{"id":103950,"date":"2020-02-20T20:34:22","date_gmt":"2020-02-20T12:34:22","guid":{"rendered":"http:\/\/4563.org\/?p=103950"},"modified":"2020-02-20T20:34:22","modified_gmt":"2020-02-20T12:34:22","slug":"%e5%9b%9e%e6%ba%af%e7%ae%97%e6%b3%95%e6%a1%86%e6%9e%b6%e8%af%a6%e8%a7%a3%e5%85%a8%e6%8e%92%e5%88%97%e5%92%8c-n-%e7%9a%87%e5%90%8e%e9%97%ae%e9%a2%98","status":"publish","type":"post","link":"http:\/\/4563.org\/?p=103950","title":{"rendered":"\u56de\u6eaf\u7b97\u6cd5\u6846\u67b6\u8be6\u89e3\u5168\u6392\u5217\u548c N \u7687\u540e\u95ee\u9898"},"content":{"rendered":"
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\u56de\u6eaf\u7b97\u6cd5\u6846\u67b6\u8be6\u89e3\u5168\u6392\u5217\u548c N \u7687\u540e\u95ee\u9898 <\/h1>\n

<\/p>\n

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\u8cc7\u6df1\u5927\u4f6c : fudonglai <\/span> <\/i> 59<\/span> <\/div>\n
<\/div>\n<\/p><\/div>\n<\/p><\/div>\n<\/p><\/div>\n
<\/p>\n

\u8fd9\u7bc7\u6587\u7ae0\u662f\u5f88\u4e45\u4e4b\u524d\u7684\u4e00\u7bc7\u300a\u56de\u6eaf\u7b97\u6cd5\u8be6\u89e3\u300b\u7684\u8fdb\u9636\u7248\uff0c\u4e4b\u524d\u90a3\u7bc7\u4e0d\u591f\u6e05\u695a\uff0c\u5c31\u4e0d\u5fc5\u770b\u4e86\uff0c\u770b\u8fd9\u7bc7\u5c31\u884c\u3002\u628a\u6846\u67b6\u7ed9\u4f60\u8bb2\u6e05\u695a\uff0c\u4f60\u4f1a\u53d1\u73b0\u56de\u6eaf\u7b97\u6cd5\u95ee\u9898\u90fd\u662f\u4e00\u4e2a\u5957\u8def\u3002<\/p>\n

\u5e9f\u8bdd\u4e0d\u591a\u8bf4\uff0c\u76f4\u63a5\u4e0a\u56de\u6eaf\u7b97\u6cd5\u6846\u67b6\u3002\u89e3\u51b3\u4e00\u4e2a\u56de\u6eaf\u95ee\u9898\uff0c\u5b9e\u9645\u4e0a\u5c31\u662f\u4e00\u4e2a\u51b3\u7b56\u6811\u7684\u904d\u5386\u8fc7\u7a0b<\/strong>\u3002\u4f60\u53ea\u9700\u8981\u601d\u8003 3 \u4e2a\u95ee\u9898\uff1a<\/p>\n

1\u3001\u8def\u5f84\uff1a\u4e5f\u5c31\u662f\u5df2\u7ecf\u505a\u51fa\u7684\u9009\u62e9\u3002<\/p>\n

2\u3001\u9009\u62e9\u5217\u8868\uff1a\u4e5f\u5c31\u662f\u4f60\u5f53\u524d\u53ef\u4ee5\u505a\u7684\u9009\u62e9\u3002<\/p>\n

3\u3001\u7ed3\u675f\u6761\u4ef6\uff1a\u4e5f\u5c31\u662f\u5230\u8fbe\u51b3\u7b56\u6811\u5e95\u5c42\uff0c\u65e0\u6cd5\u518d\u505a\u9009\u62e9\u7684\u6761\u4ef6\u3002<\/p>\n

\u5982\u679c\u4f60\u4e0d\u7406\u89e3\u8fd9\u4e09\u4e2a\u8bcd\u8bed\u7684\u89e3\u91ca\uff0c\u6ca1\u5173\u7cfb\uff0c\u6211\u4eec\u540e\u9762\u4f1a\u7528\u300c\u5168\u6392\u5217\u300d\u548c\u300c N \u7687\u540e\u95ee\u9898\u300d\u8fd9\u4e24\u4e2a\u7ecf\u5178\u7684\u56de\u6eaf\u7b97\u6cd5\u95ee\u9898\u6765\u5e2e\u4f60\u7406\u89e3\u8fd9\u4e9b\u8bcd\u8bed\u662f\u4ec0\u4e48\u610f\u601d\uff0c\u73b0\u5728\u4f60\u5148\u7559\u7740\u5370\u8c61\u3002<\/p>\n

\u4ee3\u7801\u65b9\u9762\uff0c\u56de\u6eaf\u7b97\u6cd5\u7684\u6846\u67b6\uff1a<\/p>\n

result = [] def backtrack(\u8def\u5f84, \u9009\u62e9\u5217\u8868):     if \u6ee1\u8db3\u7ed3\u675f\u6761\u4ef6:         result.add(\u8def\u5f84)         return          for \u9009\u62e9 in \u9009\u62e9\u5217\u8868:         \u505a\u9009\u62e9         backtrack(\u8def\u5f84, \u9009\u62e9\u5217\u8868)         \u64a4\u9500\u9009\u62e9 <\/code><\/pre>\n
\u5176\u6838\u5fc3\u5c31\u662f for \u5faa\u73af\u91cc\u9762\u7684\u9012\u5f52\uff0c\u5728\u9012\u5f52\u8c03\u7528\u4e4b\u524d\u300c\u505a\u9009\u62e9\u300d\uff0c\u5728\u9012\u5f52\u8c03\u7528\u4e4b\u540e\u300c\u64a4\u9500\u9009\u62e9\u300d<\/strong>\uff0c\u7279\u522b\u7b80\u5355\u3002<\/p>\n
\u4ec0\u4e48\u53eb\u505a\u9009\u62e9\u548c\u64a4\u9500\u9009\u62e9\u5462\uff0c\u8fd9\u4e2a\u6846\u67b6\u7684\u5e95\u5c42\u539f\u7406\u662f\u4ec0\u4e48\u5462\uff1f\u4e0b\u9762\u6211\u4eec\u5c31\u901a\u8fc7\u300c\u5168\u6392\u5217\u300d\u8fd9\u4e2a\u95ee\u9898\u6765\u89e3\u5f00\u4e4b\u524d\u7684\u7591\u60d1\uff0c\u8be6\u7ec6\u63a2\u7a76\u4e00\u4e0b\u5176\u4e2d\u7684\u5965\u5999\uff01<\/p>\n
\u4e00\u3001\u5168\u6392\u5217\u95ee\u9898<\/h3>\n
\u6211\u4eec\u5728\u9ad8\u4e2d\u7684\u65f6\u5019\u5c31\u505a\u8fc7\u6392\u5217\u7ec4\u5408\u7684\u6570\u5b66\u9898\uff0c\u6211\u4eec\u4e5f\u77e5\u9053 n<\/code> \u4e2a\u4e0d\u91cd\u590d\u7684\u6570\uff0c\u5168\u6392\u5217\u5171\u6709 n! \u4e2a\u3002<\/p>\n
PS\uff1a\u4e3a\u4e86\u7b80\u5355\u6e05\u6670\u8d77\u89c1\uff0c\u6211\u4eec\u8fd9\u6b21\u8ba8\u8bba\u7684\u5168\u6392\u5217\u95ee\u9898\u4e0d\u5305\u542b\u91cd\u590d\u7684\u6570\u5b57<\/strong>\u3002<\/p>\n
\u90a3\u4e48\u6211\u4eec\u5f53\u65f6\u662f\u600e\u4e48\u7a77\u4e3e\u5168\u6392\u5217\u7684\u5462\uff1f\u6bd4\u65b9\u8bf4\u7ed9\u4e09\u4e2a\u6570 [1,2,3]<\/code>\uff0c\u4f60\u80af\u5b9a\u4e0d\u4f1a\u65e0\u89c4\u5f8b\u5730\u4e71\u7a77\u4e3e\uff0c\u4e00\u822c\u662f\u8fd9\u6837\uff1a<\/p>\n
\u5148\u56fa\u5b9a\u7b2c\u4e00\u4f4d\u4e3a 1\uff0c\u7136\u540e\u7b2c\u4e8c\u4f4d\u53ef\u4ee5\u662f 2\uff0c\u90a3\u4e48\u7b2c\u4e09\u4f4d\u53ea\u80fd\u662f 3 \uff1b\u7136\u540e\u53ef\u4ee5\u628a\u7b2c\u4e8c\u4f4d\u53d8\u6210 3\uff0c\u7b2c\u4e09\u4f4d\u5c31\u53ea\u80fd\u662f 2 \u4e86\uff1b\u7136\u540e\u5c31\u53ea\u80fd\u53d8\u5316\u7b2c\u4e00\u4f4d\uff0c\u53d8\u6210 2\uff0c\u7136\u540e\u518d\u7a77\u4e3e\u540e\u4e24\u4f4d\u2026\u2026<\/p>\n
\u5176\u5b9e\u8fd9\u5c31\u662f\u56de\u6eaf\u7b97\u6cd5\uff0c\u6211\u4eec\u9ad8\u4e2d\u65e0\u5e08\u81ea\u901a\u5c31\u4f1a\u7528\uff0c\u6216\u8005\u6709\u7684\u540c\u5b66\u76f4\u63a5\u753b\u51fa\u5982\u4e0b\u8fd9\u68f5\u56de\u6eaf\u6811\uff1a<\/p>\n
\"\u56de\u6eaf\u7b97\u6cd5\u6846\u67b6\u8be6\u89e3\u5168\u6392\u5217\u548c<\/p>\n
\u53ea\u8981\u4ece\u6839\u904d\u5386\u8fd9\u68f5\u6811\uff0c\u8bb0\u5f55\u8def\u5f84\u4e0a\u7684\u6570\u5b57\uff0c\u5176\u5b9e\u5c31\u662f\u6240\u6709\u7684\u5168\u6392\u5217\u3002\u6211\u4eec\u4e0d\u59a8\u628a\u8fd9\u68f5\u6811\u79f0\u4e3a\u56de\u6eaf\u7b97\u6cd5\u7684\u300c\u51b3\u7b56\u6811\u300d<\/strong>\u3002<\/p>\n
\u4e3a\u5565\u8bf4\u8fd9\u662f\u51b3\u7b56\u6811\u5462\uff0c\u56e0\u4e3a\u4f60\u5728\u6bcf\u4e2a\u8282\u70b9\u4e0a\u5176\u5b9e\u90fd\u5728\u505a\u51b3\u7b56<\/strong>\u3002\u6bd4\u5982\u8bf4\u4f60\u7ad9\u5728\u4e0b\u56fe\u7684\u7ea2\u8272\u8282\u70b9\u4e0a\uff1a<\/p>\n
\"\u56de\u6eaf\u7b97\u6cd5\u6846\u67b6\u8be6\u89e3\u5168\u6392\u5217\u548c<\/p>\n
\u4f60\u73b0\u5728\u5c31\u5728\u505a\u51b3\u7b56\uff0c\u53ef\u4ee5\u9009\u62e9 1 \u90a3\u6761\u6811\u679d\uff0c\u4e5f\u53ef\u4ee5\u9009\u62e9 3 \u90a3\u6761\u6811\u679d\u3002\u4e3a\u5565\u53ea\u80fd\u5728 1 \u548c 3 \u4e4b\u4e2d\u9009\u62e9\u5462\uff1f\u56e0\u4e3a 2 \u8fd9\u4e2a\u6811\u679d\u5728\u4f60\u8eab\u540e\uff0c\u8fd9\u4e2a\u9009\u62e9\u4f60\u4e4b\u524d\u505a\u8fc7\u4e86\uff0c\u800c\u5168\u6392\u5217\u662f\u4e0d\u5141\u8bb8\u91cd\u590d\u4f7f\u7528\u6570\u5b57\u7684\u3002<\/p>\n
\u73b0\u5728\u53ef\u4ee5\u89e3\u7b54\u5f00\u5934\u7684\u51e0\u4e2a\u540d\u8bcd\uff1a[2]<\/code> \u5c31\u662f\u300c\u8def\u5f84\u300d\uff0c\u8bb0\u5f55\u4f60\u5df2\u7ecf\u505a\u8fc7\u7684\u9009\u62e9\uff1b[1,3]<\/code> \u5c31\u662f\u300c\u9009\u62e9\u5217\u8868\u300d\uff0c\u8868\u793a\u4f60\u5f53\u524d\u53ef\u4ee5\u505a\u51fa\u7684\u9009\u62e9\uff1b\u300c\u7ed3\u675f\u6761\u4ef6\u300d\u5c31\u662f\u904d\u5386\u5230\u6811\u7684\u5e95\u5c42\uff0c\u5728\u8fd9\u91cc\u5c31\u662f\u9009\u62e9\u5217\u8868\u4e3a\u7a7a\u7684\u65f6\u5019<\/strong>\u3002<\/p>\n
\u5982\u679c\u660e\u767d\u4e86\u8fd9\u51e0\u4e2a\u540d\u8bcd\uff0c\u53ef\u4ee5\u628a\u300c\u8def\u5f84\u300d\u548c\u300c\u9009\u62e9\u300d\u5217\u8868\u4f5c\u4e3a\u51b3\u7b56\u6811\u4e0a\u6bcf\u4e2a\u8282\u70b9\u7684\u5c5e\u6027<\/strong>\uff0c\u6bd4\u5982\u4e0b\u56fe\u5217\u51fa\u4e86\u51e0\u4e2a\u8282\u70b9\u7684\u5c5e\u6027\uff1a<\/p>\n
\"\u56de\u6eaf\u7b97\u6cd5\u6846\u67b6\u8be6\u89e3\u5168\u6392\u5217\u548c<\/p>\n
\u6211\u4eec\u5b9a\u4e49\u7684 backtrack<\/code> \u51fd\u6570\u5176\u5b9e\u5c31\u50cf\u4e00\u4e2a\u6307\u9488\uff0c\u5728\u8fd9\u68f5\u6811\u4e0a\u6e38\u8d70\uff0c\u540c\u65f6\u8981\u6b63\u786e\u7ef4\u62a4\u6bcf\u4e2a\u8282\u70b9\u7684\u5c5e\u6027\uff0c\u6bcf\u5f53\u8d70\u5230\u6811\u7684\u5e95\u5c42\uff0c\u5176\u300c\u8def\u5f84\u300d\u5c31\u662f\u4e00\u4e2a\u5168\u6392\u5217<\/strong>\u3002<\/p>\n
\u518d\u8fdb\u4e00\u6b65\uff0c\u5982\u4f55\u904d\u5386\u4e00\u68f5\u6811\uff1f\u8fd9\u4e2a\u5e94\u8be5\u4e0d\u96be\u5427\u3002\u56de\u5fc6\u4e00\u4e0b\u4e4b\u524d\u300c\u5b66\u4e60\u6570\u636e\u7ed3\u6784\u7684\u6846\u67b6\u601d\u7ef4\u300d\u5199\u8fc7\uff0c\u5404\u79cd\u641c\u7d22\u95ee\u9898\u5176\u5b9e\u90fd\u662f\u6811\u7684\u904d\u5386\u95ee\u9898\uff0c\u800c\u591a\u53c9\u6811\u7684\u904d\u5386\u6846\u67b6\u5c31\u662f\u8fd9\u6837\uff1a<\/p>\n
void traverse(TreeNode root) {     for (TreeNode child : root.childern)         \/\/ \u524d\u5e8f\u904d\u5386\u9700\u8981\u7684\u64cd\u4f5c         traverse(child);         \/\/ \u540e\u5e8f\u904d\u5386\u9700\u8981\u7684\u64cd\u4f5c } <\/code><\/pre>\n
\u800c\u6240\u8c13\u7684\u524d\u5e8f\u904d\u5386\u548c\u540e\u5e8f\u904d\u5386\uff0c\u4ed6\u4eec\u53ea\u662f\u4e24\u4e2a\u5f88\u6709\u7528\u7684\u65f6\u95f4\u70b9\uff0c\u6211\u7ed9\u4f60\u753b\u5f20\u56fe\u4f60\u5c31\u660e\u767d\u4e86\uff1a<\/p>\n
\"\u56de\u6eaf\u7b97\u6cd5\u6846\u67b6\u8be6\u89e3\u5168\u6392\u5217\u548c<\/p>\n
\u524d\u5e8f\u904d\u5386\u7684\u4ee3\u7801\u5728\u8fdb\u5165\u67d0\u4e00\u4e2a\u8282\u70b9\u4e4b\u524d\u7684\u90a3\u4e2a\u65f6\u95f4\u70b9\u6267\u884c\uff0c\u540e\u5e8f\u904d\u5386\u4ee3\u7801\u5728\u79bb\u5f00\u67d0\u4e2a\u8282\u70b9\u4e4b\u540e\u7684\u90a3\u4e2a\u65f6\u95f4\u70b9\u6267\u884c<\/strong>\u3002<\/p>\n
\u56de\u60f3\u6211\u4eec\u521a\u624d\u8bf4\u7684\uff0c\u300c\u8def\u5f84\u300d\u548c\u300c\u9009\u62e9\u300d\u662f\u6bcf\u4e2a\u8282\u70b9\u7684\u5c5e\u6027\uff0c\u51fd\u6570\u5728\u6811\u4e0a\u6e38\u8d70\u8981\u6b63\u786e\u7ef4\u62a4\u8282\u70b9\u7684\u5c5e\u6027\uff0c\u90a3\u4e48\u5c31\u8981\u5728\u8fd9\u4e24\u4e2a\u7279\u6b8a\u65f6\u95f4\u70b9\u641e\u70b9\u52a8\u4f5c\uff1a<\/p>\n
\"\u56de\u6eaf\u7b97\u6cd5\u6846\u67b6\u8be6\u89e3\u5168\u6392\u5217\u548c<\/p>\n
\u73b0\u5728\uff0c\u4f60\u662f\u5426\u7406\u89e3\u4e86\u56de\u6eaf\u7b97\u6cd5\u7684\u8fd9\u6bb5\u6838\u5fc3\u6846\u67b6\uff1f<\/p>\n
for \u9009\u62e9 in \u9009\u62e9\u5217\u8868:     # \u505a\u9009\u62e9     \u5c06\u8be5\u9009\u62e9\u4ece\u9009\u62e9\u5217\u8868\u79fb\u9664     \u8def\u5f84.add(\u9009\u62e9)     backtrack(\u8def\u5f84, \u9009\u62e9\u5217\u8868)     # \u64a4\u9500\u9009\u62e9     \u8def\u5f84.remove(\u9009\u62e9)     \u5c06\u8be5\u9009\u62e9\u518d\u52a0\u5165\u9009\u62e9\u5217\u8868 <\/code><\/pre>\n
\u6211\u4eec\u53ea\u8981\u5728\u9012\u5f52\u4e4b\u524d\u505a\u51fa\u9009\u62e9\uff0c\u5728\u9012\u5f52\u4e4b\u540e\u64a4\u9500\u521a\u624d\u7684\u9009\u62e9<\/strong>\uff0c\u5c31\u80fd\u6b63\u786e\u5f97\u5230\u6bcf\u4e2a\u8282\u70b9\u7684\u9009\u62e9\u5217\u8868\u548c\u8def\u5f84\u3002<\/p>\n
\u4e0b\u9762\uff0c\u76f4\u63a5\u770b\u5168\u6392\u5217\u4ee3\u7801\uff1a<\/p>\n
List<List<Integer>> res = new LinkedList<>();  \/* \u4e3b\u51fd\u6570\uff0c\u8f93\u5165\u4e00\u7ec4\u4e0d\u91cd\u590d\u7684\u6570\u5b57\uff0c\u8fd4\u56de\u5b83\u4eec\u7684\u5168\u6392\u5217 *\/ List<List<Integer>> permute(int[] nums) {     \/\/ \u8bb0\u5f55\u300c\u8def\u5f84\u300d     LinkedList<Integer> track = new LinkedList<>();     backtrack(nums, track);     return res; }  \/\/ \u8def\u5f84\uff1a\u8bb0\u5f55\u5728 track \u4e2d \/\/ \u9009\u62e9\u5217\u8868\uff1anums \u4e2d\u4e0d\u5b58\u5728\u4e8e track \u7684\u90a3\u4e9b\u5143\u7d20 \/\/ \u7ed3\u675f\u6761\u4ef6\uff1anums \u4e2d\u7684\u5143\u7d20\u5168\u90fd\u5728 track \u4e2d\u51fa\u73b0 void backtrack(int[] nums, LinkedList<Integer> track) {     \/\/ \u89e6\u53d1\u7ed3\u675f\u6761\u4ef6     if (track.size() == nums.length) {         res.add(new LinkedList(track));         return;     }          for (int i = 0; i < nums.length; i++) {         \/\/ \u6392\u9664\u4e0d\u5408\u6cd5\u7684\u9009\u62e9         if (track.contains(nums[i]))             continue;         \/\/ \u505a\u9009\u62e9         track.add(nums[i]);         \/\/ \u8fdb\u5165\u4e0b\u4e00\u5c42\u51b3\u7b56\u6811         backtrack(nums, track);         \/\/ \u53d6\u6d88\u9009\u62e9         track.removeLast();     } } <\/code><\/pre>\n
\u6211\u4eec\u8fd9\u91cc\u7a0d\u5fae\u505a\u4e86\u4e9b\u53d8\u901a\uff0c\u6ca1\u6709\u663e\u5f0f\u8bb0\u5f55\u300c\u9009\u62e9\u5217\u8868\u300d\uff0c\u800c\u662f\u901a\u8fc7 nums<\/code> \u548c track<\/code> \u63a8\u5bfc\u51fa\u5f53\u524d\u7684\u9009\u62e9\u5217\u8868\uff1a<\/p>\n
\"\u56de\u6eaf\u7b97\u6cd5\u6846\u67b6\u8be6\u89e3\u5168\u6392\u5217\u548c<\/p>\n
\u81f3\u6b64\uff0c\u6211\u4eec\u5c31\u901a\u8fc7\u5168\u6392\u5217\u95ee\u9898\u8be6\u89e3\u4e86\u56de\u6eaf\u7b97\u6cd5\u7684\u5e95\u5c42\u539f\u7406\u3002\u5f53\u7136\uff0c\u8fd9\u4e2a\u7b97\u6cd5\u89e3\u51b3\u5168\u6392\u5217\u4e0d\u662f\u5f88\u9ad8\u6548\uff0c\u5e94\u4e3a\u5bf9\u94fe\u8868\u4f7f\u7528 contains<\/code> \u65b9\u6cd5\u9700\u8981 O(N) \u7684\u65f6\u95f4\u590d\u6742\u5ea6\u3002\u6709\u66f4\u597d\u7684\u65b9\u6cd5\u901a\u8fc7\u4ea4\u6362\u5143\u7d20\u8fbe\u5230\u76ee\u7684\uff0c\u4f46\u662f\u96be\u7406\u89e3\u4e00\u4e9b\uff0c\u8fd9\u91cc\u5c31\u4e0d\u5199\u4e86\uff0c\u6709\u5174\u8da3\u53ef\u4ee5\u81ea\u884c\u641c\u7d22\u4e00\u4e0b\u3002<\/p>\n
\u4f46\u662f\u5fc5\u987b\u8bf4\u660e\u7684\u662f\uff0c\u4e0d\u7ba1\u600e\u4e48\u4f18\u5316\uff0c\u90fd\u7b26\u5408\u56de\u6eaf\u6846\u67b6\uff0c\u800c\u4e14\u65f6\u95f4\u590d\u6742\u5ea6\u90fd\u4e0d\u53ef\u80fd\u4f4e\u4e8e O(N!)\uff0c\u56e0\u4e3a\u7a77\u4e3e\u6574\u68f5\u51b3\u7b56\u6811\u662f\u65e0\u6cd5\u907f\u514d\u7684\u3002\u8fd9\u4e5f\u662f\u56de\u6eaf\u7b97\u6cd5\u7684\u4e00\u4e2a\u7279\u70b9\uff0c\u4e0d\u50cf\u52a8\u6001\u89c4\u5212\u5b58\u5728\u91cd\u53e0\u5b50\u95ee\u9898\u53ef\u4ee5\u4f18\u5316\uff0c\u56de\u6eaf\u7b97\u6cd5\u5c31\u662f\u7eaf\u66b4\u529b\u7a77\u4e3e\uff0c\u590d\u6742\u5ea6\u4e00\u822c\u90fd\u5f88\u9ad8<\/strong>\u3002<\/p>\n
\u660e\u767d\u4e86\u5168\u6392\u5217\u95ee\u9898\uff0c\u5c31\u53ef\u4ee5\u76f4\u63a5\u5957\u56de\u6eaf\u7b97\u6cd5\u6846\u67b6\u4e86\uff0c\u4e0b\u9762\u7b80\u5355\u770b\u770b N \u7687\u540e\u95ee\u9898\u3002<\/p>\n
\u4e8c\u3001N \u7687\u540e\u95ee\u9898<\/h3>\n
\u8fd9\u4e2a\u95ee\u9898\u5f88\u7ecf\u5178\u4e86\uff0c\u7b80\u5355\u89e3\u91ca\u4e00\u4e0b\uff1a\u7ed9\u4f60\u4e00\u4e2a N\u00d7N \u7684\u68cb\u76d8\uff0c\u8ba9\u4f60\u653e\u7f6e N \u4e2a\u7687\u540e\uff0c\u4f7f\u5f97\u5b83\u4eec\u4e0d\u80fd\u4e92\u76f8\u653b\u51fb\u3002<\/p>\n
PS\uff1a\u7687\u540e\u53ef\u4ee5\u653b\u51fb\u540c\u4e00\u884c\u3001\u540c\u4e00\u5217\u3001\u5de6\u4e0a\u5de6\u4e0b\u53f3\u4e0a\u53f3\u4e0b\u56db\u4e2a\u65b9\u5411\u7684\u4efb\u610f\u5355\u4f4d\u3002<\/p>\n
\u8fd9\u4e2a\u95ee\u9898\u672c\u8d28\u4e0a\u8ddf\u5168\u6392\u5217\u95ee\u9898\u5dee\u4e0d\u591a\uff0c\u51b3\u7b56\u6811\u7684\u6bcf\u4e00\u5c42\u8868\u793a\u68cb\u76d8\u4e0a\u7684\u6bcf\u4e00\u884c\uff1b\u6bcf\u4e2a\u8282\u70b9\u53ef\u4ee5\u505a\u51fa\u7684\u9009\u62e9\u662f\uff0c\u5728\u8be5\u884c\u7684\u4efb\u610f\u4e00\u5217\u653e\u7f6e\u4e00\u4e2a\u7687\u540e\u3002<\/p>\n
\u76f4\u63a5\u5957\u7528\u6846\u67b6:<\/p>\n
vector<vector<string>> res;  \/* \u8f93\u5165\u68cb\u76d8\u8fb9\u957f n\uff0c\u8fd4\u56de\u6240\u6709\u5408\u6cd5\u7684\u653e\u7f6e *\/ vector<vector<string>> solveNQueens(int n) {     \/\/ '.' \u8868\u793a\u7a7a\uff0c'Q' \u8868\u793a\u7687\u540e\uff0c\u521d\u59cb\u5316\u7a7a\u68cb\u76d8\u3002     vector<string> board(n, string(n, '.'));     backtrack(board, 0);     return res; }  \/\/ \u8def\u5f84\uff1aboard \u4e2d\u5c0f\u4e8e row \u7684\u90a3\u4e9b\u884c\u90fd\u5df2\u7ecf\u6210\u529f\u653e\u7f6e\u4e86\u7687\u540e \/\/ \u9009\u62e9\u5217\u8868\uff1a\u7b2c row \u884c\u7684\u6240\u6709\u5217\u90fd\u662f\u653e\u7f6e\u7687\u540e\u7684\u9009\u62e9 \/\/ \u7ed3\u675f\u6761\u4ef6\uff1arow \u8d85\u8fc7 board \u7684\u6700\u540e\u4e00\u884c void backtrack(vector<string>& board, int row) {     \/\/ \u89e6\u53d1\u7ed3\u675f\u6761\u4ef6     if (row == board.size()) {         res.push_back(board);         return;     }          int n = board[row].size();     for (int col = 0; col < n; col++) {         \/\/ \u6392\u9664\u4e0d\u5408\u6cd5\u9009\u62e9         if (!isValid(board, row, col))              continue;         \/\/ \u505a\u9009\u62e9         board[row][col] = 'Q';         \/\/ \u8fdb\u5165\u4e0b\u4e00\u884c\u51b3\u7b56         backtrack(board, row + 1);         \/\/ \u64a4\u9500\u9009\u62e9         board[row][col] = '.';     } } <\/code><\/pre>\n
\u8fd9\u90e8\u5206\u4e3b\u8981\u4ee3\u7801\uff0c\u5176\u5b9e\u8ddf\u5168\u6392\u5217\u95ee\u9898\u5dee\u4e0d\u591a\uff0cisValid<\/code> \u51fd\u6570\u7684\u5b9e\u73b0\u4e5f\u5f88\u7b80\u5355\uff1a<\/p>\n
\/* \u662f\u5426\u53ef\u4ee5\u5728 board[row][col] \u653e\u7f6e\u7687\u540e\uff1f *\/ bool isValid(vector<string>& board, int row, int col) {     int n = board.size();     \/\/ \u68c0\u67e5\u5217\u662f\u5426\u6709\u7687\u540e\u4e92\u76f8\u51b2\u7a81     for (int i = 0; i < n; i++) {         if (board[i][col] == 'Q')             return false;     }     \/\/ \u68c0\u67e5\u53f3\u4e0a\u65b9\u662f\u5426\u6709\u7687\u540e\u4e92\u76f8\u51b2\u7a81     for (int i = row - 1, j = col + 1;              i >= 0 && j < n; i--, j++) {         if (board[i][j] == 'Q')             return false;     }     \/\/ \u68c0\u67e5\u5de6\u4e0a\u65b9\u662f\u5426\u6709\u7687\u540e\u4e92\u76f8\u51b2\u7a81     for (int i = row - 1, j = col - 1;             i >= 0 && j >= 0; i--, j--) {         if (board[i][j] == 'Q')             return false;     }     return true; } <\/code><\/pre>\n
\u51fd\u6570 backtrack<\/code> \u4f9d\u7136\u50cf\u4e2a\u5728\u51b3\u7b56\u6811\u4e0a\u6e38\u8d70\u7684\u6307\u9488\uff0c\u901a\u8fc7 row<\/code> \u548c col<\/code> \u5c31\u53ef\u4ee5\u8868\u793a\u51fd\u6570\u904d\u5386\u5230\u7684\u4f4d\u7f6e\uff0c\u901a\u8fc7 isValid<\/code> \u51fd\u6570\u53ef\u4ee5\u5c06\u4e0d\u7b26\u5408\u6761\u4ef6\u7684\u60c5\u51b5\u526a\u679d\uff1a<\/p>\n
\"\u56de\u6eaf\u7b97\u6cd5\u6846\u67b6\u8be6\u89e3\u5168\u6392\u5217\u548c<\/p>\n
\u5982\u679c\u76f4\u63a5\u7ed9\u4f60\u8fd9\u4e48\u4e00\u5927\u6bb5\u89e3\u6cd5\u4ee3\u7801\uff0c\u53ef\u80fd\u662f\u61f5\u903c\u7684\u3002\u4f46\u662f\u73b0\u5728\u660e\u767d\u4e86\u56de\u6eaf\u7b97\u6cd5\u7684\u6846\u67b6\u5957\u8def\uff0c\u8fd8\u6709\u5565\u96be\u7406\u89e3\u7684\u5462\uff1f\u65e0\u975e\u662f\u6539\u6539\u505a\u9009\u62e9\u7684\u65b9\u5f0f\uff0c\u6392\u9664\u4e0d\u5408\u6cd5\u9009\u62e9\u7684\u65b9\u5f0f\u800c\u5df2\uff0c\u53ea\u8981\u6846\u67b6\u5b58\u4e8e\u5fc3\uff0c\u4f60\u9762\u5bf9\u7684\u53ea\u5269\u4e0b\u5c0f\u95ee\u9898\u4e86\u3002<\/p>\n
\u5f53 N = 8<\/code> \u65f6\uff0c\u5c31\u662f\u516b\u7687\u540e\u95ee\u9898\uff0c\u6570\u5b66\u5927\u4f6c\u9ad8\u65af\u7a77\u5c3d\u4e00\u751f\u90fd\u6ca1\u6709\u6570\u6e05\u695a\u516b\u7687\u540e\u95ee\u9898\u5230\u5e95\u6709\u51e0\u79cd\u53ef\u80fd\u7684\u653e\u7f6e\u65b9\u6cd5\uff0c\u4f46\u662f\u6211\u4eec\u7684\u7b97\u6cd5\u53ea\u9700\u8981\u4e00\u79d2\u5c31\u53ef\u4ee5\u7b97\u51fa\u6765\u6240\u6709\u53ef\u80fd\u7684\u7ed3\u679c\u3002<\/p>\n
\u4e0d\u8fc7\u771f\u7684\u4e0d\u602a\u9ad8\u65af\u3002\u8fd9\u4e2a\u95ee\u9898\u7684\u590d\u6742\u5ea6\u786e\u5b9e\u975e\u5e38\u9ad8\uff0c\u770b\u770b\u6211\u4eec\u7684\u51b3\u7b56\u6811\uff0c\u867d\u7136\u6709 isValid<\/code> \u51fd\u6570\u526a\u679d\uff0c\u4f46\u662f\u6700\u574f\u65f6\u95f4\u590d\u6742\u5ea6\u4ecd\u7136\u662f O(N^(N+1))\uff0c\u800c\u4e14\u65e0\u6cd5\u4f18\u5316\u3002\u5982\u679c N = 10<\/code> \u7684\u65f6\u5019\uff0c\u8ba1\u7b97\u5c31\u5df2\u7ecf\u5f88\u8017\u65f6\u4e86\u3002<\/p>\n
\u6709\u7684\u65f6\u5019\uff0c\u6211\u4eec\u5e76\u4e0d\u60f3\u5f97\u5230\u6240\u6709\u5408\u6cd5\u7684\u7b54\u6848\uff0c\u53ea\u60f3\u8981\u4e00\u4e2a\u7b54\u6848\uff0c\u600e\u4e48\u529e\u5462<\/strong>\uff1f\u6bd4\u5982\u89e3\u6570\u72ec\u7684\u7b97\u6cd5\uff0c\u627e\u6240\u6709\u89e3\u6cd5\u590d\u6742\u5ea6\u592a\u9ad8\uff0c\u53ea\u8981\u627e\u5230\u4e00\u79cd\u89e3\u6cd5\u5c31\u53ef\u4ee5\u3002<\/p>\n
\u5176\u5b9e\u7279\u522b\u7b80\u5355\uff0c\u53ea\u8981\u7a0d\u5fae\u4fee\u6539\u4e00\u4e0b\u56de\u6eaf\u7b97\u6cd5\u7684\u4ee3\u7801\u5373\u53ef\uff1a<\/p>\n
\/\/ \u51fd\u6570\u627e\u5230\u4e00\u4e2a\u7b54\u6848\u540e\u5c31\u8fd4\u56de true bool backtrack(vector<string>& board, int row) {     \/\/ \u89e6\u53d1\u7ed3\u675f\u6761\u4ef6     if (row == board.size()) {         res.push_back(board);         return true;     }     ...     for (int col = 0; col < n; col++) {         ...         board[row][col] = 'Q';          if (backtrack(board, row + 1))             return true;                  board[row][col] = '.';     }      return false; } <\/code><\/pre>\n
\u8fd9\u6837\u4fee\u6539\u540e\uff0c\u53ea\u8981\u627e\u5230\u4e00\u4e2a\u7b54\u6848\uff0cfor \u5faa\u73af\u7684\u540e\u7eed\u9012\u5f52\u7a77\u4e3e\u90fd\u4f1a\u88ab\u963b\u65ad\u3002\u4e5f\u8bb8\u4f60\u53ef\u4ee5\u5728 N \u7687\u540e\u95ee\u9898\u7684\u4ee3\u7801\u6846\u67b6\u4e0a\uff0c\u7a0d\u52a0\u4fee\u6539\uff0c\u5199\u4e00\u4e2a\u89e3\u6570\u72ec\u7684\u7b97\u6cd5\uff1f<\/p>\n
\u4e09\u3001\u6700\u540e\u603b\u7ed3<\/h3>\n
\u56de\u6eaf\u7b97\u6cd5\u5c31\u662f\u4e2a\u591a\u53c9\u6811\u7684\u904d\u5386\u95ee\u9898\uff0c\u5173\u952e\u5c31\u662f\u5728\u524d\u5e8f\u904d\u5386\u548c\u540e\u5e8f\u904d\u5386\u7684\u4f4d\u7f6e\u505a\u4e00\u4e9b\u64cd\u4f5c\uff0c\u7b97\u6cd5\u6846\u67b6\u5982\u4e0b\uff1a<\/p>\n
def backtrack(...):     for \u9009\u62e9 in \u9009\u62e9\u5217\u8868:         \u505a\u9009\u62e9         backtrack(...)         \u64a4\u9500\u9009\u62e9 <\/code><\/pre>\n
\u5199 backtrack<\/code> \u51fd\u6570\u65f6\uff0c\u9700\u8981\u7ef4\u62a4\u8d70\u8fc7\u7684\u300c\u8def\u5f84\u300d\u548c\u5f53\u524d\u53ef\u4ee5\u505a\u7684\u300c\u9009\u62e9\u5217\u8868\u300d\uff0c\u5f53\u89e6\u53d1\u300c\u7ed3\u675f\u6761\u4ef6\u300d\u65f6\uff0c\u5c06\u300c\u8def\u5f84\u300d\u8bb0\u5165\u7ed3\u679c\u96c6<\/strong>\u3002<\/p>\n
\u5176\u5b9e\u60f3\u60f3\u770b\uff0c\u56de\u6eaf\u7b97\u6cd5\u548c\u52a8\u6001\u89c4\u5212\u662f\u4e0d\u662f\u6709\u70b9\u50cf\u5462\uff1f\u6211\u4eec\u5728\u52a8\u6001\u89c4\u5212\u7cfb\u5217\u6587\u7ae0\u4e2d\u591a\u6b21\u5f3a\u8c03\uff0c\u52a8\u6001\u89c4\u5212\u7684\u4e09\u4e2a\u9700\u8981\u660e\u786e\u7684\u70b9\u5c31\u662f\u300c\u72b6\u6001\u300d\u300c\u9009\u62e9\u300d\u548c\u300c base case \u300d\uff0c\u662f\u4e0d\u662f\u5c31\u5bf9\u5e94\u7740\u8d70\u8fc7\u7684\u300c\u8def\u5f84\u300d\uff0c\u5f53\u524d\u7684\u300c\u9009\u62e9\u5217\u8868\u300d\u548c\u300c\u7ed3\u675f\u6761\u4ef6\u300d\uff1f<\/p>\n
\u67d0\u79cd\u7a0b\u5ea6\u4e0a\u8bf4\uff0c\u52a8\u6001\u89c4\u5212\u7684\u66b4\u529b\u6c42\u89e3\u9636\u6bb5\u5c31\u662f\u56de\u6eaf\u7b97\u6cd5\u3002\u53ea\u662f\u6709\u7684\u95ee\u9898\u5177\u6709\u91cd\u53e0\u5b50\u95ee\u9898\u6027\u8d28\uff0c\u53ef\u4ee5\u7528 dp table \u6216\u8005\u5907\u5fd8\u5f55\u4f18\u5316\uff0c\u5c06\u9012\u5f52\u6811\u5927\u5e45\u526a\u679d\uff0c\u8fd9\u5c31\u53d8\u6210\u4e86\u52a8\u6001\u89c4\u5212\u3002\u800c\u4eca\u5929\u7684\u4e24\u4e2a\u95ee\u9898\uff0c\u90fd\u6ca1\u6709\u91cd\u53e0\u5b50\u95ee\u9898\uff0c\u4e5f\u5c31\u662f\u56de\u6eaf\u7b97\u6cd5\u95ee\u9898\u4e86\uff0c\u590d\u6742\u5ea6\u975e\u5e38\u9ad8\u662f\u4e0d\u53ef\u907f\u514d\u7684\u3002<\/p>\n
\u5982\u679c\u672c\u6587\u5bf9\u4f60\u6709\u5e2e\u52a9\uff0c\u6b22\u8fce\u5173\u6ce8\u6211\u7684\u516c\u4f17\u53f7 labuladong\uff0c\u81f4\u529b\u4e8e\u628a\u7b97\u6cd5\u95ee\u9898\u8bb2\u6e05\u695a\uff5e<\/p>\n
\"\u56de\u6eaf\u7b97\u6cd5\u6846\u67b6\u8be6\u89e3\u5168\u6392\u5217\u548c<\/p>\n<\/p><\/div>\n
 \u5927\u4f6c\u6709\u8a71\u8aaa<\/b> (0<\/span>)        <\/div>\n
 <\/div>\n<\/p><\/div>\n<\/p><\/div>\n
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