5b89\u5168\u3067\u3059\u3002<\/li>\n<li><strong>\u30c7\u30fc\u30bf\u7279\u6027\u3067\u5fae\u8abf\u6574<\/strong>\uff1a\u91cd\u8907\u304c\u591a\u3044\u306a\u3089<strong>3-way QS<\/strong>\u3001\u90e8\u5206\u6574\u5217\u306a\u3089<strong>Timsort<\/strong>\u306e\u5f97\u610f\u9818\u57df\u3002\u8981\u4ef6\u00d7\u30c7\u30fc\u30bf\u00d7\u65e2\u5b9a\u5b9f\u88c5\u306e\u4ea4\u70b9\u3067\u6c7a\u3081\u308b\u3068\u3001\u6700\u77ed\u3067\u201c\u901f\u304f\u3066\u58ca\u308c\u306a\u3044\u201d\u9078\u629e\u306b\u306a\u308a\u307e\u3059\u3002<\/li>\n<\/ul>\n<p>\u5fc5\u8981\u306a\u3089\u3001\u3042\u306a\u305f\u306e\u30c7\u30fc\u30bf\u898f\u6a21\u30fb\u91cd\u8907\u7387\u30fb\u30e1\u30e2\u30ea\u4e88\u7b97\uff08\u4f8b\uff1a\u30aa\u30f3\u30e1\u30e2\u30ea\u3007GB\uff09\u3092\u524d\u63d0\u306b\u3001\u5177\u4f53\u7684\u306a\u5b9f\u88c5\u30b9\u30b1\u30eb\u30c8\u30f3\uff08Python\/Java\uff09\u3068\u30d9\u30f3\u30c1\u30de\u30fc\u30af\u8a08\u753b\u307e\u3067\u843d\u3068\u3057\u8fbc\u307f\u307e\u3059\u3002<\/p>\n<p><script async src=\"https:\/\/pagead2.googlesyndication.com\/pagead\/js\/adsbygoogle.js?client=ca-pub-5641494373062258\" crossorigin=\"anonymous\"><\/script><br \/>\n<!-- \u8a18\u4e8b\u5185\u5e83\u544a\u30b9\u30af\u30a8\u30a2 --><br \/>\n<ins class=\"adsbygoogle\" style=\"display: block;\" data-ad-client=\"ca-pub-5641494373062258\" data-ad-slot=\"6864483099\" data-ad-format=\"auto\" data-full-width-responsive=\"true\"><\/ins><br \/>\n<script>\n     (adsbygoogle = window.adsbygoogle || []).push({});\n<\/script><\/p>\n","protected":false},"excerpt":{"rendered":"1. \u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8\u306e\u6982\u8981\uff08\u5b9a\u7fa9\u30fb\u4ed5\u7d44\u307f\uff09 1-1. \u5206\u5272\u7d71\u6cbb\u6cd5\u306e\u8003\u3048\u65b9\u3068\u76f4\u611f\u7684\u7406\u89e3 \u5206\u5272\u7d71\u6cbb\u6cd5\u306e\u8003\u3048\u65b9\u3068\u76f4\u611f\u7684\u7406\u89e3 \u7d50\u8ad6 \u5206\u5272\u7d71\u6cbb\u6cd5\uff08Divide &amp; Conquer\uff09\u306f\u3001\u554f\u984c\u3092\u5c0f\u3055\u304f\u5206\u5272\u2192\u5404\u5c0f\u554f\u984c\u3092\u72ec\u7acb\u306b\u89e3\u304f [&hellip;]","protected":false},"author":1,"featured_media":340,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[],"class_list":["post-339","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-3"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.iso-g.com\/index.php\/wp-json\/wp\/v2\/posts\/339","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.iso-g.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.iso-g.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.iso-g.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.iso-g.com\/index.php\/wp-json\/wp\/v2\/comments?post=339"}],"version-history":[{"count":3,"href":"https:\/\/www.iso-g.com\/index.php\/wp-json\/wp\/v2\/posts\/339\/revisions"}],"predecessor-version":[{"id":742,"href":"https:\/\/www.iso-g.com\/index.php\/wp-json\/wp\/v2\/posts\/339\/revisions\/742"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.iso-g.com\/index.php\/wp-json\/wp\/v2\/media\/340"}],"wp:attachment":[{"href":"https:\/\/www.iso-g.com\/index.php\/wp-json\/wp\/v2\/media?parent=339"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.iso-g.com\/index.php\/wp-json\/wp\/v2\/categories?post=339"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.iso-g.com\/index.php\/wp-json\/wp\/v2\/tags?post=339"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}