{"id":51380,"date":"2025-08-10T21:59:40","date_gmt":"2025-08-10T13:59:40","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/51380.html"},"modified":"2025-08-10T21:59:40","modified_gmt":"2025-08-10T13:59:40","slug":"java%e7%ae%97%e6%b3%95%e5%ad%a6%e4%b9%a0%e5%9b%9b-%e5%b8%8c%e5%b0%94%e6%8e%92%e5%ba%8f-%e6%8e%92%e5%ba%8f%e8%bf%87%e7%a8%8b%e6%8b%86%e8%a7%a3%e4%b8%8e%e7%ae%97%e6%b3%95%e4%bc%98%e5%8c%96","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/51380.html","title":{"rendered":"(Java)\u7b97\u6cd5\u5b66\u4e60(\u56db): \u5e0c\u5c14\u6392\u5e8f-\u6392\u5e8f\u8fc7\u7a0b\u62c6\u89e3\u4e0e\u7b97\u6cd5\u4f18\u5316"},"content":{"rendered":"<h3>\u59cb:\u5e0c\u5c14\u6392\u5e8f\u7684\u7b80\u5355\u4ecb\u7ecd<\/h3>\n<p>\u5e0c\u5c14\u6392\u5e8f&#xff08;Shell Sort&#xff09;\u662f\u4e00\u79cd\u57fa\u4e8e\u63d2\u5165\u6392\u5e8f\u7684\u6539\u8fdb\u7b97\u6cd5&#xff0c;\u7531Donald Shell\u4e8e1959\u5e74\u63d0\u51fa\u3002\u5b83\u901a\u8fc7\u5c06\u539f\u59cb\u5217\u8868\u5206\u5272\u6210\u591a\u4e2a\u5b50\u5e8f\u5217\u8fdb\u884c\u63d2\u5165\u6392\u5e8f&#xff0c;\u9010\u6b65\u7f29\u5c0f\u5b50\u5e8f\u5217\u7684\u95f4\u9694&#xff0c;\u6700\u7ec8\u5b8c\u6210\u6574\u4f53\u6392\u5e8f\u3002\u5e0c\u5c14\u6392\u5e8f\u7684\u6838\u5fc3\u601d\u60f3\u662f\u51cf\u5c11\u9006\u5e8f\u5bf9&#xff0c;\u4ece\u800c\u63d0\u5347\u6392\u5e8f\u6548\u7387\u3002<\/p>\n<h4>1.\u7b97\u6cd5\u539f\u7406<\/h4>\n<p>\u5e0c\u5c14\u6392\u5e8f\u901a\u8fc7\u5b9a\u4e49\u4e00\u4e2a\u95f4\u9694\u5e8f\u5217&#xff08;Gap Sequence&#xff09;\u6765\u5212\u5206\u5b50\u5e8f\u5217\u3002\u521d\u59cb\u95f4\u9694\u8f83\u5927&#xff0c;\u9010\u6b65\u7f29\u5c0f\u81f31&#xff08;\u5373\u666e\u901a\u7684\u63d2\u5165\u6392\u5e8f&#xff09;\u3002\u6bcf\u6b21\u6309\u5f53\u524d\u95f4\u9694\u5206\u7ec4\u540e&#xff0c;\u5bf9\u6bcf\u7ec4\u8fdb\u884c\u63d2\u5165\u6392\u5e8f\u3002\u968f\u7740\u95f4\u9694\u51cf\u5c0f&#xff0c;\u5217\u8868\u9010\u6e10\u8d8b\u4e8e\u6709\u5e8f&#xff0c;\u6700\u7ec8\u5b8c\u6210\u6392\u5e8f\u3002<\/p>\n<h4>2.\u95f4\u9694\u5e8f\u5217\u9009\u62e9<\/h4>\n<p>\u95f4\u9694\u5e8f\u5217\u7684\u9009\u62e9\u76f4\u63a5\u5f71\u54cd\u7b97\u6cd5\u6548\u7387\u3002\u5e38\u89c1\u9009\u62e9\u5305\u62ec&#xff1a;<\/p>\n<ul>\n<li>Shell\u539f\u59cb\u5e8f\u5217&#xff1a;$gap &#061; \\\\frac{n}{2}, \\\\frac{n}{4}, \\\\ldots, 1$&#xff08;\u9010\u6b65\u6298\u534a&#xff09;\u3002<\/li>\n<li>Hibbard\u5e8f\u5217&#xff1a;$gap &#061; 2^k &#8211; 1$&#xff08;\u59821, 3, 7, 15\u2026&#xff09;&#xff0c;\u65f6\u95f4\u590d\u6742\u5ea6\u53ef\u4f18\u5316\u81f3$O(n^{3\/2})$\u3002<\/li>\n<\/ul>\n<h4>3.\u65f6\u95f4\u590d\u6742\u5ea6<\/h4>\n<ul>\n<li>\u6700\u574f\u60c5\u51b5&#xff1a;\u53d6\u51b3\u4e8e\u95f4\u9694\u5e8f\u5217&#xff0c;\u4e00\u822c\u4e3a$O(n^2)$\u3002<\/li>\n<li>\u6700\u4f73\u60c5\u51b5&#xff1a;$O(n \\\\log n)$&#xff08;\u5982\u4f7f\u7528Sedgewick\u5e8f\u5217&#xff09;\u3002<\/li>\n<\/ul>\n<h4>4.\u4f18\u7f3a\u70b9<\/h4>\n<ul>\n<li>\u4f18\u70b9&#xff1a;\u6bd4\u7b80\u5355\u63d2\u5165\u6392\u5e8f\u9ad8\u6548&#xff0c;\u5c24\u5176\u5bf9\u4e2d\u7b49\u89c4\u6a21\u6570\u636e\u8868\u73b0\u826f\u597d\u3002<\/li>\n<li>\u7f3a\u70b9&#xff1a;\u65f6\u95f4\u590d\u6742\u5ea6\u4e0d\u7a33\u5b9a&#xff0c;\u4f9d\u8d56\u95f4\u9694\u5e8f\u5217\u7684\u9009\u62e9&#xff1b;\u4e0d\u9002\u5408\u5927\u89c4\u6a21\u6570\u636e\u3002<\/li>\n<\/ul>\n<h3>\u4e00.\u6587\u5b57\u63cf\u8ff0\u6d41\u7a0b<\/h3>\n<p>\u6b65\u957f\u5e8f\u5217\u51b3\u5b9a\u65f6\u95f4\u590d\u6742\u5ea6 \u5e0c\u5c14\u6392\u5e8f\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u53d6\u51b3\u4e8e\u6b65\u957f\u5e8f\u5217\u7684\u9009\u62e9\u3002\u5e38\u89c1\u5e8f\u5217\u5305\u62ec\u5e0c\u5c14\u589e\u91cf\u5e8f\u5217&#xff08;O(n\u00b2)&#xff09;\u548c\u66f4\u4f18\u7684Hibbard\u5e8f\u5217&#xff08;O(n^1.5)&#xff09;\u3002<\/p>\n<hr \/>\n<h4>\u6392\u5e8f\u8fc7\u7a0b\u793a\u4f8b:<\/h4>\n<p>\u4ee5\u6570\u7ec4\u00a0[2, 8, 9, 4, 7, 9, 6, 12]\u00a0\u4e3a\u4f8b&#xff1a;<\/p>\n<p>\u521d\u59cb\u6b65\u957f i&#061;4 \u5206\u7ec4&#xff1a;<\/p>\n<ul>\n<li>\u7ec41: 2, 7<\/li>\n<li>\u7ec42: 8, 9<\/li>\n<li>\u7ec43: 9, 6<\/li>\n<li>\u7ec44: 4, 12<\/li>\n<\/ul>\n<p>\u63d2\u5165\u6392\u5e8f\u540e&#xff1a;<\/p>\n<ul>\n<li>\u7ec41: 2, 7<\/li>\n<li>\u7ec42: 8, 9<\/li>\n<li>\u7ec43: 6, 9<\/li>\n<li>\u7ec44: 4, 12<\/li>\n<\/ul>\n<p>\u6b65\u957f i&#061;2 \u5206\u7ec4&#xff1a;<\/p>\n<ul>\n<li>\u7ec41: 2, 9, 7, 6<\/li>\n<li>\u7ec42: 8, 4, 9, 12<\/li>\n<\/ul>\n<p>\u63d2\u5165\u6392\u5e8f\u540e&#xff1a;<\/p>\n<ul>\n<li>\u7ec41: 2, 6, 7, 9<\/li>\n<li>\u7ec42: 4, 8, 9, 12<\/li>\n<\/ul>\n<p>\u6b65\u957f i&#061;1 \u5206\u7ec4&#xff1a;<\/p>\n<ul>\n<li>\u7ec41: 2, 4, 6, 8, 7, 9, 9, 12<\/li>\n<\/ul>\n<p>\u63d2\u5165\u6392\u5e8f\u540e&#xff1a;<\/p>\n<ul>\n<li>\u6700\u7ec8\u7ed3\u679c:\u00a0[2, 4, 6, 7, 8, 9, 9, 12]<\/li>\n<\/ul>\n<h3>\u4e8c.\u4ee3\u7801\u5b9e\u73b0<\/h3>\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u5e0c\u5c14\u6392\u5e8f\u4e2d\u5e94\u7528\u5230\u4e86\u63d2\u5165\u6392\u5e8f&#xff0c;\u6240\u4ee5\u8981\u9488\u5bf9\u5e0c\u5c14\u6392\u5e8f\u7684\u7279\u6027\u6765\u5bf9\u4e4b\u524d\u6240\u4ecb\u7ecd\u7684\u201c<span style=\"color:#494949\">\u65e0\u76d1\u7763\u63d2\u5165\u6392\u5e8f<\/span>\u201d\u6765\u8fdb\u884c\u4e00\u5b9a\u7684\u4fee\u6539\u3002<\/p>\n<p>\u4ee5\u4e0b\u662f\u4f7f\u7528\u4e86<span style=\"color:#956fe7\">\u5e0c\u5c14\u5e8f\u5217<\/span>\u7684\u5e0c\u5c14\u6392\u5e8f\u672c\u4f53:<\/p>\n<p>\/\/\u5e94\u7528\u5e0c\u5c14\u5e8f\u5217\u7684\u5e0c\u5c14\u6392\u5e8f\u672c\u4f53<br \/>\n    static void sell_sort(int[] arr, int arrLength) {<br \/>\n        \/\/\u5e8f\u5217:\u8fd9\u91cc\u4f7f\u7528\u5e0c\u5c14\u5e8f\u5217 -&gt; \u5e0c\u5c14\u589e\u91cf\u5e8f\u5217<br \/>\n        \/*\u5e0c\u5c14\u589e\u91cf\u5e8f\u5217[O(n^2)]: n\/2 n\/4 n\/8 n\/16*\/<br \/>\n        \/\/\u5b9a\u4e49\u6b65\u957fk \u4ee5\u53ca \u6b65step<br \/>\n        int k &#061; 2, step;<br \/>\n        \/\/\u5916\u90e8\u5206\u7ec4<br \/>\n        do {<br \/>\n            \/\/\u83b7\u5f97\u6b65 -&gt; \u5373\u5206\u4e3a\u4e86\u51e0\u7ec4<br \/>\n            step &#061; (arrLength \/ k &#061;&#061; 0) ? 1 : (arrLength \/ k);<br \/>\n            \/\/\u6bcf\u4e00\u7ec4\u90fd\u505a\u63d2\u5165\u6392\u5e8f<br \/>\n            for (int i &#061; 0; i &lt; step; i&#043;&#043;) {<br \/>\n              \/\/\/\/\/\u65e0\u76d1\u7763\u7684\u63d2\u5165\u6392\u5e8f\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/<br \/>\n                sell_unguarded_insert_sort(arr, i, arrLength, step);<br \/>\n              \/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/<br \/>\n            }<br \/>\n            k *&#061; 2;<br \/>\n        } while (step !&#061; 1);<br \/>\n    } <\/p>\n<p>\u4ee5\u4e0b\u662f\u9488\u5bf9\u5e0c\u5c14\u6392\u5e8f\u6539\u8fdb\u7684\u65e0\u76d1\u7763\u63d2\u5165\u6392\u5e8f:<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u5e0c\u5c14\u6392\u5e8f\u4e0b\u7684\u65e0\u76d1\u7763\u63d2\u5165\u6392\u5e8f&#xff0c;\u7531\u4e8e\u9009\u53d6\u5143\u7d20\u662f\u6309\u7167\u6b65\u957f\u957f\u5ea6\u6765\u8df3\u8dc3\u5f0f\u9009\u53d6\u7684&#xff0c;\u6240\u4ee5\u5728\u521d\u59cb\u5316\u4ee5\u53ca\u8fed\u4ee3\u6570\u636e\u7684\u65f6\u5019\u8981\u5c06\u539f\u672c\u7684&#043;1\u6539\u53d8\u4e3a&#043;step(\u6b65\u957f)&#xff0c;\u76f8\u5e94\u7684-1\u4e5f\u5e94\u6539\u4e3a -step\u3002<\/p>\n<p>\/\/\u5e0c\u5c14\u6392\u5e8f\u4e0b\u7684\u63d2\u5165\u6392\u5e8f -&gt; \u6839\u636e\u6b65\u957f\u6765\u8df3\u8dc3\u5f0f\u9009\u53d6\u5143\u7d20<br \/>\n\/\/\u4f20\u5165: arr\u6570\u7ec4, \u8d77\u59cb\u5143\u7d20\u4e0b\u6807(0,1,2&#8230;..step-1), arrLength\u6570\u7ec4\u957f\u5ea6, step\u6b65\u957f<br \/>\nstatic void sell_unguarded_insert_sort(int[] arr, int i, int arrLength, int step) {<br \/>\n    int minIndex &#061; i;<br \/>\n    \/\/\u627e\u6700\u5c0f\u503c\u7684\u4e0b\u6807<br \/>\n    for (int j &#061; i &#043; step; j &lt; arrLength; j &#043;&#061; step) {<br \/>\n        if (arr[minIndex] &gt; arr[j]) {<br \/>\n            minIndex &#061; j;<br \/>\n        }<br \/>\n    }<br \/>\n    \/\/\u6700\u5c0f\u503c\u524d\u7f6e<br \/>\n    while (minIndex &gt; i) {<br \/>\n        MyMath.swap(arr, minIndex, minIndex &#8211; step);<br \/>\n        minIndex -&#061; step;<br \/>\n    }<br \/>\n    \/\/\u6392\u5e8f<br \/>\n    for (int j &#061; i &#043; step * 2; j &lt; arrLength; j &#043;&#061; step) {<br \/>\n        int k &#061; j;<br \/>\n        while (arr[k] &lt; arr[k &#8211; step]) {<br \/>\n            MyMath.swap(arr, k, k &#8211; step);<br \/>\n            k -&#061; step;<br \/>\n        }<br \/>\n    }<br \/>\n} <\/p>\n<h3>\u4e09.\u4ee3\u7801\u4f18\u5316<\/h3>\n<p>\u5e0c\u5c14\u6392\u5e8f\u7684<span style=\"color:#ed7976\">\u6838\u5fc3<\/span>\u5c31\u662f&#xff1a; <span style=\"color:#ed7976\">\u6b65\u957f\u5e8f\u5217<\/span><\/p>\n<p><span style=\"color:#fe2c24\">\u5e0c\u5c14\u6392\u5e8f\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u662f\u53ef\u53d8\u7684(\u91cd\u8981!)<\/span><\/p>\n<p>\u5e0c\u5c14\u6392\u5e8f\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e0e\u6b65\u957f\u5e8f\u5217\u6709\u5173&#xff0c;\u6240\u4ee5\u6539\u53d8\u6b65\u957f\u5e8f\u5217\u5c31\u4f1a\u6539\u53d8\u5e0c\u5c14\u6392\u5e8f\u7684\u65f6\u95f4\u590d\u6742\u5ea6&#xff0c;\u4f18\u5316\u6b65\u957f\u5e8f\u5217\u5c31\u4f1a\u4f18\u5316\u5e0c\u5c14\u6392\u5e8f\u7684\u8fd0\u884c\u901f\u5ea6&#xff01;<\/p>\n<p>\u4f18\u5316: \u4f7f\u7528\u66f4\u52a0\u4f18\u79c0\u7684\u201cHibbard\u589e\u91cf\u5e8f\u5217\u201d<\/p>\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u5e0c\u5c14\u589e\u91cf\u5e8f\u5217: \u00a0n\/2 n\/4 n\/8 n\/16 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0-&gt; \u65f6\u95f4\u590d\u6742\u5ea6: o(n^2)<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 Hibbard\u589e\u91cf\u5e8f\u5217:\u00a01 3 7 &#8230;.. 2^(k-1) \u00a0 \u00a0 \u00a0 \u00a0-&gt; \u65f6\u95f4\u590d\u6742\u5ea6:o(n^1.5)<\/p>\n<p>\u4ee3\u7801\u5982\u4e0b&#xff1a;<\/p>\n<p> \/\/\u5e94\u7528Hibbard\u589e\u91cf\u5e8f\u5217\u7684\u5e0c\u5c14\u6392\u5e8f\u672c\u4f53<br \/>\n    static void sell_sort_hibbard(int[] arr, int arrLength) {<br \/>\n        \/\/\u5e8f\u5217:\u8fd9\u91cc\u4f7f\u7528Hibbard\u589e\u91cf\u5e8f\u5217<br \/>\n        \/*(\u76f8\u6bd4\u5e0c\u5c14\u5e8f\u5217\u66f4\u4f18\u79c0)Hibbard\u589e\u91cf\u5e8f\u5217[O(n^1.5)]: 1 3 7 15 31 &#8230;.. 2^(k-1)*\/<br \/>\n        \/* \u89c4\u5f8b\u4e00<br \/>\n         *  3 &#061; 1 * 2 &#043; 1<br \/>\n         *  7 &#061; 3 * 2 &#043; 1<br \/>\n         *  &#8230;&#8230;..<br \/>\n         *  \u89c4\u5f8b\u4e8c<br \/>\n         *  7 \/ 2 &#061; 3<br \/>\n         *  15 \/ 2 &#061; 7<br \/>\n         * *\/<br \/>\n        int step &#061; 1;<br \/>\n\/\/\u5982\u679cstep\u7684\u6b65\u957f\u5927\u7b49\u4e8e\u4e86\u6570\u7ec4\u5168\u957f\u76841\/2 -&gt; \u90a3\u4e48\u6211\u6bcf\u4e00\u4e2a\u5206\u7ec4\u90fd\u53ea\u6709\u4e8c\u4e2a\u5143\u7d20,\u5373\u5e0c\u5c14\u589e\u91cf\u4e2d\u7684 n\/2<br \/>\n\/\/\u4f46\u662fHibbard\u589e\u91cf\u5e8f\u5217\u7684\u89c4\u5f8b\u5bfc\u81f4\u5f80\u5f80\u627e\u4e0d\u5230\u4e00\u4e2a\u7b49\u4e8e\u5168\u957f1\/2\u7684\u6570\u636e<br \/>\n\/\/\u6240\u4ee5\u8981\u5c06\u4e00\u5f00\u59cb\u7684step\u8bbe\u7f6e\u4e3a\u5927\u4e8e\u5168\u957f\u76841\/2\u7684\u6700\u5c0f\u89c4\u5f8b\u6570,\u518d\u5f00\u59cb\u8fdb\u884cstep\u6570\u636e\u7684\u8fed\u4ee3,\u5373step\u4ece\u591a\u5f80\u5c11\u6765<br \/>\n        while ((step * 2 &#043; 1) &lt;&#061; arrLength \/ 2) step &#061; (step * 2) &#043; 1;<br \/>\n        do {<br \/>\n            for (int i &#061; 0; i &lt; step; i&#043;&#043;) {<br \/>\n                sell_unguarded_insert_sort(arr, i, arrLength, step);<br \/>\n            }<br \/>\n            step \/&#061; 2;<br \/>\n        } while (step &gt; 1);<br \/>\n    } <\/p>\n<h3>\u56db.\u6027\u80fd\u6d4b\u8bd5<\/h3>\n<p>\u8bf7\u8f93\u5165\u8981\u6d4b\u8bd5\u7684\u6570\u7ec4\u957f\u5ea6(\u8d85\u8fc710\u4e0d\u6253\u5370):<br \/>\n1000<br \/>\n(\u5e0c\u5c14\u589e\u91cf)\u8fd0\u884c\u65f6\u95f4:1.0ms<br \/>\n(Hibbard)\u8fd0\u884c\u65f6\u95f4:0.0ms<\/p>\n<p>&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;<\/p>\n<p>\u8bf7\u8f93\u5165\u8981\u6d4b\u8bd5\u7684\u6570\u7ec4\u957f\u5ea6(\u8d85\u8fc710\u4e0d\u6253\u5370):<br \/>\n10000<br \/>\n(\u5e0c\u5c14\u589e\u91cf)\u8fd0\u884c\u65f6\u95f4:5.0ms<br \/>\n(Hibbard)\u8fd0\u884c\u65f6\u95f4:2.0ms<\/p>\n<p>&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;<\/p>\n<p>\u8bf7\u8f93\u5165\u8981\u6d4b\u8bd5\u7684\u6570\u7ec4\u957f\u5ea6(\u8d85\u8fc710\u4e0d\u6253\u5370):<br \/>\n100000<br \/>\n(\u5e0c\u5c14\u589e\u91cf)\u8fd0\u884c\u65f6\u95f4:25.0ms<br \/>\n(Hibbard)\u8fd0\u884c\u65f6\u95f4:17.0ms<\/p>\n<p>&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;<\/p>\n<p>\u8bf7\u8f93\u5165\u8981\u6d4b\u8bd5\u7684\u6570\u7ec4\u957f\u5ea6(\u8d85\u8fc710\u4e0d\u6253\u5370):<br \/>\n1000000<br \/>\n(\u5e0c\u5c14\u589e\u91cf)\u8fd0\u884c\u65f6\u95f4:157.0ms<br \/>\n(Hibbard)\u8fd0\u884c\u65f6\u95f4:186.0ms<\/p>\n<p>&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;<\/p>\n<p>\u8bf7\u8f93\u5165\u8981\u6d4b\u8bd5\u7684\u6570\u7ec4\u957f\u5ea6(\u8d85\u8fc710\u4e0d\u6253\u5370):<br \/>\n10000000<br \/>\n(\u5e0c\u5c14\u589e\u91cf)\u8fd0\u884c\u65f6\u95f4:2408.0ms<br \/>\n(Hibbard)\u8fd0\u884c\u65f6\u95f4:2921.0ms <\/p>\n<p>\u4ece\u6d4b\u8bd5\u6570\u636e\u53ef\u4ee5\u770b\u51fa&#xff0c;\u5728\u4e0d\u540c\u6570\u636e\u89c4\u6a21\u4e0b&#xff0c;Hibbard\u589e\u91cf\u5e8f\u5217\u548c\u5e0c\u5c14\u589e\u91cf\u5e8f\u5217\u7684\u8868\u73b0\u5b58\u5728\u5dee\u5f02&#xff1a;<\/p>\n<ul>\n<li>\n<p>\u5c0f\u89c4\u6a21\u6570\u636e&#xff08;10^3-10^5&#xff09;&#xff1a; Hibbard\u589e\u91cf&#xff08;1, 3, 7, 15&#8230;&#xff09;\u8fd0\u884c\u65f6\u95f4\u66f4\u77ed 1000\u5143\u7d20\u65f6\u5feb1.0ms&#xff0c;10000\u5143\u7d20\u65f6\u5feb3.0ms&#xff0c;100000\u5143\u7d20\u65f6\u5feb8.0ms<\/p>\n<\/li>\n<li>\n<p>\u5927\u89c4\u6a21\u6570\u636e&#xff08;10^6-10^7&#xff09;&#xff1a; \u5e0c\u5c14\u589e\u91cf&#xff08;n\/2, n\/4&#8230;&#xff09;\u53cd\u8d85 1000000\u5143\u7d20\u65f6\u5feb29.0ms&#xff0c;10000000\u5143\u7d20\u65f6\u5feb513.0ms<\/p>\n<\/li>\n<\/ul>\n<h4>1.\u6027\u80fd\u5dee\u5f02\u539f\u56e0<\/h4>\n<p>Hibbard\u589e\u91cf\u5728\u5c0f\u6570\u636e\u91cf\u7684\u4f18\u52bf&#xff1a;\u00a0\u589e\u91cf\u5e8f\u5217\u7684\u6570\u5b66\u6027\u8d28\u66f4\u4f18&#xff08;2^k-1&#xff09;&#xff0c;\u80fd\u51cf\u5c11\u65e0\u6548\u6bd4\u8f83\u6b21\u6570 \u5143\u7d20\u79fb\u52a8\u8ddd\u79bb\u66f4\u5408\u7406&#xff0c;\u6570\u636e\u5c40\u90e8\u6709\u5e8f\u6027\u5efa\u7acb\u66f4\u5feb<\/p>\n<p>\u5e0c\u5c14\u589e\u91cf\u5728\u5927\u6570\u636e\u91cf\u7684\u4f18\u52bf&#xff1a;\u00a0\u65e9\u671f\u589e\u91cf\u4e0b\u964d\u8f83\u6162&#xff08;n\/2\u5f00\u59cb&#xff09;&#xff0c;\u9002\u5408\u5927\u89c4\u6a21\u6570\u636e\u7684\u521d\u59cb\u7c97\u8c03 \u51cf\u5c11\u4e86\u5927\u89c4\u6a21\u6570\u636e\u65f6Hibbard\u589e\u91cf\u53ef\u80fd\u4ea7\u751f\u7684\u91cd\u590d\u5b50\u5e8f\u5217\u5904\u7406\u5f00\u9500<\/p>\n<h4>2.\u9009\u62e9\u5efa\u8bae<\/h4>\n<p>\u5904\u740610^5\u4ee5\u4e0b\u89c4\u6a21\u6570\u636e\u65f6\u4f18\u5148\u8003\u8651Hibbard\u589e\u91cf \u5904\u7406\u66f4\u5927\u89c4\u6a21\u6570\u636e\u65f6&#xff0c;\u5e0c\u5c14\u589e\u91cf\u6216Sedgewick\u589e\u91cf\u53ef\u80fd\u66f4\u5408\u9002<\/p>\n<p>\u5c3e.\u4e2a\u4eba\u60f3\u8bf4\u7684\u8bdd&#xff1a; \u00a0 \u00a0 \u00a0 \u00a0 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