{"id":53542,"date":"2025-08-12T12:30:19","date_gmt":"2025-08-12T04:30:19","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/53542.html"},"modified":"2025-08-12T12:30:19","modified_gmt":"2025-08-12T04:30:19","slug":"%e3%80%90%e7%ae%97%e6%b3%95%e3%80%91%e5%a0%86%ef%bc%88heap%ef%bc%89%e7%9a%84%e6%a6%82%e5%bf%b5%e3%80%81%e6%87%92%e5%88%a0%e9%99%a4%ef%bc%88lazy-deletion%ef%bc%89%e4%b8%8e%e5%a0%86%e6%8e%92%e5%ba%8f","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/53542.html","title":{"rendered":"\u3010\u7b97\u6cd5\u3011\u5806\uff08Heap\uff09\u7684\u6982\u5ff5\u3001\u61d2\u5220\u9664\uff08Lazy Deletion\uff09\u4e0e\u5806\u6392\u5e8f\uff08Heap Sort\uff09"},"content":{"rendered":"<\/p>\n<h4><\/h4>\n<h2>\u6587\u7ae0\u76ee\u5f55<\/h2>\n<ul>\n<li>\u3010\u7b97\u6cd5\u3011\u5806&#xff08;Heap&#xff09;\u7684\u6982\u5ff5\u3001\u61d2\u5220\u9664\u4e0e\u5806\u6392\u5e8f<\/li>\n<li>\n<ul>\n<li>1. \u5806\u7684\u6982\u5ff5<\/li>\n<li>\n<ul>\n<li>1.1 \u5806\u7684\u7279\u70b9<\/li>\n<li>1.2 \u5806\u7684\u5b58\u50a8<\/li>\n<li>1.3 \u5806\u7684\u64cd\u4f5c<\/li>\n<li>\n<ul>\n<li>1.3.1 \u6784\u5efa<\/li>\n<li>1.3.2 \u63d2\u5165<\/li>\n<li>1.3.3 \u5220\u9664<\/li>\n<li>1.3.4 \u8bbf\u95ee\u6700\u5927\u503c<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<li>2. \u5806\u7684\u61d2\u5220\u9664&#xff08;Lazy Deletion&#xff09;<\/li>\n<li>\n<ul>\n<li>2.1 \u5220\u9664\u7b2c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>             x<\/p>\n<p>            x<\/p>\n<p>         <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">x<\/span><\/span><\/span><\/span><\/span> \u4e2a\u63d2\u5165\u5806\u7684\u5143\u7d20<\/li>\n<li>2.2 \u5220\u9664\u5143\u7d20 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>             x<\/p>\n<p>            x<\/p>\n<p>         <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">x<\/span><\/span><\/span><\/span><\/span><\/li>\n<\/ul>\n<\/li>\n<li>3. \u5806\u6392\u5e8f&#xff08;Heap Sort&#xff09;<\/li>\n<li>\n<ul>\n<li>3.1 \u56de\u987e\u9009\u62e9\u6392\u5e8f<\/li>\n<li>3.2 \u5806\u6392\u5e8f<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h2>\u3010\u7b97\u6cd5\u3011\u5806&#xff08;Heap&#xff09;\u7684\u6982\u5ff5\u3001\u61d2\u5220\u9664\u4e0e\u5806\u6392\u5e8f<\/h2>\n<p>\u5806&#xff0c;\u8fd9\u662f\u4e00\u79cd\u9ad8\u7ea7\u6570\u636e\u7ed3\u6784&#xff0c;\u53ef\u4ee5\u5728\u4e00\u5806\u6570\u4e2d\u627e\u5230\u6700\u5927\u503c\u6216\u6700\u5c0f\u503c&#xff0c;\u5b83\u662f\u6811\u5f62\u7ed3\u6784&#xff0c;\u666e\u904d\u662f\u5b8c\u5168\u4e8c\u53c9\u6811\u3002\u5b83\u8fd8\u53ef\u4ee5\u8fdb\u884c\u6392\u5e8f\u3001\u9009\u62e9\u4e4b\u7c7b\u7684\u64cd\u4f5c<\/p>\n<h3>1. \u5806\u7684\u6982\u5ff5<\/h3>\n<p>\u5806&#xff08;Heap&#xff09;&#xff0c;\u8fd9\u662f\u4e00\u79cd\u9ad8\u7ea7\u6570\u636e\u7ed3\u6784&#xff0c;\u4e00\u822c\u60c5\u51b5\u4e0b\u5806\u662f\u4e00\u79cd\u5b8c\u5168\u4e8c\u53c9\u6811&#xff0c;\u5b83\u79f0\u4e3a\u4e8c\u53c9\u5806&#xff0c;\u8fd9\u7bc7\u6587\u7ae0\u6211\u4eec\u9ed8\u8ba4\u5806\u4e3a\u4e8c\u53c9\u5806<\/p>\n<h4>1.1 \u5806\u7684\u7279\u70b9<\/h4>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/08\/20250812043009-689ac3519dfa6.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" width=\"300\" \/> \u4e0a\u56fe\u662f\u4e00\u4e2a\u5c0f\u6839\u5806&#xff08;\u5c0f\u9876\u5806&#xff09;&#xff0c;\u5c0f\u6839\u5806\u7684\u6839\u8282\u70b9\u5bf9\u5e94\u503c\u6700\u5c0f&#xff0c;\u4e14\u6bcf\u4e00\u6761\u4ece\u4e0a\u5230\u4e0b\u7684\u8def\u5f84\u90fd\u662f\u5347\u5e8f\u7684<\/p>\n<p>5 -&gt; 7 -&gt; 16<br \/>\n5 -&gt; 7 -&gt; 13<br \/>\n5 -&gt; 11 -&gt; 14<br \/>\n5 -&gt; 11 -&gt; 12<\/p>\n<p>\u4e3a\u4ec0\u4e48\u6709\u5e8f\u5462&#xff1f;\u4f60\u8fd8\u4f1a\u53d1\u73b0\u7b2c\u4e09\u4e2a\u7279\u70b9&#xff0c;\u5c0f\u6839\u5806\u4efb\u610f\u4e00\u4e2a\u8282\u70b9\u7684\u5de6\u5b69\u5b50\u4e0e\u53f3\u5b69\u5b50\u90fd\u5c0f\u4e8e\u7b49\u4e8e\u5b83\u81ea\u5df1\u3002\u4f8b\u5982\u6839\u8282\u70b9\u5de6\u5b69\u5b50\u4e0e\u53f3\u5b69\u5b50\u5c0f\u4e8e\u6839\u8282\u70b9&#xff0c;\u5de6\u5b69\u5b50\u7684\u5de6\u5b69\u5b50\u548c\u53f3\u5b69\u5b50\u4e5f\u5c0f\u4e8e\u5de6\u5b69\u5b50&#xff0c;\u53f3\u5b69\u5b50\u7684\u5de6\u5b69\u5b50\u548c\u53f3\u5b69\u5b50\u8fd8\u5c0f\u4e8e\u53f3\u5b69\u5b50\u2026\u2026<\/p>\n<p>\u53cd\u4e4b&#xff0c;\u5927\u9876\u5806\u7684\u6839\u8282\u70b9\u503c\u6700\u5927&#xff0c;\u6bcf\u4e00\u6761\u4ece\u4e0a\u5230\u4e0b\u7684\u8def\u5f84\u90fd\u662f\u964d\u5e8f\u7684&#xff0c;\u4efb\u610f\u4e00\u4e2a\u8282\u70b9\u5927\u4e8e\u5de6\u53f3\u5b69\u5b50<\/p>\n<p>\u4e0d\u8fc7\u6b63\u56e0\u4e3a\u8fd9\u6837\u7684\u5957\u5a03&#xff0c;\u4e5f\u8ba9\u5806\u8fd9\u79cd\u7ed3\u6784\u51fa\u73b0&#xff0c;\u4e14\u63d2\u5165\u5220\u9664\u65f6\u95f4\u590d\u6742\u5ea6\u5747\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        \u0398<\/p>\n<p>        (<\/p>\n<p>        n<\/p>\n<p>        log<\/p>\n<p>        \u2061<\/p>\n<p>        n<\/p>\n<p>        )<\/p>\n<p>       \\\\Theta(n\\\\log n)<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u0398<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mop\">lo<span style=\"margin-right: 0.0139em\">g<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/p>\n<h4>1.2 \u5806\u7684\u5b58\u50a8<\/h4>\n<p>\u53ef\u80fd\u6709\u7684\u4eba\u4f1a\u60f3\u5230\u6811\u7684\u6811\u5f62\u5b58\u50a8\u2014\u2014\u6570\u636e\u3001\u5de6\u5b69\u5b50\u8282\u70b9\u6307\u9488\u3001\u53f3\u5b69\u5b50\u8282\u70b9\u6307\u9488\u3001\u7236\u8282\u70b9\u6307\u9488\u3002\u5176\u5b9e\u8fd9\u4e2a\u6ca1\u6709\u5fc5\u8981&#xff0c;\u6b63\u56e0\u4e3a\u8fd9\u662f\u4e00\u4e2a\u5b8c\u5168\u4e8c\u53c9\u6811&#xff0c;\u4e14\u4e2d\u95f4\u6ca1\u6709\u7a7a\u9699&#xff0c;\u6240\u4ee5\u6211\u4eec\u53ef\u4ee5\u7528\u987a\u5e8f\u8868\u5b58\u50a8\u65b9\u6cd5&#xff0c;\u4e5f\u5c31\u662f\u5806\u957f\u8fd9\u6837&#xff0c;\u987a\u5e8f\u8868\u957f\u8fd9\u6837&#xff08;\u4e0b\u6807\u4ece <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        1<\/p>\n<p>       1<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span> \u5f00\u59cb&#xff09; <img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/08\/20250812043009-689ac3519dfa6.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" width=\"300\" \/><\/p>\n<table>\n<tr>\u4e0b\u68071234567<\/tr>\n<tbody>\n<tr>\n<td>\u6570\u636e<\/td>\n<td>5<\/td>\n<td>7<\/td>\n<td>11<\/td>\n<td>16<\/td>\n<td>13<\/td>\n<td>14<\/td>\n<td>12<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u8fd8\u8bb0\u5f97\u987a\u5e8f\u8868\u5b58\u50a8\u6811\u7684\u8bbf\u95ee\u65b9\u5f0f\u5417&#xff1f; \u6839\u8282\u70b9\u4e0b\u8868\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        1<\/p>\n<p>       1<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span> &#xff0c;\u4e0b\u6807\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        x<\/p>\n<p>       x<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">x<\/span><\/span><\/span><\/span><\/span> \u7684\u8282\u70b9\u5de6\u5b69\u5b50\u4e0b\u6807\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        2<\/p>\n<p>        x<\/p>\n<p>       2x<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">2<\/span><span class=\"mord mathnormal\">x<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u53f3\u5b69\u5b50\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        2<\/p>\n<p>        x<\/p>\n<p>        &#043;<\/p>\n<p>        1<\/p>\n<p>       2x&#043;1<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7278em;vertical-align: -0.0833em\"><\/span><span class=\"mord\">2<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u7236\u8282\u70b9\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        \u230a<\/p>\n<p>          x<\/p>\n<p>          2<\/p>\n<p>        \u230b<\/p>\n<p>       \\\\lfloor\\\\cfrac x 2\\\\rfloor<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 2.276em;vertical-align: -0.686em\"><\/span><span class=\"mopen\">\u230a<\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.59em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">2<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.74em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.686em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"\"><\/span><\/span><span class=\"mclose\">\u230b<\/span><\/span><\/span><\/span><\/span><\/p>\n<h4>1.3 \u5806\u7684\u64cd\u4f5c<\/h4>\n<h5>1.3.1 \u6784\u5efa<\/h5>\n<p>\u6784\u5efa\u64cd\u4f5c\u662f\u7ed9\u51fa\u4e00\u4e2a\u987a\u5e8f\u8868&#xff0c;\u8ba9\u4f60\u5c06\u5176\u6784\u5efa\u4e3a\u4e00\u4e2a\u5927\u6839\u5806\/\u5c0f\u6839\u5806&#xff0c;\u8fd9\u91cc\u6211\u4eec\u90fd\u4ee5\u5927\u9876\u5806\u4e3a\u4f8b&#xff0c;\u5c0f\u9876\u5806\u5c31\u7ed3\u5408\u601d\u8def\u7406\u89e3&#xff0c;\u5305\u62ec\u540e\u9762\u7684\u63d2\u5165\u3001\u5220\u9664\u3001\u8be2\u95ee\u64cd\u4f5c<\/p>\n<p>\u6211\u4eec\u77e5\u9053\u5927\u9876\u5806\u6709\u4e00\u4e2a\u6700\u5927\u7684\u7279\u70b9&#xff0c;\u5c31\u662f\u6bcf\u4e00\u4e2a\u8282\u70b9\u5927\u4e8e\u5de6\u53f3\u5b69\u5b50\u3002\u90a3\u4e48\u6211\u4eec\u5148\u5c06\u987a\u5e8f\u8868\u53d8\u6210\u5b8c\u5168\u4e8c\u53c9\u6811\u7684\u7ed3\u6784&#xff08;\u4f46\u662f\u5b58\u50a8\u7ed3\u6784\u4e0a\u5b8c\u5168\u4e0d\u53d8&#xff0c;\u73b0\u5728\u8bb2\u7684\u662f\u903b\u8f91&#xff0c;\u624b\u5199\u540e\u9762\u8bb2&#xff09;<\/p>\n<p>\u4f8b\u5982\u8fd9\u4e48\u4e00\u4e2a\u987a\u5e8f\u8868<\/p>\n<table>\n<tr>\u4e0b\u6807123456789<\/tr>\n<tbody>\n<tr>\n<td>\u6570\u636e<\/td>\n<td>38<\/td>\n<td>78<\/td>\n<td>66<\/td>\n<td>20<\/td>\n<td>48<\/td>\n<td>91<\/td>\n<td>39<\/td>\n<td>50<\/td>\n<td>82<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u5c31\u53ef\u4ee5\u53d8\u6210\u8fd9\u6837 <img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/08\/20250812043011-689ac35304491.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" width=\"300\" \/> \u968f\u540e\u4ece\u6811\u7684 BFS \u5e8f\u4e2d\u6700\u540e\u4e00\u4e2a\u7236\u8282\u70b9&#xff08;\u4e5f\u5c31\u662f\u6700\u540e\u4e00\u4e2a\u8282\u70b9\u7684\u7236\u8282\u70b9&#xff09;\u5f00\u59cb&#xff0c;\u4e0d\u65ad\u8c03\u6574&#xff0c;\u8c03\u6574\u5b8c\u540e\u518d\u5230\u5012\u6570\u7b2c\u4e8c\u4e2a\u7236\u8282\u70b9\u3001\u5012\u6570\u7b2c\u4e09\u3001\u5012\u6570\u7b2c\u56db\u2026\u2026\u76f4\u5230\u904d\u5386\u5b8c\u6839\u8282\u70b9&#xff0c;\u6bcf\u6b21\u5c06\u81ea\u5df1\u4e0e\u5de6\u53f3\u8282\u70b9\u8fdb\u884c\u6bd4\u8f83&#xff0c;\u5982\u679c\u81ea\u5df1\u5927\u4e8e\u5de6\u53f3\u8282\u70b9\u90a3\u5c31\u4e0d\u7ba1\u4e86&#xff0c;\u5426\u5219\u627e\u5230\u6700\u5927\u7684\u90a3\u4e2a\u8282\u70b9&#xff0c;\u4e0e\u5176\u8fdb\u884c\u4ea4\u6362&#xff0c;\u518d\u8df3\u5230\u4ea4\u6362\u540e\u7684\u539f\u8282\u70b9\u7ee7\u7eed\u8c03\u6574&#xff0c;\u76f4\u5230\u81ea\u5df1\u5927\u4e8e\u5de6\u53f3\u8282\u70b9<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/08\/20250812043011-689ac3536ec6c.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" width=\"300\" \/>\u8c03\u6574 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        20<\/p>\n<p>       20<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">20<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u53d1\u73b0\u4e0d\u7b26\u5408\u5806\u6027\u8d28 <img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/08\/20250812043011-689ac353c03d8.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" width=\"300\" \/>\u5c06 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        82<\/p>\n<p>       82<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">82<\/span><\/span><\/span><\/span><\/span> \u4e0e <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        20<\/p>\n<p>       20<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">20<\/span><\/span><\/span><\/span><\/span> \u5bf9\u8c03&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        20<\/p>\n<p>       20<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">20<\/span><\/span><\/span><\/span><\/span> \u6062\u590d\u5806\u6027\u8d28 <img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/08\/20250812043012-689ac35412d2a.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" width=\"300\" \/>\u8c03\u6574 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        66<\/p>\n<p>       66<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">66<\/span><\/span><\/span><\/span><\/span> \u53d1\u73b0\u4e5f\u4e0d\u7b26\u5408\u6027\u8d28 <img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/08\/20250812043012-689ac35476525.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" width=\"300\" \/>\u4e0e <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        91<\/p>\n<p>       91<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">91<\/span><\/span><\/span><\/span><\/span> \u5bf9\u8c03\u540e\u53d1\u73b0\u5806\u6027\u8d28\u6062\u590d <img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/08\/20250812043012-689ac354e9d8b.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" width=\"300\" \/><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        78<\/p>\n<p>       78<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">78<\/span><\/span><\/span><\/span><\/span> \u4efb\u65e7\u4e0d\u7b26\u5408\u5806\u6027\u8d28 <img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/08\/20250812043013-689ac3556b63a.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" width=\"300\" \/>\u4e0e <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        82<\/p>\n<p>       82<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">82<\/span><\/span><\/span><\/span><\/span> \u4ea4\u6362\u540e\u6062\u590d\u6027\u8d28 <img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/08\/20250812043013-689ac355e4a34.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" width=\"300\" \/>\u8c03\u6574 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        38<\/p>\n<p>       38<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">38<\/span><\/span><\/span><\/span><\/span> \u53d1\u73b0\u4e5f\u4e0d\u7b26\u5408\u5806\u6027\u8d28 <img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/08\/20250812043014-689ac3562118c.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" width=\"300\" \/>\u4e0e <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        91<\/p>\n<p>       91<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">91<\/span><\/span><\/span><\/span><\/span> \u4ea4\u6362\u540e\u53d1\u73b0\u4e0d\u7b26\u5408\u5806\u6027\u8d28<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/08\/20250812043014-689ac35657094.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" width=\"300\" \/>\u4e0e <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        66<\/p>\n<p>       66<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">66<\/span><\/span><\/span><\/span><\/span> \u4ea4\u6362\u540e\u8c03\u6574\u5b8c\u6bd5&#xff0c;\u540c\u65f6\u5806\u6784\u5efa\u5b8c\u6210<\/p>\n<p>\u8fd9\u4e2a\u64cd\u4f5c\u7684\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        \u0398<\/p>\n<p>        (<\/p>\n<p>        n<\/p>\n<p>        )<\/p>\n<p>       \\\\Theta(n)<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u0398<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u6709\u7684\u4eba&#xff08;\u6bd4\u5982\u6211&#xff09;\u4ee5\u524d\u8ba4\u4e3a\u65f6\u95f4\u590d\u6742\u5ea6\u5e94\u8be5\u662f <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        \u0398<\/p>\n<p>        (<\/p>\n<p>        n<\/p>\n<p>        log<\/p>\n<p>        \u2061<\/p>\n<p>        n<\/p>\n<p>        )<\/p>\n<p>       \\\\Theta(n \\\\log n)<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u0398<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mop\">lo<span style=\"margin-right: 0.0139em\">g<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u4e0d\u8fc7&#xff0c;\u8fd9\u4e2a\u6709\u81ea\u5df1\u7684\u6570\u5b66\u8bc1\u660e\u8fc7\u7a0b<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/08\/20250812043014-689ac356d9451.png\" alt=\"\" \/> \u4e0d\u8fc7&#xff0c;\u5728\u5b9e\u9645\u64cd\u4f5c\u4e2d&#xff0c;\u5806\u4e2d\u7684\u5143\u7d20\u4f1a\u6839\u636e\u8bbf\u95ee\u516c\u5f0f\u6765\u8fdb\u884c\u8c03\u6574<\/p>\n<h5>1.3.2 \u63d2\u5165<\/h5>\n<p>\u90a3\u4e48&#xff0c;\u5728\u5806\u4e2d\u53c8\u5e94\u8be5\u5982\u4f55\u63d2\u5165\u5143\u7d20\u5462&#xff1f;\u9996\u5148&#xff0c;\u5c06\u5143\u7d20\u653e\u5728\u987a\u5e8f\u8868\u6700\u540e&#xff0c;\u4e5f\u5c31\u662f\u5927\u5c0f <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        &#043;<\/p>\n<p>        1<\/p>\n<p>       &#043;1<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7278em;vertical-align: -0.0833em\"><\/span><span class=\"mord\">&#043;<\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span> \u7684\u4f4d\u7f6e&#xff0c;\u63d2\u5165\u8fc7\u540e&#xff0c;\u5c06\u81ea\u5df1\u4e0e\u81ea\u5df1\u7684\u7236\u4eb2\u8fdb\u884c\u6bd4\u8f83&#xff0c;\u5982\u679c\u6bd4\u7236\u4eb2\u5927\u5c31\u4e0e\u7236\u4eb2\u5bf9\u8c03&#xff0c;\u8c03\u6362\u540e\u7ee7\u7eed\u4e0e\u81ea\u5df1\u7236\u4eb2\u6bd4\u8f83&#xff0c;\u76f4\u5230\u81ea\u5df1\u6bd4\u7236\u4eb2\u5c0f\u6216\u7b49\u4e8e\u4e3a\u6b62&#xff0c;\u8fd9\u4e2a\u5f88\u7c7b\u4f3c\u4e8e\u63d2\u5165\u6392\u5e8f\u7684\u8fc7\u7a0b<\/p>\n<p>\u4f8b\u5982\u5728\u8fd9\u4e2a\u5806\u4e2d\u63d2\u5165\u8282\u70b9 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        88<\/p>\n<p>       88<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">88<\/span><\/span><\/span><\/span><\/span> <img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/08\/20250812043015-689ac357eadac.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" width=\"300\" \/>\u63d2\u5165\u8fc7\u540e&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        88<\/p>\n<p>       88<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">88<\/span><\/span><\/span><\/span><\/span> \u6bd4\u7236\u8282\u70b9 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        48<\/p>\n<p>       48<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">48<\/span><\/span><\/span><\/span><\/span> \u5927 <img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/08\/20250812043016-689ac3582e982.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" width=\"300\" \/>\u5bf9\u8c03\u8fc7\u540e\u81ea\u5df1\u4f9d\u65e7\u6bd4\u7236\u8282\u70b9 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        82<\/p>\n<p>       82<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">82<\/span><\/span><\/span><\/span><\/span> \u5927 <img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/08\/20250812043016-689ac358614b2.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" width=\"300\" \/>\u518d\u6b21\u5bf9\u8c03&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        88<\/p>\n<p>       88<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">88<\/span><\/span><\/span><\/span><\/span> \u6bd4\u7236\u8282\u70b9 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        91<\/p>\n<p>       91<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">91<\/span><\/span><\/span><\/span><\/span> \u5c0f&#xff0c;\u8c03\u6574\u5b8c\u6bd5<\/p>\n<p>\u8fd9\u79cd\u64cd\u4f5c\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        \u0398<\/p>\n<p>        (<\/p>\n<p>        log<\/p>\n<p>        \u2061<\/p>\n<p>        n<\/p>\n<p>        )<\/p>\n<p>       \\\\Theta(\\\\log n)<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u0398<\/span><span class=\"mopen\">(<\/span><span class=\"mop\">lo<span style=\"margin-right: 0.0139em\">g<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u56e0\u4e3a\u6700\u5dee\u60c5\u51b5\u662f\u63d2\u5165\u4e86\u4e00\u4e2a\u6bd4\u5806\u9876\u8fd8\u5927\u7684\u6570\u5b57&#xff0c;\u968f\u540e\u4e00\u8def\u5411\u4e0a\u5230\u6839\u8282\u70b9<\/p>\n<h5>1.3.3 \u5220\u9664<\/h5>\n<p>\u5728\u5806\u4e2d&#xff0c;\u5220\u9664\u5143\u7d20\u4e00\u822c\u53ea\u5220\u9664\u5806\u9876&#xff0c;\u800c\u5220\u9664\u5806\u4e2d\u67d0\u4e2a\u5143\u7d20\u7684\u65b9\u6cd5\u4f1a\u5728\u8fd9\u4e00\u7ae0\u8bb2\u5230<\/p>\n<p>\u5220\u9664\u5143\u7d20\u53c8\u5e94\u8be5\u548b\u529e\u5462&#xff1f;\u76f4\u63a5\u5220\u4e86\u8c03\u6574\u8d77\u6765\u4e0d\u4ec5\u4e0d\u77e5\u9053\u5982\u4f55\u8c03\u6574&#xff0c;\u800c\u4e14\u5806\u6839\u8282\u70b9\u90fd\u6ca1\u4e86\u53c8\u5e94\u8be5\u548b\u6574<\/p>\n<p>\u6211\u4eec\u5e94\u8be5\u6362\u4f4d\u601d\u8003&#xff0c;\u53ef\u4ee5\u5c06\u5806\u7684\u6700\u540e\u4e00\u5c42\u7684\u6700\u540e\u4e00\u4e2a&#xff08;\u4e5f\u5c31\u662f\u987a\u5e8f\u8868\u6700\u540e\u4e00\u9879&#xff09;\u5143\u7d20\u8d4b\u503c\u7ed9\u7b2c\u4e00\u4e2a\u5143\u7d20&#xff0c;\u7136\u540e\u628a\u5b83\u81ea\u5df1\u5220\u6389\u3002\u8fd9\u6837&#xff0c;\u5934\u6ca1\u6709\u7f3a\u5931&#xff0c;\u4e5f\u5f88\u597d\u4fee\u6539\u4e86<\/p>\n<p>\u90a3\u4e48\u8fd9\u4e2a\u53c8\u5e94\u8be5\u5982\u4f55\u4fee\u6539\u5462&#xff1f;\u9996\u5148&#xff0c;\u5c06\u672b\u5c3e\u66ff\u6362\u7ed9\u5934\u540e\u5220\u9664&#xff0c;\u968f\u540e\u5c06\u5934\u4f5c\u4e3a\u5f53\u524d\u8282\u70b9&#xff0c;\u4e0e\u81ea\u5df1\u7684\u5de6\u53f3\u5b69\u5b50\u6bd4\u8f83\u3002\u5982\u679c\u5f53\u524d\u8282\u70b9\u5927\u4e8e\u7b49\u4e8e\u5de6\u53f3\u5b69\u5b50&#xff0c;\u90a3\u4e48\u8c03\u6574\u5b8c\u6210&#xff1b;\u5426\u5219\u5c31\u8ba9\u5f53\u524d\u8282\u70b9\u4e0e\u5de6\u53f3\u5b69\u5b50\u4e2d\u6700\u5927\u7684\u90a3\u4e2a\u8282\u70b9\u4e0e\u5176\u5bf9\u8c03&#xff0c;\u5bf9\u8c03\u540e\u7ee7\u7eed\u770b\u662f\u5426\u6ee1\u8db3\u5806\u7684\u6027\u8d28&#xff0c;\u76f4\u5230\u6210\u529f\u6ee1\u8db3\u4e3a\u4e4b<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/08\/20250812043016-689ac358adbcb.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" width=\"300\" \/>\u5220\u9664\u5806\u9876 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        91<\/p>\n<p>       91<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">91<\/span><\/span><\/span><\/span><\/span> <img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/08\/20250812043017-689ac3590a787.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" width=\"300\" \/>\u7528 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        11<\/p>\n<p>       11<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">11<\/span><\/span><\/span><\/span><\/span> \u66ff\u6362 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        91<\/p>\n<p>       91<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">91<\/span><\/span><\/span><\/span><\/span> \u540e\u5220\u9664&#xff0c;\u53d1\u73b0\u81ea\u5df1\u5c0f\u4e8e\u5de6\u53f3\u5b69\u5b50 <img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/08\/20250812043017-689ac3596f676.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" width=\"300\" \/><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        11<\/p>\n<p>       11<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">11<\/span><\/span><\/span><\/span><\/span> \u4e0e <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        88<\/p>\n<p>       88<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">88<\/span><\/span><\/span><\/span><\/span> \u4ea4\u6362&#xff0c;\u4f9d\u65e7\u5c0f\u4e8e\u5de6\u53f3\u5b69\u5b50 <img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/08\/20250812043017-689ac359b8edd.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" width=\"300\" \/>\u518d\u6b21\u4e0e <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        82<\/p>\n<p>       82<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">82<\/span><\/span><\/span><\/span><\/span> \u4ea4\u6362&#xff0c;\u5c0f\u4e8e\u5de6\u5b69\u5b50 <img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/08\/20250812043018-689ac35a3b48e.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" width=\"300\" \/>\u4ea4\u6362\u540e\u6210\u529f\u7b26\u5408\u5806\u7684\u6027\u8d28&#xff0c;\u8c03\u6574\u5b8c\u6bd5<\/p>\n<p>\u8fd9\u4e2a\u64cd\u4f5c\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e5f\u662f <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        \u0398<\/p>\n<p>        (<\/p>\n<p>        log<\/p>\n<p>        \u2061<\/p>\n<p>        n<\/p>\n<p>        )<\/p>\n<p>       \\\\Theta(\\\\log n)<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u0398<\/span><span class=\"mopen\">(<\/span><span class=\"mop\">lo<span style=\"margin-right: 0.0139em\">g<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u4f46\u662f\u4e0d\u7ba1\u548b\u6837\u90fd\u662f\u8fd9\u4e2a\u65f6\u95f4\u590d\u6742\u5ea6&#xff0c;\u800c\u4e0d\u50cf\u63d2\u5165\u6700\u5229\u60c5\u51b5\u53ef\u4ee5\u8fbe\u5230 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        \u0398<\/p>\n<p>        (<\/p>\n<p>        1<\/p>\n<p>        )<\/p>\n<p>       \\\\Theta(1)<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u0398<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">1<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u51b5\u4e14\u4f60\u5220\u9664\u9876\u5806&#xff0c;\u5374\u7528\u4e86\u4e00\u4e2a\u5c42\u6570\u6700\u4f4e\u7684\u503c\u66ff\u8865&#xff0c;\u800c\u5c42\u6570\u9ad8\u7684\u4efb\u610f\u4e00\u4e2a\u503c\u90fd\u5927\u4e8e\u7b49\u4e8e\u5c42\u6570\u4f4e\u7684\u4efb\u610f\u4e00\u4e2a\u503c<\/p>\n<h5>1.3.4 \u8bbf\u95ee\u6700\u5927\u503c<\/h5>\n<p>\u8bf4\u767d\u4e86\u5c31\u662f\u8bbf\u95ee\u5806\u9876&#xff0c;\u8fd9\u4e2a\u5f88\u597d\u8bf4\u5427&#xff01;\u5c31\u662f\u8bbf\u95ee\u987a\u5e8f\u8868\u7b2c\u4e00\u9879<\/p>\n<p>\u65f6\u95f4\u590d\u6742\u5ea6 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        \u0398<\/p>\n<p>        (<\/p>\n<p>        1<\/p>\n<p>        )<\/p>\n<p>       \\\\Theta(1)<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u0398<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">1<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/p>\n<h3>2. \u5806\u7684\u61d2\u5220\u9664&#xff08;Lazy Deletion&#xff09;<\/h3>\n<p>\u6709\u7684\u65f6\u5019&#xff0c;\u4e00\u4e9b\u6570\u636e\u7ed3\u6784\u53ef\u4ee5\u5ef6\u8fdf\u505a\u4e8b&#xff0c;\u4f8b\u5982\u5806\u548c\u7ebf\u6bb5\u6811&#xff0c;\u5c31\u50cf\u6691\u5047\u524d\u4e00\u5929\u4f7f\u52b2\u8865\u4f5c\u4e1a&#xff08;\u8bf7\u52ff\u6a21\u4eff&#xff09;\u4e00\u6837&#xff0c;\u5220\u9664\u8fd9\u4ef6\u4e8b\u653e\u5728\u8be2\u95ee&#xff08;\u68c0\u67e5\u4f5c\u4e1a&#xff09;\u65f6\u518d\u505a&#xff0c;\u8fd9\u5c31\u662f\u5806\u7684\u61d2\u5220\u9664<\/p>\n<h4>2.1 \u5220\u9664\u7b2c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        x<\/p>\n<p>       x<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">x<\/span><\/span><\/span><\/span><\/span> \u4e2a\u63d2\u5165\u5806\u7684\u5143\u7d20<\/h4>\n<p>\u5728\u5806\u7684\u5220\u9664\u64cd\u4f5c\u4e2d\u53ea\u80fd\u5220\u9664\u5806\u9876\u7684\u5143\u7d20&#xff0c;\u4f46\u662f\u6211\u4eec\u6709\u6ca1\u6709\u529e\u6cd5\u8ba9\u5b83\u4e5f\u53ef\u4ee5\u5220\u9664\u5806\u7b2c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        x<\/p>\n<p>       x<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">x<\/span><\/span><\/span><\/span><\/span> \u4e2a\u63d2\u5165\u7684\u5143\u7d20\u5462&#xff1f;\u786e\u5b9e\u6709\u7684<\/p>\n<p>\u65e2\u7136\u6bcf\u4e00\u6b21\u8be2\u95ee\u5806\u4e2d\u6700\u5927\u503c\/\u6700\u5c0f\u503c&#xff0c;\u90a3\u4e48\u6bcf\u4e00\u6b21\u8be2\u95ee\u5c31\u53ea\u8ddf\u5806\u9876\u6709\u5173\u7cfb\u3002\u6240\u4ee5&#xff0c;\u6211\u4eec\u53ef\u4ee5\u5b9a\u4e49\u4e00\u4e2a\u6570\u7ec4 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        D<\/p>\n<p>       D<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><\/span><\/span><\/span><\/span>&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         D<\/p>\n<p>         i<\/p>\n<p>       D_i<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0278em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u8868\u793a\u7b2c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        i<\/p>\n<p>       i<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6595em\"><\/span><span class=\"mord mathnormal\">i<\/span><\/span><\/span><\/span><\/span> \u4e2a\u63d2\u5165\u7684\u5143\u7d20\u662f\u5426\u88ab\u5220\u9664\u4e86&#xff0c;\u5220\u9664\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        1<\/p>\n<p>       1<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u672a\u5220\u9664\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        0<\/p>\n<p>       0<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0<\/span><\/span><\/span><\/span><\/span> \u3002\u968f\u540e&#xff0c;\u5982\u679c\u6211\u4eec\u60f3\u8981\u63d2\u5165\u4e00\u4e2a\u5143\u7d20&#xff0c;\u90a3\u4e48\u5c31\u7ed9\u5806\u4e2d\u63d2\u5165\u5b83\u7684\u63d2\u5165\u7f16\u53f7\u4e0e\u5b83\u7684\u6570\u636e\u6240\u6784\u6210\u7684\u96c6\u5408&#xff0c;\u6bd4\u8f83\u5668\u6839\u636e\u5b83\u7684\u6570\u636e\u6392\u5e8f<\/p>\n<p>\u968f\u540e&#xff0c;\u5220\u9664\u7b2c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        x<\/p>\n<p>       x<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">x<\/span><\/span><\/span><\/span><\/span> \u4e2a\u63d2\u5165\u5806\u7684\u5143\u7d20\u7684\u65f6\u5019&#xff0c;\u53ea\u9700\u8981\u6807\u8bb0 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         D<\/p>\n<p>         x<\/p>\n<p>       D_x<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0278em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">x<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u9879\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        1<\/p>\n<p>       1<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span> \u5c31\u53ef\u4ee5\u4e86<\/p>\n<p>\u8be2\u95ee\u5806\u9876\u7684\u65f6\u5019&#xff0c;\u6211\u4eec\u5148\u5224\u65ad\u5806\u9876\u5143\u7d20\u7684\u63d2\u5165\u7f16\u53f7\u662f\u5426\u5728 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        D<\/p>\n<p>       D<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><\/span><\/span><\/span><\/span> \u4e2d\u5df2\u7ecf\u88ab\u6807\u8bb0\u6210\u4e86\u5df2\u5220\u9664\u72b6\u6001&#xff0c;\u5982\u679c\u5df2\u5220\u9664\u90a3\u5c31\u5220\u9664\u5806\u9876&#xff0c;\u5426\u5219\u8f93\u51fa\u5806\u9876\u3002\u5c31\u8fd9\u4e48\u7b80\u5355<\/p>\n<h4>2.2 \u5220\u9664\u5143\u7d20 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        x<\/p>\n<p>       x<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">x<\/span><\/span><\/span><\/span><\/span><\/h4>\n<p>\u5bf9\u4e8e\u8fd9\u4e2a\u95ee\u9898&#xff0c;\u6211\u4eec\u79f0\u64cd\u4f5c\u7528\u7684\u5806\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        H<\/p>\n<p>       H<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0813em\">H<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u518d\u7ef4\u62a4\u4e00\u4e2a\u7528\u4e8e\u5220\u9664\u7684\u5bb9\u5668 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        D<\/p>\n<p>       D<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u8fd9\u4e2a\u6709\u4e00\u4e2a\u524d\u63d0\u6761\u4ef6&#xff0c;\u90a3\u5c31\u662f\u5220\u9664\u7684\u5143\u7d20\u662f\u5806\u4e2d\u51fa\u73b0\u8fc7\u7684<\/p>\n<p>\u5982\u679c\u53ef\u4ee5\u4fdd\u8bc1&#xff0c;\u6211\u4eec\u5c31\u53ef\u4ee5\u5c06 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        D<\/p>\n<p>       D<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><\/span><\/span><\/span><\/span> \u7ef4\u62a4\u6210\u5806&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        H<\/p>\n<p>       H<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0813em\">H<\/span><\/span><\/span><\/span><\/span> \u53d6\u6700\u5927\/\u6700\u5c0f&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        D<\/p>\n<p>       D<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><\/span><\/span><\/span><\/span> \u4e5f\u53d6\u6700\u5927\u548c\u6700\u5c0f&#xff0c;\u90a3\u4e48\u5982\u679c\u76f8\u7b49&#xff0c;\u5c31\u62b5\u6d88&#xff1b;\u5982\u679c\u4e0d\u76f8\u7b49&#xff0c;\u5c31\u8f93\u51fa<\/p>\n<p>\u5982\u679c\u4e0d\u80fd\u4fdd\u8bc1&#xff0c;\u6211\u4eec\u5c31\u53ef\u4ee5\u5c06 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        D<\/p>\n<p>       D<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><\/span><\/span><\/span><\/span> \u7ef4\u62a4\u6210\u4e8c\u53c9&#xff08;\u5e73\u8861&#xff09;\u641c\u7d22\u6811&#xff0c;\u6bcf\u6b21\u53d6\u5806\u9876&#xff0c;\u5728\u91cc\u9762\u5bfb\u627e\u6709\u6ca1\u6709\u8fd9\u4e2a\u503c&#xff0c;\u6709\u7684\u8bdd\u62b5\u6d88&#xff0c;\u6ca1\u6709\u7684\u8bdd\u8f93\u51fa<\/p>\n<h3>3. \u5806\u6392\u5e8f&#xff08;Heap Sort&#xff09;<\/h3>\n<p>\u5806\u6392\u5e8f&#xff08;Heap Sort&#xff09;\u662f\u4e00\u79cd\u4e0d\u7a33\u5b9a\u6392\u5e8f&#xff0c;\u4f46\u662f\u5b83\u7684\u6392\u5e8f\u65f6\u95f4\u975e\u5e38\u5e73\u8861&#xff0c;\u6ca1\u6709\u5feb\u901f\u6392\u5e8f\u4f1a\u88ab\u6570\u636e\u5361\u6210 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        \u0398<\/p>\n<p>        (<\/p>\n<p>         n<\/p>\n<p>         2<\/p>\n<p>        )<\/p>\n<p>       \\\\Theta(n^2)<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.0641em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u0398<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">n<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u7684\u60c5\u51b5&#xff0c;\u4e5f\u6ca1\u6709\u5192\u6ce1\u6700\u4f18\u90fd <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        \u0398<\/p>\n<p>        (<\/p>\n<p>        n<\/p>\n<p>        )<\/p>\n<p>       \\\\Theta(n)<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u0398<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u7684\u60c5\u51b5&#xff0c;\u65f6\u95f4\u590d\u6742\u5ea6\u90fd\u662f\u5747\u8861\u7684 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        \u0398<\/p>\n<p>        (<\/p>\n<p>        n<\/p>\n<p>        log<\/p>\n<p>        \u2061<\/p>\n<p>        n<\/p>\n<p>        )<\/p>\n<p>       \\\\Theta(n\\\\log n)<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u0398<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mop\">lo<span style=\"margin-right: 0.0139em\">g<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u8fd9\u5c31\u5f88\u597d<\/p>\n<h4>3.1 \u56de\u987e\u9009\u62e9\u6392\u5e8f<\/h4>\n<p>\u8fd8\u8bb0\u5f97\u9009\u62e9\u6392\u5e8f\u7684\u601d\u8def\u5417&#xff1f;\u6bcf\u6b21\u5728\u4e00\u5806\u6570\u5b57\u4e2d\u627e\u5230\u6700\u5927\u503c&#xff0c;\u7136\u540e\u5c06\u6700\u5927\u503c\u4e0e\u987a\u5e8f\u8868\u6700\u540e\u4e00\u9879\u4ea4\u6362&#xff0c;\u518d\u6392\u9664\u6700\u5927\u503c\u7ee7\u7eed\u627e&#xff0c;\u628a\u6700\u5927\u503c\u4e0e\u5012\u6570\u7b2c\u4e8c\u9879\u4ea4\u6362\u2026\u2026\u76f4\u5230\u6700\u7ec8\u5168\u90e8\u6392\u5e8f\u5b8c\u6bd5<\/p>\n<p>\u5f53\u7136&#xff0c;\u8fd9\u4e2a\u4e5f\u53ef\u4ee5\u53cd\u7740\u6765&#xff0c;\u90a3\u5c31\u662f\u5728\u6240\u6709\u5143\u7d20\u4e2d\u627e\u5230\u6700\u5c0f\u503c\u4e0e\u7b2c\u4e00\u9879\u4ea4\u6362&#xff0c;\u518d\u627e\u7b2c\u4e00\u9879\u540e\u7684\u6700\u5c0f\u503c\u4e0e\u7b2c\u4e8c\u9879\u4ea4\u6362\u2026\u2026\u76f4\u5230\u5168\u90e8\u6392\u5e8f\u5b8c <img decoding=\"async\" src=\"2025-08-124zn5z55bnao.gif\" alt=\"\" \/><\/p>\n<h4>3.2 \u5806\u6392\u5e8f<\/h4>\n<p>\u65e2\u7136\u9009\u62e9\u6392\u5e8f\u8981\u5728\u4e00\u5806\u6570\u4e2d\u627e\u5230\u6700\u5927\u503c\u5e76\u653e\u5728\u6700\u540e&#xff0c;\u7136\u540e\u627e\u5230\u7b2c\u4e8c\u5927\u3001\u7b2c\u4e09\u5927\u3001\u7b2c\u56db\u5927\u2026\u2026\u76f4\u5230\u6392\u5e8f\u5b8c\u6bd5&#xff0c;\u90a3\u4e48\u54ea\u4e2a\u5bb9\u5668\u53ef\u4ee5\u9ad8\u6548\u5730\u627e\u5230\u6700\u5927\u503c\u518d\u5220\u9664\u5462&#xff1f;\u5806&#xff01;<\/p>\n<p>\u6211\u4eec\u53ef\u4ee5\u4e00\u4e2a\u987a\u5e8f\u8868\u6784\u5efa\u6210\u4e3a\u4e00\u4e2a\u5927\u9876\u5806&#xff0c;\u968f\u540e\u5c06\u7b2c\u4e00\u9879\u4e0e\u6700\u540e\u4e00\u9879\u4ea4\u6362&#xff0c;\u7136\u540e\u201c\u5220\u6389\u201d&#xff0c;\u8c03\u6574&#xff0c;\u7b2c\u4e8c\u5927\u53c8\u4f1a\u51fa\u73b0&#xff0c;\u201c\u5220\u6389\u201d&#xff0c;\u8c03\u6574&#xff0c;\u7b2c\u4e09\u5927&#xff0c;\u201c\u5220\u6389\u201d\u2026\u2026\u6700\u7ec8&#xff0c;\u76f4\u5230\u5806\u4e2d\u4ec0\u4e48\u4e5f\u6ca1\u6709\u4e86\u5c31\u662f\u6392\u5e8f\u5b8c\u6210\u4e86<\/p>\n<p>\u6709\u4eba\u53ef\u80fd\u95ee\u4e3a\u4ec0\u4e48\u662f\u4ea4\u6362&#xff0c;\u4e0d\u662f\u66ff\u6362\u5417&#xff1f;\u4f46\u662f&#xff0c;\u6211\u4eec\u53ef\u4ee5\u7ef4\u62a4\u5806\u9876 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        n<\/p>\n<p>       n<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">n<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u4ea4\u6362\u540e\u5220\u9664\u5143\u7d20\u5c31\u662f\u5c06 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        n<\/p>\n<p>       n<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">n<\/span><\/span><\/span><\/span><\/span> \u5411\u524d\u632a\u4e00\u4f4d\u800c\u5df2&#xff0c;\u8fd9\u4e5f\u662f\u201c\u5220\u6389\u201d\u4e3a\u4ec0\u4e48\u6253\u4e86\u5f15\u53f7\u7684\u539f\u56e0&#xff0c;\u8fd9\u79cd\u64cd\u4f5c\u4e5f\u53eb\u505a\u4f2a\u5220\u9664<\/p>\n<hr \/>\n<p>\u4e0b\u4e00\u7bc7\u535a\u6587\u4f1a\u8bb2\u4e0e\u5806\u6709\u5173\u7684\u5bb9\u5668\/\u51fd\u6570&#xff0c;\u5806\u4e0e\u5806\u6392\u5e8f\u7684\u624b\u5199\u65b9\u6cd5<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u6587\u7ae0\u6d4f\u89c8\u9605\u8bfb62\u6b21\u3002\u672c\u6587\u4ecb\u7ecd\u4e86\u5806\uff08Heap\uff09\u6570\u636e\u7ed3\u6784\u7684\u6982\u5ff5\u3001\u64cd\u4f5c\u53ca\u5176\u5e94\u7528\u3002\u5806\u662f\u4e00\u79cd\u5b8c\u5168\u4e8c\u53c9\u6811\uff0c\u5206\u4e3a\u5927\u9876\u5806\u548c\u5c0f\u9876\u5806\uff0c\u5177\u6709\u9ad8\u6548\u7684\u63d2\u5165\u3001\u5220\u9664\u548c\u67e5\u8be2\u64cd\u4f5c\u3002\u5806\u7684\u5b58\u50a8\u91c7\u7528\u987a\u5e8f\u8868\uff0c\u901a\u8fc7\u7279\u5b9a\u516c\u5f0f\u8bbf\u95ee\u7236\u5b50\u8282\u70b9\u3002\u5806\u7684\u64cd\u4f5c\u5305\u62ec\u6784\u5efa\uff08O(n)\uff09\u3001\u63d2\u5165\uff08O(log n)\uff09\u3001\u5220\u9664\u5806\u9876\uff08O(log n)\uff09\u548c\u8bbf\u95ee\u6700\u5927\u503c\uff08O(1)\uff09\u3002 \u6587\u7ae0\u8fd8\u4ecb\u7ecd\u4e86\u5806\u7684\u61d2\u5220\u9664\u6280\u672f\uff0c\u901a\u8fc7\u6807\u8bb0\u5220\u9664\u72b6\u6001\u5b9e\u73b0\u5ef6\u8fdf\u5220\u9664\uff0c\u652f\u6301\u5220\u9664\u7279\u5b9a\u63d2\u5165\u987a\u5e8f\u7684\u5143\u7d20\u6216\u7279\u5b9a\u503c\u3002\u6700\u540e\u63d0\u5230\u5806\u6392\u5e8f\uff0c\u5229\u7528\u5806\u7684\u7279\u6027\u5b9e\u73b0\u9ad8\u6548\u6392\u5e8f\u3002\u5806\u7ed3\u6784\u5728\u6570\u636e\u5904\u7406\u548c\u7b97\u6cd5\u8bbe\u8ba1\u4e2d\u5177\u6709\u91cd\u8981\u5e94\u7528\u4ef7\u503c\u3002<\/p>\n","protected":false},"author":2,"featured_media":53522,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[5066,427],"topic":[],"class_list":["post-53542","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-server","tag-c-c","tag-427"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.3 - 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