{"id":288,"date":"2025-06-15T22:34:19","date_gmt":"2025-06-15T13:34:19","guid":{"rendered":"https:\/\/www.iso-g.com\/?p=288"},"modified":"2026-02-26T21:26:40","modified_gmt":"2026-02-26T12:26:40","slug":"5%e5%88%86%e3%81%a7%e8%85%91%e3%81%ab%e8%90%bd%e3%81%a1%e3%82%8b%e3%83%92%e3%83%bc%e3%83%97%e3%82%bd%e3%83%bc%e3%83%88%e8%ac%9b%e5%ba%a7","status":"publish","type":"post","link":"https:\/\/www.iso-g.com\/index.php\/2025\/06\/15\/5%e5%88%86%e3%81%a7%e8%85%91%e3%81%ab%e8%90%bd%e3%81%a1%e3%82%8b%e3%83%92%e3%83%bc%e3%83%97%e3%82%bd%e3%83%bc%e3%83%88%e8%ac%9b%e5%ba%a7\/","title":{"rendered":"5\u5206\u3067\u8151\u306b\u843d\u3061\u308b\u30d2\u30fc\u30d7\u30bd\u30fc\u30c8\u8b1b\u5ea7"},"content":{"rendered":"<p>\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u5c02\u9580\u66f8\u309210\u518a\u4ee5\u4e0a\u57f7\u7b46\u3057\u305f\u7b46\u8005\u304c\u3001\u60c5\u5831\u51e6\u7406\u8a66\u9a13\u306e\u51fa\u984c\u50be\u5411\u3068\u73fe\u5834\u3067\u306e\u5229\u7528\u4f8b\u3092\u8e0f\u307e\u3048\u3066\u30d2\u30fc\u30d7\u30bd\u30fc\u30c8\u3092\u5fb9\u5e95\u89e3\u8aac\u3002<\/p>\n<p>\u7406\u8ad6\u3060\u3051\u3067\u306a\u304f Python\uff0fC++ \u306e\u5b9f\u88c5\u3068\u53ef\u8996\u5316\u30c4\u30fc\u30eb\u307e\u3067\u7db2\u7f85\u3057\u3001\u660e\u65e5\u304b\u3089\u306e\u30b3\u30fc\u30c7\u30a3\u30f3\u30b0\u306b\u76f4\u7d50\u3059\u308b\u5185\u5bb9\u3092\u4fdd\u8a3c\u3057\u307e\u3059\u3002<\/p>\n<p><img decoding=\"async\" class=\"alignnone size-medium wp-image-291\" src=\"https:\/\/www.iso-g.com\/wp-content\/uploads\/2025\/06\/programming-898961_640-212x300.jpg\" alt=\"\" width=\"212\" height=\"300\" srcset=\"https:\/\/www.iso-g.com\/wp-content\/uploads\/2025\/06\/programming-898961_640-212x300.jpg 212w, https:\/\/www.iso-g.com\/wp-content\/uploads\/2025\/06\/programming-898961_640.jpg 452w\" sizes=\"(max-width: 212px) 100vw, 212px\" \/><\/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<h2>1 \u30d2\u30fc\u30d7\u30bd\u30fc\u30c8\u3068\u306f\uff1f<\/h2>\n<h3>1-1 \u6982\u8981<\/h3>\n<h4>1-1-1 \u6574\u5217\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u4f4d\u7f6e\u4ed8\u3051<\/h4>\n<p>\u30d2\u30fc\u30d7\u30bd\u30fc\u30c8\u306f\u6bd4\u8f03\u30bd\u30fc\u30c8\u306e\u4e00\u7a2e\u3067\u3001<strong>\u5e38\u306b\u6700\u60aa O(n log n)<\/strong>\u30fb\u8ffd\u52a0\u30e1\u30e2\u30ea\u0398(1)\u3092\u4fdd\u8a3c\u3059\u308b\u70b9\u3067\u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8\u3084\u30de\u30fc\u30b8\u30bd\u30fc\u30c8\u3068\u4e00\u7dda\u3092\u753b\u3057\u307e\u3059\u3002<\/p>\n<p>\u5b9f\u884c\u901f\u5ea6\u306e\u5e73\u5747\u5024\u3067\u306f\u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8\u304c\u52dd\u308b\u3082\u306e\u306e\u3001\u6574\u5217\u6e08\u307f\u3084\u9006\u9806\u306e\u3088\u3046\u306a\u300c\u504f\u3063\u305f\u5165\u529b\u300d\u3067\u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8\u304c O(n\u00b2) \u306b\u52a3\u5316\u3059\u308b\u306e\u306b\u5bfe\u3057\u3001\u30d2\u30fc\u30d7\u30bd\u30fc\u30c8\u306f\u5165\u529b\u5206\u5e03\u306b\u5de6\u53f3\u3055\u308c\u307e\u305b\u3093\u3002<\/p>\n<p>SLA \u304c\u53b3\u3057\u3044\u91d1\u878d\u30b7\u30b9\u30c6\u30e0\u3084\u30ea\u30a2\u30eb\u30bf\u30a4\u30e0 OS \u3067\u300c\u901f\u5ea6\u3088\u308a\u78ba\u5b9a\u6027\u300d\u304c\u8a55\u4fa1\u3055\u308c\u63a1\u7528\u3055\u308c\u308b\u6240\u4ee5\u3067\u3059\u3002<\/p>\n<h4>1-1-2 \u30d2\u30fc\u30d7\u30bd\u30fc\u30c8\u306e\u8a95\u751f\u53f2<\/h4>\n<p>1964 \u5e74\u3001J. W. J. Williams \u304c CACM \u8a8c\u306b \u201cAlgorithm 232 HEAPSORT\u201d \u3092\u6295\u7a3f\u3057\u3001\u4e8c\u5206\u30d2\u30fc\u30d7\u3092\u30c7\u30fc\u30bf\u69cb\u9020\u3068\u3057\u3066\u521d\u3081\u3066\u6574\u5217\u306b\u5fdc\u7528\u3057\u307e\u3057\u305f\u3002<\/p>\n<p>\u7d9a\u3044\u3066\u540c\u5e74 Robert Floyd \u304c\u30d3\u30eb\u30c9\u30d2\u30fc\u30d7\u5de5\u7a0b\u3092 <strong>O(n)<\/strong> \u3078\u77ed\u7e2e\u3059\u308b\u6539\u826f\u3092\u767a\u8868\u3057\u3001\u73fe\u5728\u4e3b\u6d41\u306e\u5f62\u304c\u78ba\u7acb\u3057\u307e\u3057\u305f\u3002<\/p>\n<h3>1-2 \u4f7f\u7528\u5834\u9762<\/h3>\n<h4>1-2-1 \u5927\u898f\u6a21\u30c7\u30fc\u30bf\u306b\u5f37\u3044\u7406\u7531<\/h4>\n<p>\u30d2\u30fc\u30d7\u30bd\u30fc\u30c8\u306f\u300c\u30eb\u30fc\u30c8\u3068\u672b\u5c3e\u306e\u307f\u3092 swap\u300d\u3059\u308b\u5c40\u6240\u30a2\u30af\u30bb\u30b9\u3067\u9032\u3080\u305f\u3081\u30ad\u30e3\u30c3\u30b7\u30e5\u30df\u30b9\u304c\u6bd4\u8f03\u7684\u5c11\u306a\u304f\u30011,000 \u4e07\u4ef6\u898f\u6a21\u3067\u3082\u5b89\u5b9a\u3057\u3066\u8d70\u308a\u307e\u3059\u3002<\/p>\n<p>\u307e\u305f\u30a4\u30f3\u30d7\u30ec\u30fc\u30b9\u52d5\u4f5c\u3086\u3048\u30e1\u30e2\u30ea\u62e1\u5f35\u304c\u3067\u304d\u306a\u3044\u7d44\u8fbc\u307f\u6a5f\u5668\u3067\u3082\u6271\u3044\u3084\u3059\u3044\u2015\u2015\u5b9f\u969b\u306b\u7d44\u8fbc\u307f Linux \u30d9\u30f3\u30c0\u306e\u6cbb\u5177\u3067\u306f\u3001\u9006\u9806\u5165\u529b\u3067\u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8\u304c 8 \u79d2\u304b\u304b\u3063\u305f\u3068\u3053\u308d\u30d2\u30fc\u30d7\u30bd\u30fc\u30c8\u306f 5.5 \u79d2\u3067\u5b8c\u8d70\u3057\u307e\u3057\u305f\uff08\u793e\u5185\u8a08\u6e2c\uff09\u3002<\/p>\n<h4>1-2-2 \u30b9\u30c8\u30ea\u30fc\u30e0\u51e6\u7406\u3068\u306e\u76f8\u6027<\/h4>\n<p>\u30d2\u30fc\u30d7\u30bd\u30fc\u30c8\u306f\u30aa\u30d5\u30e9\u30a4\u30f3\u6574\u5217\u3067\u3059\u304c\u3001\u5185\u90e8\u3067\u4f7f\u3046\u300c\u30d2\u30fc\u30d7\u69cb\u9020\u300d\u81ea\u4f53\u304c\u30aa\u30f3\u30e9\u30a4\u30f3\u96c6\u8a08\u306e\u512a\u5148\u5ea6\u4ed8\u304d\u30ad\u30e5\u30fc\u3068\u540c\u4e00\u3067\u3059\u3002<\/p>\n<p>\u305f\u3068\u3048\u3070\u30b9\u30c8\u30ea\u30fc\u30e0\u304b\u3089\u30d9\u30b9\u30c8 k \u8981\u7d20\u3092\u7d99\u7d9a\u62bd\u51fa\u3059\u308b\u51e6\u7406\u306f min-heap \u3067 O((n+k) log n) \u306b\u53ce\u307e\u308a\u307e\u3059\u3002<\/p>\n<p>\u30d2\u30fc\u30d7\u30bd\u30fc\u30c8\u3092\u7406\u89e3\u3059\u308b\u3068\u30ea\u30a2\u30eb\u30bf\u30a4\u30e0\u5206\u6790\u57fa\u76e4\u306e\u6839\u5e79\u3082\u898b\u901a\u3057\u304c\u826f\u304f\u306a\u308a\u307e\u3059\u3002<\/p>\n<hr \/>\n<h2>2 \u30d2\u30fc\u30d7\u6728\u306e\u57fa\u790e<\/h2>\n<h3>2-1 \u5b8c\u5168\u4e8c\u5206\u6728<\/h3>\n<h4>2-1-1 \u914d\u5217\u3068\u6728\u306e\u5bfe\u5fdc\u8868<\/h4>\n<p>\u5b8c\u5168\u4e8c\u5206\u6728\u3092 0 \u59cb\u307e\u308a\u914d\u5217\u3067\u8868\u3059\u3068\u3001\u89aa <em>i<\/em> \u2192 \u5de6\u5b50 2<em>i<\/em>+1\uff0f\u53f3\u5b50 2<em>i<\/em>+2\u3001\u5b50 <em>j<\/em> \u2192 \u89aa\u230a(j\u22121)\/2\u230b \u306e\u5358\u7d14\u5f0f\u3067\u6e08\u307f\u3001\u30dd\u30a4\u30f3\u30bf\u3092\u8fbf\u3089\u305a\u306b\u30d2\u30fc\u30d7\u64cd\u4f5c\u304c O(1) \u3067\u66f8\u3051\u307e\u3059\u3002<\/p>\n<p>\u30d2\u30fc\u30d7\u6761\u4ef6\uff08\u89aa \u2265 \u5b50 or \u2264 \u5b50\uff09\u306f\u3053\u306e\u5199\u50cf\u304c\u3042\u308b\u304b\u3089\u3053\u305d\u9ad8\u901f\u306b\u4fdd\u305f\u308c\u307e\u3059\u3002<\/p>\n<h4>2-1-2 \u89aa\u5b50\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u8a08\u7b97<\/h4>\n<p>1 \u30d9\u30fc\u30b9\u7cfb\u306e\u64ec\u4f3c\u30b3\u30fc\u30c9\u3092 0 \u30d9\u30fc\u30b9\u306b\u79fb\u690d\u3059\u308b\u969b\u306f +1\/-1 \u6f14\u7b97\u306e\u6df7\u5165\u304c\u30d0\u30b0\u6e90\u3067\u3059\u3002<\/p>\n<p>IDE \u306e\u30a6\u30a9\u30c3\u30c1\u5f0f\u306b <code>left = 2*i + 1<\/code> \u3092\u767b\u9332\u3057\u5883\u754c\u5916\u30a2\u30af\u30bb\u30b9\u3092\u5373\u691c\u51fa\u3059\u308b\u7fd2\u6163\u3092\u3064\u3051\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>Stack Overflow \u3067\u3082\u300c\u914d\u5217\u8d8a\u3048 segfault\u300d\u306f\u5b9a\u756a\u8cea\u554f\u3067\u3059\u3002<\/p>\n<h3>2-2 \u6700\u5927\u30d2\u30fc\u30d7\u30fb\u6700\u5c0f\u30d2\u30fc\u30d7<\/h3>\n<h4>2-2-1 \u6027\u8cea\u6bd4\u8f03<\/h4>\n<p>\u6700\u5927\u30d2\u30fc\u30d7\u306f\u89aa \u2265 \u5b50\u3067\u6607\u9806\u30bd\u30fc\u30c8\u306b\u3001\u6700\u5c0f\u30d2\u30fc\u30d7\u306f\u89aa \u2264 \u5b50\u3067\u964d\u9806\u3084\u6700\u5c0f\u5024\u5148\u53d6\u308a\u306b\u4f7f\u308f\u308c\u307e\u3059\u3002<\/p>\n<p>\u8a08\u7b97\u91cf\u306f\u540c\u3058\u3067\u3082\u3001max-heap \u306f swap \u304c\u591a\u304f\u3001min-heap \u306f\u6bd4\u8f03\u304c\u591a\u304f\u306a\u308b\u50be\u5411\u304c\u3042\u308a\u3001CPU \u5206\u5c90\u4e88\u6e2c\u3068\u306e\u76f8\u6027\u3067\u5fae\u5dee\u304c\u51fa\u308b\u3053\u3068\u304c\u8fd1\u5e74\u5831\u544a\u3055\u308c\u3066\u3044\u307e\u3059\u3002<\/p>\n<h4>2-2-2 \u512a\u5148\u5ea6\u4ed8\u304d\u30ad\u30e5\u30fc\u3068\u306e\u95a2\u4fc2<\/h4>\n<p>Python <code>heapq<\/code>\u3001Java <code>PriorityQueue<\/code>\u3001C++ <code>std::priority_queue<\/code> \u306f\u3059\u3079\u3066\u4e8c\u5206\u30d2\u30fc\u30d7\u5b9f\u88c5\u3067 push\/pop \u304c O(log n)\u3002<\/p>\n<p>Dijkstra \u6cd5\u3084\u30ec\u30b3\u30e1\u30f3\u30c9\u306e\u30ea\u30a2\u30eb\u30bf\u30a4\u30e0\u96c6\u8a08\u3067\u6b20\u304b\u305b\u307e\u305b\u3093\u3002<\/p>\n<hr \/>\n<h2>3 \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u624b\u9806<\/h2>\n<h3>3-1 \u30d3\u30eb\u30c9\u30d2\u30fc\u30d7<\/h3>\n<h4>3-1-1 heapify \u306e\u6d41\u308c<\/h4>\n<p>Floyd \u306e\u65b9\u6cd5\u3067\u306f\u300c\u6700\u5f8c\u306e\u89aa \u230a(n\u22122)\/2\u230b \u304b\u3089 0 \u3078\u9006\u8d70\u3057 sift-down\u300d\u3092\u884c\u3044 <strong>O(n)<\/strong> \u3067\u30d2\u30fc\u30d7\u3092\u69cb\u7bc9\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\u968e\u5c64 d \u306e\u30ce\u30fc\u30c9\u6570 2\u1d48 \u3068\u4e0b\u964d\u8ddd\u96e2 (h\u2212d) \u306e\u7dcf\u548c\u304c\u7dda\u5f62\u306b\u53ce\u675f\u3059\u308b\u8a08\u7b97\u306f\u9762\u63a5\u3067\u983b\u51fa\u306a\u306e\u3067\u3001\u5fc5\u305a\u624b\u66f8\u304d\u8a3c\u660e\u3057\u3066\u304a\u304d\u307e\u3057\u3087\u3046\u3002<\/p>\n<h4>3-1-2 \u518d\u5e30\u3068\u53cd\u5fa9\u306e\u9078\u629e<\/h4>\n<p>\u518d\u5e30\u7248\u306f\u8aad\u307f\u3084\u3059\u3044\u304c\u30b9\u30bf\u30c3\u30af\u3092 log n \u30d5\u30ec\u30fc\u30e0\u6d88\u8cbb\u3001\u53cd\u5fa9\u7248\u306f while \u3067\u66f8\u3051\u308b\u304c\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u6f14\u7b97\u304c\u7169\u96d1\u3002<\/p>\n<p>C++ <code>std::make_heap<\/code> \u306f\u5f8c\u8005\u3092\u63a1\u7528\u3057\u3066\u3044\u307e\u3059\u3002\u5b66\u7fd2\u6bb5\u968e\u3067\u306f\u4e21\u65b9\u5b9f\u88c5\u3057\u3001pytest \u3084 GoogleTest \u3067\u540c\u4e00\u30b1\u30fc\u30b9\u3092\u901a\u3059\u3068\u5dee\u7570\u304c\u8151\u306b\u843d\u3061\u307e\u3059\u3002<\/p>\n<h3>3-2 \u30bd\u30fc\u30c8\u30eb\u30fc\u30d7<\/h3>\n<h4>3-2-1 \u30eb\u30fc\u30c8\u4ea4\u63db\u2192\u518d\u30d2\u30fc\u30d7\u5316<\/h4>\n<p>\u6700\u5927\u5024\u3092\u672b\u5c3e\u3078 swap\u3001\u30d2\u30fc\u30d7\u30b5\u30a4\u30ba\u3092 1 \u6e1b\u3089\u3057 sift-down\u2015\u2015\u3053\u308c\u3092 n\u22121 \u56de\u3002<\/p>\n<p>\u518d\u30d2\u30fc\u30d7\u5316\u306f\u9ad8\u3055 log m \u3067\u7d42\u308f\u308b\u305f\u3081\u5408\u8a08 <strong>O(n log n)<\/strong>\u3002\u672a\u6574\u5217\u7bc4\u56f2\u3092\u8aa4\u3063\u3066\u542b\u3081\u308b\u3068\u518d\u30d0\u30d6\u30eb\u30c0\u30a6\u30f3\u304c\u767a\u751f\u3057\u4e71\u9806\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<h4>3-2-2 \u5b8c\u4e86\u5224\u5b9a<\/h4>\n<p><code>while(heap_size&gt;1)<\/code> \u304b <code>for(end=last; end!=first; --end)<\/code> \u304c\u5b9a\u77f3\u3002<\/p>\n<p><code>&gt;=<\/code> \u3068\u66f8\u304f\u3068\u7121\u9650\u30eb\u30fc\u30d7\u3001<code>&lt;=<\/code> \u3068\u66f8\u304f\u3068\u65e9\u671f\u7d42\u4e86\u30d0\u30b0\u2015\u2015CI \u306b AddressSanitizer \u3092\u7d44\u307f\u8fbc\u3080\u3068\u4e00\u77ac\u3067\u767a\u899a\u3057\u307e\u3059\u3002<\/p>\n<hr \/>\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>4 \u8a08\u7b97\u91cf\u3068\u30e1\u30e2\u30ea\u52b9\u7387<\/h2>\n<h3>4-1 \u6642\u9593\u8a08\u7b97\u91cf<\/h3>\n<h4>4-1-1 O(n log n) \u8a3c\u660e<\/h4>\n<p>build-heap \u306e O(n) \u3068 sort-loop \u306e (n\u22121) log n \u3092\u5408\u7b97\u3057 O(n log n)\u3002<\/p>\n<p>\u30d2\u30fc\u30d7\u306f\u5165\u529b\u5206\u5e03\u3092\u9078\u3070\u305a\u6700\u60aa\u3067\u3082\u3053\u306e\u8a08\u7b97\u91cf\u306b\u5f35\u308a\u4ed8\u304f\u305f\u3081 SLA \u306e\u3042\u308b\u30b7\u30b9\u30c6\u30e0\u3067\u91cd\u5b9d\u3055\u308c\u307e\u3059\u3002<\/p>\n<h4>4-1-2 \u6700\u60aa\u30fb\u5e73\u5747\u30fb\u6700\u826f\u30b1\u30fc\u30b9<\/h4>\n<p>\u30d2\u30fc\u30d7\u30bd\u30fc\u30c8\u306f\u5e73\u5747\u3082\u6700\u826f\u3082 O(n log n) \u304b\u3089\u4e0b\u304c\u308a\u307e\u305b\u3093\u304c\u3001\u3060\u304b\u3089\u3053\u305d\u5b9f\u884c\u6642\u9593\u306e\u3070\u3089\u3064\u304d\u304c \u00b15 % \u570f\u5185\u306b\u53ce\u307e\u308a\u3001\u30ec\u30a4\u30c6\u30f3\u30b7\u4fdd\u8a3c\u304c\u5bb9\u6613\u3067\u3059\u3002<\/p>\n<h3>4-2 \u7a7a\u9593\u8a08\u7b97\u91cf<\/h3>\n<h4>4-2-1 \u30a4\u30f3\u30d7\u30ec\u30fc\u30b9\u306e\u5229\u70b9<\/h4>\n<p>\u8ffd\u52a0\u30e1\u30e2\u30ea\u306f swap \u7528\u4e00\u6642\u5909\u6570\u306e\u307f\u306e \u0398(1)\u3002\u30aa\u30f3\u30e1\u30e2\u30ea DB \u3084\u30de\u30a4\u30b3\u30f3\u3067\u3082\u9069\u7528\u53ef\u3067\u3001\u30d2\u30fc\u30d7\u69cb\u9020\u304c\u30ad\u30e3\u30c3\u30b7\u30e5\u30e9\u30a4\u30f3\u3092\u307e\u305f\u3044\u3067\u3082 \u201c\u52d5\u304f\u201d \u3053\u3068\u304c\u6700\u512a\u5148\u306e\u73fe\u5834\u3067\u63a1\u629e\u3055\u308c\u307e\u3059\u3002<\/p>\n<h4>4-2-2 \u30ad\u30e3\u30c3\u30b7\u30e5\u52b9\u7387<\/h4>\n<p>swap \u306f\u5fc5\u305a 2 \u30e9\u30a4\u30f3\u3092\u6c5a\u3059\u305f\u3081 L1\/L2 \u30df\u30b9\u7387\u304c\u9ad8\u3081\u3002\u30d2\u30fc\u30d7\u3092\u30d6\u30ed\u30c3\u30af\u5206\u5272\u3057 SIMD \u3067\u90e8\u5206\u30bd\u30fc\u30c8\u5f8c\u30de\u30fc\u30b8\u3059\u308b\u7814\u7a76\u3082\u3042\u308a\u307e\u3059\u304c\u3001\u5b9f\u88c5\u7dad\u6301\u304c\u96e3\u3057\u304f\u4e00\u822c\u958b\u767a\u3067\u306f\u63a1\u7528\u4f8b\u304c\u5c11\u306a\u3044\u306e\u304c\u73fe\u5b9f\u3067\u3059\u3002<\/p>\n<hr \/>\n<h2>5 \u5b9f\u88c5\u30ac\u30a4\u30c9<\/h2>\n<h3>5-1 Python<\/h3>\n<h4>5-1-1 \u6a19\u6e96\u30e9\u30a4\u30d6\u30e9\u30ea\u3067\u66f8\u304f<\/h4>\n<p><code>heapq.heapify<\/code> \u3067\u30ea\u30b9\u30c8\u3092 min-heap \u5316\u3057 <code>heappop<\/code> \u3092 n \u56de\u547c\u3076\u3060\u3051\u3002<\/p>\n<p>\u6700\u5927\u30d2\u30fc\u30d7\u5316\u3057\u305f\u3044\u3068\u304d\u306f\u5024\u3092 \u22121 \u500d\u3057\u3066\u5165\u308c\u308b\u30c6\u30af\u30cb\u30c3\u30af\u304c\u5e83\u304f\u4f7f\u308f\u308c\u307e\u3059\u3002<\/p>\n<h4>5-1-2 \u81ea\u524d\u5b9f\u88c5\u3067\u5b66\u3076<\/h4>\n<p>(1) heapify\u3001(2) sift-down\u3001(3) swap\u3001(4) sort-loop \u306e\uff14\u95a2\u6570\u306b\u5206\u5272\u3057 pytest \u3067\u6bb5\u968e\u7684\u306b\u30c6\u30b9\u30c8\u3059\u308b\u3068\u7406\u89e3\u304c\u7206\u901f\u3067\u6df1\u307e\u308a\u307e\u3059\u3002<\/p>\n<h3>5-2 C\/C++<\/h3>\n<h4>5-2-1 STL make_heap \u5229\u7528<\/h4>\n<p><code>std::make_heap<\/code> \u2192 <code>std::sort_heap<\/code> \u306e 2 \u884c\u3067\u5b8c\u7d50\u3002<\/p>\n<p>\u30c7\u30d5\u30a9\u30eb\u30c8\u6bd4\u8f03\u306f max-heap \u306a\u306e\u3067\u964d\u9806\u6574\u5217\u306f <code>std::greater&lt;&gt;{}<\/code> \u3092\u6e21\u3057\u3066\u53cd\u8ee2\u3055\u305b\u307e\u3059\u3002<\/p>\n<h4>5-2-2 \u30dd\u30a4\u30f3\u30bf\u64cd\u4f5c\u306e\u6ce8\u610f<\/h4>\n<p>C \u914d\u5217\u5148\u982d\u306b\u30c0\u30df\u30fc 0 \u756a\u5730\u3092\u7f6e\u304f\u64ec\u4f3c 1 \u30d9\u30fc\u30b9\u5b9f\u88c5\u306f\u5168\u30a2\u30af\u30bb\u30b9\u306b \u00b11 \u88dc\u6b63\u304c\u5165\u308a\u6700\u9069\u5316\u304c\u52b9\u304d\u307e\u305b\u3093\u3002<\/p>\n<p>0 \u30d9\u30fc\u30b9\u5f0f\uff0b\u30b3\u30e1\u30f3\u30c8\u3067 1 \u30d9\u30fc\u30b9\u63db\u7b97\u3092\u793a\u3059\u306e\u304c\u6700\u5c11\u30d0\u30b0\u30fb\u6700\u9ad8\u901f\u306e\u738b\u9053\u3067\u3059\u3002<\/p>\n<hr \/>\n<h2>6 \u53ef\u8996\u5316\u30c4\u30fc\u30eb\u6d3b\u7528<\/h2>\n<h3>6-1 GIF \u5b66\u7fd2<\/h3>\n<h4>6-1-1 \u30b9\u30c6\u30c3\u30d7\u8868\u793a<\/h4>\n<p>USFCA \u306e\u53ef\u8996\u5316\u30b5\u30a4\u30c8\u306f\u914d\u5217\u3068\u6728\u3092\u540c\u6642\u30cf\u30a4\u30e9\u30a4\u30c8\u3057\u300croot \u2194 last \u2192 sift-down\u300d\u306e\u7e70\u308a\u8fd4\u3057\u304c\u4e00\u76ee\u77ad\u7136\u3002\u8b1b\u7fa9\u3084\u81ea\u7fd2\u306b\u6700\u9069\u3067\u3059\u3002<\/p>\n<h4>6-1-2 \u9006\u518d\u751f\u3067\u7406\u89e3<\/h4>\n<p>YouTube \u6559\u80b2\u52d5\u753b\u3092 0.25\u00d7 \u901f\u5ea6\u3067\u9006\u518d\u751f\u3059\u308b\u3068\u3001\u30d2\u30fc\u30d7\u6761\u4ef6\u304c\u3069\u306e\u9806\u3067\u58ca\u308c\u30fb\u4fee\u5fa9\u3055\u308c\u308b\u304b\u304c\u76f4\u611f\u3067\u63b4\u3081\u307e\u3059\u3002<\/p>\n<h3>6-2 Web\u30b5\u30fc\u30d3\u30b9<\/h3>\n<h4>6-2-1 algorithm-visualizer<\/h4>\n<p>algorithm-visualizer \u3067\u306f\u4efb\u610f\u306e\u521d\u671f\u30d2\u30fc\u30d7\u3092\u8a2d\u5b9a\u3067\u304d\u3001\u6700\u60aa\u30b1\u30fc\u30b9\u3092\u4eba\u5de5\u751f\u6210\u3057\u3066\u6bd4\u8f03\u56de\u6570\u3092 CSV \u3067\u5f97\u3089\u308c\u307e\u3059\u3002\u7814\u7a76\u30fb\u6388\u696d\u8ab2\u984c\u306b\u3082\u6700\u9069\u3002<\/p>\n<h4>6-2-2 \u30bd\u30fc\u30c8\u30a2\u30d7\u30ea\u6bd4\u8f03<\/h4>\n<p>\u30b9\u30de\u30db\u30a2\u30d7\u30ea\u300cAlgoViz\u300d\u307b\u304b\u3067\u306f\u8907\u6570\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u4e26\u8d70\u3055\u305b swap\u30fb\u6bd4\u8f03\u56de\u6570\u3092\u30ea\u30a2\u30eb\u30bf\u30a4\u30e0\u8868\u793a\u3057\u3001\u79fb\u52d5\u4e2d\u3067\u3082\u5fa9\u7fd2\u3067\u304d\u307e\u3059\u3002<\/p>\n<hr \/>\n<h2>7 \u3088\u304f\u3042\u308b\u30a8\u30e9\u30fc<\/h2>\n<h3>7-1 \u30aa\u30d5\u30d0\u30a4\u30ef\u30f3<\/h3>\n<h4>7-1-1 \u672b\u5c3e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u8aa4\u7b97<\/h4>\n<p>\u30d2\u30fc\u30d7\u30b5\u30a4\u30ba\u3092 n \u3068\u521d\u671f\u5316\u2192heapify \u3067\u914d\u5217\u5916\u30a2\u30af\u30bb\u30b9\u3001\u306f Stack Overflow \u5e38\u9023\u306e\u4e8b\u6545\u3002<\/p>\n<p>\u5358\u4f53\u30c6\u30b9\u30c8\u306b\u6574\u5217\u6e08\u307f\u30fb\u9006\u9806\u30fb\u540c\u5024\u914d\u5217\u3092\u5fc5\u305a\u5165\u308c\u307e\u3057\u3087\u3046\u3002<\/p>\n<h4>7-1-2 heapify \u7bc4\u56f2\u5916\u53c2\u7167<\/h4>\n<p>\u5b50\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u304c heap_size \u4ee5\u4e0a\u306a\u3089 while \u30eb\u30fc\u30d7\u3092\u629c\u3051\u308b\u6761\u4ef6\u3092 <code>&gt;<\/code> \u3067\u306a\u304f <code>&gt;=<\/code> \u3068\u66f8\u3044\u3066\u7121\u9650\u30eb\u30fc\u30d7\u306f\u3042\u308b\u3042\u308b\u3002\u9759\u7684\u89e3\u6790\u3084 AddressSanitizer \u304c\u6709\u52b9\u3067\u3059\u3002<\/p>\n<h3>7-2 \u30b9\u30ef\u30c3\u30d7\u5fd8\u308c<\/h3>\n<h4>7-2-1 \u5178\u578b\u30d0\u30b0\u4f8b<\/h4>\n<p>\u201cheap sort doesn\u2019t work\u201d \u6295\u7a3f\u306e\u5927\u534a\u306f sift-down \u5185\u306e swap \u6f0f\u308c\u3002<\/p>\n<p>\u30c7\u30d0\u30c3\u30ac\u3067\u30eb\u30fc\u30c8\u3068\u5b50\u306e\u5024\u3092\u30a6\u30aa\u30c3\u30c1\u3059\u308b\u3068\u5373\u7279\u5b9a\u3067\u304d\u307e\u3059\u3002<\/p>\n<h4>7-2-2 \u30c7\u30d0\u30c3\u30b0\u624b\u6cd5<\/h4>\n<p>(1) \u914d\u5217\u3068\u6728\u3092\u540c\u6642\u30d7\u30ea\u30f3\u30c8\u3001(2) \u4ea4\u63db\u524d\u5f8c\u30ed\u30b0\u3001(3) \u30df\u30cb\u5165\u529b 3\u301c4 \u8981\u7d20\u3092\u7528\u610f\u2015\u2015\u6bb5\u968e\u7684\u306b\u30d0\u30b0\u3092\u8ffd\u3044\u8fbc\u3080\u3068\u4fee\u6b63\u304c\u6700\u77ed\u3067\u3059\u3002<\/p>\n<hr \/>\n<h2>8 \u4ed6\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u6bd4\u8f03<\/h2>\n<h3>8-1 \u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8<\/h3>\n<h4>8-1-1 \u5e73\u5747\u901f\u5ea6\u6bd4\u8f03<\/h4>\n<p>Baeldung \u306e\u5b9f\u6e2c\u3067\u306f\u30e9\u30f3\u30c0\u30e0\u5165\u529b\u3067\u30af\u30a4\u30c3\u30af 1.0 \u79d2\u30fb\u30d2\u30fc\u30d7 1.4 \u79d2\u3001\u9006\u9806\u3067\u306f\u30af\u30a4\u30c3\u30af 4.8 \u79d2\u30fb\u30d2\u30fc\u30d7 1.5 \u79d2\u3067\u9006\u8ee2\u3057\u307e\u3057\u305f\u3002<\/p>\n<h4>8-1-2 \u30b9\u30bf\u30c3\u30af\u30aa\u30fc\u30d0\u30d5\u30ed\u30fc\u5dee<\/h4>\n<p>\u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8\u306e\u518d\u5e30\u306f\u6700\u60aa n \u6df1\u5ea6\u3067\u30b9\u30bf\u30c3\u30af\u30aa\u30fc\u30d0\u30d5\u30ed\u30fc\u306e\u5371\u967a\u3002<\/p>\n<p>\u30a4\u30f3\u30c8\u30ed\u30bd\u30fc\u30c8\u3084\u30d2\u30fc\u30d7\u30bd\u30fc\u30c8\u3078\u306e\u30d5\u30a9\u30fc\u30eb\u30d0\u30c3\u30af\u6226\u7565\u304c\u3053\u3053\u3067\u52b9\u304d\u307e\u3059\u3002<\/p>\n<h3>8-2 \u30a4\u30f3\u30c8\u30ed\u30bd\u30fc\u30c8<\/h3>\n<h4>8-2-1 \u30cf\u30a4\u30d6\u30ea\u30c3\u30c9\u6226\u7565<\/h4>\n<p>\u30a4\u30f3\u30c8\u30ed\u30bd\u30fc\u30c8\u306f\u518d\u5e30\u6df1\u5ea6\u304c 2 log\u2082 n \u3092\u8d85\u3048\u308b\u3068\u30d2\u30fc\u30d7\u30bd\u30fc\u30c8\u306b\u5207\u308a\u66ff\u3048\u3001\u5e73\u5747\u901f\u3068\u6700\u60aa\u4fdd\u8a3c\u306e\u4e21\u53d6\u308a\u3092\u5b9f\u73fe\u3002<\/p>\n<p>C++ <code>std::sort<\/code> \u304c\u63a1\u7528\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n<h4>8-2-2 \u5b9f\u88c5\u4f8b\u306b\u898b\u308b\u5229\u70b9<\/h4>\n<p>V8 JavaScript \u30a8\u30f3\u30b8\u30f3\u306a\u3069\u4e3b\u8981\u30e9\u30f3\u30bf\u30a4\u30e0\u304c\u30a4\u30f3\u30c8\u30ed\u30bd\u30fc\u30c8\u7cfb\u3092\u4f7f\u3044\u3001\u60aa\u5165\u529b\u3067\u30d2\u30fc\u30d7\u30bd\u30fc\u30c8\u5206\u5c90\u3059\u308b\u3053\u3068\u3067\u30d6\u30e9\u30a6\u30b6\u8868\u793a\u306e\u6700\u60aa\u9045\u5ef6\u3092\u6291\u3048\u3066\u3044\u307e\u3059\u3002<\/p>\n<hr \/>\n<h2>9 \u7df4\u7fd2\u554f\u984c<\/h2>\n<h3>9-1 \u30d9\u30f3\u30c1\u30de\u30fc\u30af<\/h3>\n<h4>9-1-1 \u914d\u5217\u30b5\u30a4\u30ba\u5225\u30bf\u30a4\u30e0<\/h4>\n<p>10\u00b2\u301c10\u2077 \u8981\u7d20\u3067\u81ea\u4f5c\u30d2\u30fc\u30d7\u30bd\u30fc\u30c8\u3092\u8a08\u6e2c\u3057 log-log \u30b0\u30e9\u30d5\u5316\u3059\u308b\u3068\u50be\u304d \u2248 1 \u304c\u7406\u8ad6\u901a\u308a O(n log n) \u306e\u8a3c\u5de6\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n<h4>9-1-2 \u30d7\u30ed\u30d5\u30a1\u30a4\u30e9\u6d3b\u7528<\/h4>\n<p>Linux <code>perf<\/code> \u3067 L1 \u30df\u30b9\u7387\u3092\u53ef\u8996\u5316\u3001swap \u3092 SIMD \u6700\u9069\u5316\u3059\u308b\u3068 12 % \u6539\u5584\u3057\u305f\u4f8b\u3082\u3042\u308a\u307e\u3059\u3002<\/p>\n<h3>9-2 \u5fdc\u7528\u8ab2\u984c<\/h3>\n<h4>9-2-1 \u512a\u5148\u5ea6\u4ed8\u304d\u30ad\u30e5\u30fc\u5b9f\u88c5<\/h4>\n<p>sift-down \u3092\u524a\u9664\u3001sift-up \u3092 push \u306b\u8ee2\u7528\u3067\u30d7\u30e9\u30a4\u30aa\u30ea\u30c6\u30a3\u30ad\u30e5\u30fc\u304c\u5b8c\u6210\u3002<\/p>\n<p>Top k \u96c6\u8a08\u3092 million \u56de\u56de\u3057 log n \u30b9\u30b1\u30fc\u30eb\u3092\u4f53\u611f\u3057\u3066\u304f\u3060\u3055\u3044\u3002<\/p>\n<h4>9-2-2 \u5916\u90e8\u30bd\u30fc\u30c8\u3068\u306e\u30ea\u30f3\u30af<\/h4>\n<p>\u5916\u90e8\u30bd\u30fc\u30c8\u306e\u300c\u7f6e\u63db\u9078\u629e\u6cd5\uff0b\u30ab\u30b9\u30b1\u30fc\u30c9\u30de\u30fc\u30b8\u300d\u306f\u30d2\u30fc\u30d7\u3092\u4f7f\u3063\u3066 run \u9577\u3092 2 M \u306b\u4f38\u3070\u3057\u3001MapReduce \u521d\u671f\u30d5\u30a7\u30fc\u30ba\u304c\u307e\u3055\u306b\u3053\u306e\u30a2\u30d7\u30ed\u30fc\u30c1\u3092\u63a1\u7528\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n<hr \/>\n<h2 data-start=\"4708\" data-end=\"4731\">\u307e\u3068\u3081<\/h2>\n<p data-start=\"4733\" data-end=\"5119\">\u672c\u8a18\u4e8b\u3067\u306f\u300c\u30d2\u30fc\u30d7\u30bd\u30fc\u30c8 \u308f\u304b\u308a\u3084\u3059\u304f\u300d\u3068\u3044\u3046\u691c\u7d22\u610f\u56f3\u306b\u5fdc\u3048\u3001<strong data-start=\"4764\" data-end=\"4818\">\u2460\u6982\u5ff5\u7406\u89e3 \u2192 \u2461\u624b\u9806\u628a\u63e1 \u2192 \u2462\u30b3\u30fc\u30c9\u5b9f\u88c5 \u2192 \u2463\u53ef\u8996\u5316 \u2192 \u2464\u4ed6\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u6bd4\u8f03 \u2192 \u2465\u7df4\u7fd2\u554f\u984c<\/strong> \u3068\u3044\u3046\u4e00\u76f4\u7dda\u306e\u5b66\u7fd2\u5c0e\u7dda\u3092\u63d0\u793a\u3057\u307e\u3057\u305f\u3002<\/p>\n<p data-start=\"4733\" data-end=\"5119\">\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u5b66\u3076\u969b\u3001\u62bd\u8c61\u5ea6\u306e\u9ad8\u4f4e\u3092\u884c\u304d\u6765\u3057\u306a\u304c\u3089\u201c\u7d0d\u5f97\u611f\u201d\u3092\u7a4d\u307f\u4e0a\u3052\u308b\u3053\u3068\u304c\u91cd\u8981\u3067\u3059\u3002<\/p>\n<p data-start=\"4733\" data-end=\"5119\">\u30d2\u30fc\u30d7\u6728\u3068\u3044\u3046\u30c7\u30fc\u30bf\u69cb\u9020\u3092\u8179\u306b\u843d\u3068\u3057\u3001\u30d3\u30eb\u30c9\u30d2\u30fc\u30d7\u3068\u30eb\u30fc\u30c8\u4ea4\u63db\u306e\u610f\u5473\u3092 GIF \u3067\u8ffd\u3044\u3001\u5b9f\u88c5\u3067\u306f\u30d2\u30fc\u30d7\u30b5\u30a4\u30ba\u306e\u5883\u754c\u7ba1\u7406\u306b\u6ce8\u610f\u3059\u308b<\/p>\n<p data-start=\"4733\" data-end=\"5119\">\u2015\u2015\u3053\u308c\u3067\u300c\u30b3\u30fc\u30c9\u306f\u5199\u7d4c\u3057\u305f\u3051\u308c\u3069\u52d5\u304f\u7406\u7531\u304c\u308f\u304b\u3089\u306a\u3044\u300d\u3068\u3044\u3046\u6cbc\u304b\u3089\u629c\u3051\u51fa\u305b\u307e\u3059\u3002<\/p>\n<p data-start=\"4733\" data-end=\"5119\">\u3055\u3089\u306b\u3001\u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8\u3084\u30a4\u30f3\u30c8\u30ed\u30bd\u30fc\u30c8\u3068\u306e\u6027\u80fd\u5dee\u30fb\u5f79\u5272\u5206\u62c5\u3092\u628a\u63e1\u3059\u308c\u3070\u3001\u73fe\u5834\u306e\u201c\u6b66\u5668\u9078\u3073\u201d\u3082\u7cbe\u5ea6\u304c\u5897\u3059\u3067\u3057\u3087\u3046\u3002<\/p>\n<p data-start=\"4733\" data-end=\"5119\">\u6700\u5f8c\u306b\u7df4\u7fd2\u554f\u984c\u3067\u624b\u3092\u52d5\u304b\u3057\u3001\u512a\u5148\u5ea6\u4ed8\u304d\u30ad\u30e5\u30fc\u3078\u5fdc\u7528\u3059\u308b\u9803\u306b\u306f\u3001\u30d2\u30fc\u30d7\u30bd\u30fc\u30c8\u306f\u3082\u306f\u3084\u96e3\u89e3\u306a\u6982\u5ff5\u3067\u306f\u306a\u304f\u3001\u3042\u306a\u305f\u306e\u30c4\u30fc\u30eb\u30dc\u30c3\u30af\u30b9\u306e\u4e00\u54e1\u306b\u306a\u3063\u3066\u3044\u308b\u306f\u305a\u3067\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":"\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u5c02\u9580\u66f8\u309210\u518a\u4ee5\u4e0a\u57f7\u7b46\u3057\u305f\u7b46\u8005\u304c\u3001\u60c5\u5831\u51e6\u7406\u8a66\u9a13\u306e\u51fa\u984c\u50be\u5411\u3068\u73fe\u5834\u3067\u306e\u5229\u7528\u4f8b\u3092\u8e0f\u307e\u3048\u3066\u30d2\u30fc\u30d7\u30bd\u30fc\u30c8\u3092\u5fb9\u5e95\u89e3\u8aac\u3002 \u7406\u8ad6\u3060\u3051\u3067\u306a\u304f Python\uff0fC++ \u306e\u5b9f\u88c5\u3068\u53ef\u8996\u5316\u30c4\u30fc\u30eb\u307e\u3067\u7db2\u7f85\u3057\u3001\u660e\u65e5\u304b\u3089\u306e\u30b3\u30fc\u30c7\u30a3\u30f3\u30b0\u306b\u76f4\u7d50\u3059 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