{"id":156625,"date":"2020-09-17T15:10:07","date_gmt":"2020-09-17T07:10:07","guid":{"rendered":"http:\/\/4563.org\/?p=156625"},"modified":"2020-09-17T15:10:07","modified_gmt":"2020-09-17T07:10:07","slug":"leetcode-lintcode-%e9%a2%98%e8%a7%a3-n-%e7%9a%87%e5%90%8e%e9%97%ae%e9%a2%98","status":"publish","type":"post","link":"http:\/\/4563.org\/?p=156625","title":{"rendered":"[leetcode\/lintcode \u9898\u89e3] N \u7687\u540e\u95ee\u9898"},"content":{"rendered":"
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[leetcode\/lintcode \u9898\u89e3] N \u7687\u540e\u95ee\u9898 <\/h1>\n

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\u8cc7\u6df1\u5927\u4f6c : zzzrf <\/span> <\/i> 0<\/span> <\/div>\n
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n \u7687\u540e\u95ee\u9898\u662f\u5c06 n \u4e2a\u7687\u540e\u653e\u7f6e\u5728 n*n \u7684\u68cb\u76d8\u4e0a\uff0c\u7687\u540e\u5f7c\u6b64\u4e4b\u95f4\u4e0d\u80fd\u76f8\u4e92\u653b\u51fb(\u4efb\u610f\u4e24\u4e2a\u7687\u540e\u4e0d\u80fd\u4f4d\u4e8e\u540c\u4e00\u884c\uff0c\u540c\u4e00\u5217\uff0c\u540c\u4e00\u659c\u7ebf)\u3002<\/p>\n

\u7ed9\u5b9a\u4e00\u4e2a\u6574\u6570 n\uff0c\u8fd4\u56de\u6240\u6709\u4e0d\u540c\u7684 n \u7687\u540e\u95ee\u9898\u7684\u89e3\u51b3\u65b9\u6848\u3002<\/p>\n

\u6bcf\u4e2a\u89e3\u51b3\u65b9\u6848\u5305\u542b\u4e00\u4e2a\u660e\u786e\u7684 n \u7687\u540e\u653e\u7f6e\u5e03\u5c40\uff0c\u5176\u4e2d\u201cQ\u201d\u548c\u201c.\u201d\u5206\u522b\u8868\u793a\u4e00\u4e2a\u5973\u738b\u548c\u4e00\u4e2a\u7a7a\u4f4d\u7f6e\u3002<\/p>\n

\u70b9\u6b64\u5904\u2192\u5728\u7ebf\u505a\u9898<\/p>\n

\u6837\u4f8b 1:<\/h2>\n
\u8f93\u5165:1 \u8f93\u51fa:    [[\"Q\"]] <\/code><\/pre>\n
\u6837\u4f8b 2:<\/h2>\n
\u8f93\u5165:4 \u8f93\u51fa: [   \/\/ Solution 1   [\".Q..\",    \"...Q\",    \"Q...\",    \"..Q.\"   ],   \/\/ Solution 2   [\"..Q.\",    \"Q...\",    \"...Q\",    \".Q..\"   ] ] <\/code><\/pre>\n
\u7b97\u6cd5\uff1adfs \uff08\u56de\u6eaf\u6cd5\uff09<\/h2>\n
\u9898\u76ee\u5206\u6790<\/h2>\n
\u8fd9\u4e2a\u95ee\u9898\u8981\u6c42\u628a n \u4e2a\u7687\u540e\u653e\u5728\u4e00\u4e2a nXn \u7684\u68cb\u76d8\u4e0a\uff0c\u4f7f\u5f97\u4efb\u4f55\u4e24\u4e2a\u7687\u540e\u90fd\u4e0d\u80fd\u76f8\u4e92\u653b\u51fb\uff0c\u5373\u5b83\u4eec\u4e0d\u80fd\u540c\u884c\uff0c\u4e0d\u80fd\u540c\u5217\uff0c\u4e5f\u4e0d\u80fd\u4f4d\u4e8e\u540c\u4e00\u6761\u5bf9\u89d2\u7ebf\u4e0a\u3002\u5bf9\u4e8e n=1\uff0c\u95ee\u9898\u7684\u89e3\u5f88\u7b80\u5355\uff0c\u800c\u4e14\u5f88\u5bb9\u6613\u770b\u51fa\u5bf9\u4e8e n=2 \u548c n=3 \u6765\u8bf4\uff0c\u8fd9\u4e2a\u95ee\u9898\u662f\u65e0\u89e3\u7684\u3002\u6240\u4ee5\u6211\u4eec\u8003\u8651 4 \u7687\u540e\u95ee\u9898\uff0c\u5e76\u7528\u56de\u6eaf\u6cd5\u5bf9\u5b83\u6c42\u89e3\u3002<\/p>\n
\u7b97\u6cd5\u601d\u8def<\/h2>\n
    \n
  • \u56e0\u4e3a\u6bcf\u4e2a\u7687\u540e\u90fd\u5fc5\u987b\u5206\u522b\u5360\u636e\u4e00\u884c\uff0c\u6211\u4eec\u9700\u8981\u505a\u7684\u4e0d\u8fc7\u662f\u68cb\u76d8\u4e0a\u7684\u6bcf\u4e2a\u7687\u540e\u5206\u914d\u4e00\u5217\u3002<\/li>\n
  • \u4e0b\u9762\u6211\u4eec\u7528 4 \u7687\u540e\u7684\u6c42\u89e3\u8fc7\u7a0b\u6765\u8bb2\u89e3\u7b97\u6cd5\u601d\u8def\uff1a \u4ece\u7a7a\u68cb\u76d8\u5f00\u59cb\uff0c\u7136\u540e\u628a\u7687\u540e 1 \u653e\u5230\u5b83\u6240\u5728\u884c\u7684\u7b2c-\u4e00\u4e2a\u53ef\u80fd\u4f4d\u7f6e\u4e0a\uff0c\u4e5f\u5c31\u662f\u7b2c\u4e00-\u884c\u7b2c\u4e00\u5217\u3002\u5bf9\u4e8e\u7687\u540e 2\uff0c\u5728\u7ecf\u8fc7\u7b2c-\u5217\u548c\u7b2c\u4e8c\u5217\u7684\u5931\u8d25\u5c1d\u8bd5\u4e4b\u540e\uff0c\u6211\u4eec\u628a\u5b83\u653e\u5728\u7b2c\u4e00\u4e2a\u53ef\u80fd\u7684\u4f4d\u7f6e\uff0c\u5c31\u662f\u683c\u5b50(2, 3)\uff0c\u4f4d\u4e8e\u7b2c\u4e8c\u884c\u7b2c\u4e09\u5217\u7684\u683c\u5b50\u3002\u8fd9\u88ab\u8bc1\u660e\u662f\u4e00\u4e2a\u6b7b\u80e1\u540c\uff0c\u56e0\u4e3a\u7687\u540e 3 \u5c06\u6ca1\u6709\u4f4d\u7f6e\u53ef\u653e\u3002\u6240\u4ee5\uff0c\u8be5\u7b97\u6cd5\u8fdb\u884c\u56de\u6eaf\uff0c\u628a\u7687\u540e 2 \u653e\u5728\u4e0b\u4e00\u4e2a\u53ef\u80fd\u4f4d\u7f6e(2,4)\u4e0a\u3002\u8fd9\u6837\u7687\u540e 3 \u5c31\u53ef\u4ee5\u653e\u5728(3, 2),\u8fd9\u88ab\u8bc1\u660e\u662f\u53e6\u4e00\u4e2a\u6b7b\u80e1\u540c\u3002\u8be5\u7b97\u6cd5\u7136\u540e\u5c31\u56de\u6eaf\u5230\u5e95\uff0c\u628a\u7687\u540e 1 \u79fb\u5230(1,2)\u3002 \u63a5\u7740\u7687\u540e 2 \u5230(2,4)\uff0c \u7687\u540e 3 \u5230(3,1)\uff0c \u800c\u7687\u540e 4 \u5230(4, 3)\uff0c \u8fd9\u5c31\u662f\u8be5\u95ee\u9898\u7684\u4e00\u4e2a\u89e3\u3002<\/li>\n
  • \u6574\u4e2a\u8fc7\u7a0b\u5b9e\u9645\u4e0a\u5c31\u662f\u4e00\u4e2a\u72b6\u6001\u6811\u7684\u904d\u5386\u8fc7\u7a0b<\/li>\n
  • \u4e0b\u56fe\u4e3a\u72b6\u6001\u6811 \"[leetcode\/lintcode<\/li>\n<\/ul>\n
    \u4ee3\u7801\u601d\u8def<\/h2>\n
      \n
    • \u6309\u884c\u6446\u653e\uff0c\u5728\u786e\u5b9a\u4e00\u4e2a\u7687\u540e\u5e94\u8be5\u6446\u7684\u5217\u65f6\uff0c\u9700\u8981\u68c0\u67e5\u5f53\u524d\u5217\u662f\u5426\u5408\u6cd5\uff0c\u5982\u679c\u5408\u6cd5\uff0c\u5219\u5c06\u7687\u540e\u653e\u7f6e\u5728\u5f53\u524d\u4f4d\u7f6e\uff0c\u5e76\u8fdb\u884c\u9012\u5f52\uff0c\u56de\u6eaf\u3002\u6bcf\u884c\u90fd\u6446\u6ee1\u7687\u540e\u65f6\uff0c\u5219\u4ea7\u751f\u4e86\u4e00\u79cd\u89e3\u6cd5\uff0c\u5c06\u6240\u6709\u89e3\u6cd5\u6536\u96c6\u5e76\u8fd4\u56de\u3002<\/li>\n
    • \u5408\u6cd5\u6027\u5224\u65ad\u65b9\u6cd5\uff1a\u5f53\u524d\u5c06\u8981\u6446\u653e\u7687\u540e\u7684\u4f4d\u7f6e\u548c\u5176\u4ed6\u5df2\u6446\u653e\u7687\u540e\u7684\u4f4d\u7f6e\u4e0d\u80fd\u5728\u540c\u4e00\u5217\uff0c\u4e14\u4e0d\u80fd\u5728\u540c\u4e00\u6761\u659c\u7ebf\u4e0a\u3002\u8fd9\u91cc\u5224\u65ad\u662f\u5426\u5728\u540c\u4e00\u6761\u659c\u7ebf\u4e0a\u53ef\u4ee5\u901a\u8fc7\u4e24\u4e2a\u7687\u540e\u7684\u4f4d\u7f6e\u6a2a\u5750\u6807\u4e4b\u5dee\u548c\u7eb5\u5750\u6807\u4e4b\u5dee\u7684\u7edd\u5bf9\u503c\u662f\u5426\u76f8\u7b49\u6765\u5224\u65ad\u3002<\/li>\n<\/ul>\n
      \u590d\u6742\u5ea6\u5206\u6790<\/h2>\n
        \n
      • \u7a7a\u95f4\u590d\u6742\u5ea6\uff1aO(N!)<\/li>\n
      • \u65f6\u95f4\u590d\u6742\u5ea6\uff1aO(N!)<\/li>\n
      • \u653e\u7f6e\u7b2c\u4e00\u4e2a\u7687\u540e\u6709 N \u79cd\u53ef\u80fd\uff0c\u653e\u7f6e\u4e24\u4e2a\u7687\u540e\u4e0d\u8d85\u8fc7 N(N-2)\u79cd\u53ef\u80fd\uff0c\u653e\u7f6e\u4e09\u4e2a\u7687\u540e\u4e0d\u8d85\u8fc7 N(N – 2)(N – 4)\u79cd\u53ef\u80fd \uff0c\u4ee5\u6b64\u7c7b\u63a8\u3002<\/li>\n<\/ul>\n
        class Solution {     \/**      * Get all distinct N-Queen solutions      * @param n: The number of queens      * @return: All distinct solutions      * For example, A string '...Q' shows a queen on forth position      *\/     List<List<String>> solveNQueens(int n) {         \/\/ result \u7528\u4e8e\u5b58\u50a8\u7b54\u6848         List<List<String>> results = new ArrayList<>();         if (n <= 0) {             return results;         }                  search(results, new ArrayList<Integer>(), n);         return results;     }          \/\/ search \u51fd\u6570\u4e3a\u641c\u7d22\u51fd\u6570\uff0cn \u8868\u793a\u5df2\u7ecf\u653e\u7f6e\u4e86 n \u4e2a\u7687\u540e\uff0ccols \u8868\u793a\u6bcf\u4e2a\u7687\u540e\u6240\u5728\u7684\u5217     private void search(List<List<String>> results, List<Integer> cols, int n) {         \/\/ \u82e5\u5df2\u7ecf\u653e\u7f6e\u4e86 n \u4e2a\u7687\u540e\u8868\u793a\u51fa\u73b0\u4e86\u4e00\u79cd\u89e3\u6cd5\uff0c\u7ed8\u5236\u540e\u52a0\u5165\u7b54\u6848 result         if (cols.size() == n) {             results.add(Draw(cols));             return;         }         \/\/ \u679a\u4e3e\u5f53\u524d\u7687\u540e\u653e\u7f6e\u7684\u5217\uff0c\u82e5\u4e0d\u5408\u6cd5\u5219\u8df3\u8fc7         for (int colIndex = 0; colIndex < n; colIndex++) {             if (!isValid(cols, colIndex)) {                 continue;             }             \/\/ \u82e5\u5408\u6cd5\u5219\u9012\u5f52\u679a\u4e3e\u4e0b\u4e00\u884c\u7684\u7687\u540e             cols.add(colIndex);             search(results, cols, n);             cols.remove(cols.size() - 1);         }     }          \/\/ isValid \u51fd\u6570\u4e3a\u5408\u6cd5\u6027\u5224\u65ad\u51fd\u6570     private boolean isValid(List<Integer> cols, int col) {         int row = cols.size();         for (int rowIndex = 0; rowIndex < cols.size(); rowIndex++) {             \/\/\u82e5\u6709\u5176\u4ed6\u7687\u540e\u5728\u540c\u4e00\u5217\u6216\u540c\u4e00\u659c\u7ebf\u4e0a\u5219\u4e0d\u5408\u6cd5             if (cols.get(rowIndex) == col) {                 return false;             }             if (row + col == rowIndex + cols.get(rowIndex)) {                 return false;             }             if (row - col == rowIndex - cols.get(rowIndex)) {                 return false;             }         }         return true;     }     \/\/ Draw \u51fd\u6570\u4e3a\u5c06 cols \u6570\u7ec4\u8f6c\u6362\u4e3a\u7b54\u6848\u7684\u7ed8\u5236\u51fd\u6570     private List<String> Draw(List<Integer> cols) {         List<String> result = new ArrayList<>();         for (int i = 0; i < cols.size(); i++) {             StringBuilder sb = new StringBuilder();             for (int j = 0; j < cols.size(); j++) {                 sb.append(j == cols.get(i) ? 'Q' : '.');             }             result.add(sb.toString());         }         return result;     } } <\/code><\/pre>\n
        \u66f4\u591a\u9898\u89e3\u53c2\u8003<\/p>\n<\/p><\/div>\n
         \u5927\u4f6c\u6709\u8a71\u8aaa<\/b> (1<\/span>)        <\/div>\n
         <\/div>\n<\/p><\/div>\n<\/p><\/div>\n
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        • \n
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           \u8cc7\u6df1\u5927\u4f6c : binxin <\/span>  <\/div>\n
           <\/i>            <\/span> <\/div>\n<\/p><\/div>\n
                                                                       \u597d\u6b79\u653e\u4e00\u4e2a\u4f4d\u8fd0\u7b97\u7684\u7248\u672c\u5427\uff1f
          \u9000\u4e00\u6b65\uff0c\u8003\u8651\u4e00\u4e0b\u5de6\u53f3\u5bf9\u79f0\u6027\uff0c\u81f3\u5c11\u51cf\u5c11\u4e00\u534a\u68c0\u7d22\u91cf\uff1f                                                            <\/div>\n<\/p><\/div>\n<\/li>\n
        • \n","protected":false},"excerpt":{"rendered":"
          [leetcode\/lintcod…<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[],"tags":[],"_links":{"self":[{"href":"http:\/\/4563.org\/index.php?rest_route=\/wp\/v2\/posts\/156625"}],"collection":[{"href":"http:\/\/4563.org\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/4563.org\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/4563.org\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/4563.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=156625"}],"version-history":[{"count":0,"href":"http:\/\/4563.org\/index.php?rest_route=\/wp\/v2\/posts\/156625\/revisions"}],"wp:attachment":[{"href":"http:\/\/4563.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=156625"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/4563.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=156625"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/4563.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=156625"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}