{"id":520,"date":"2015-05-07T00:26:57","date_gmt":"2015-05-06T16:26:57","guid":{"rendered":"https:\/\/www.yesybl.com\/?p=520"},"modified":"2015-05-11T12:18:21","modified_gmt":"2015-05-11T04:18:21","slug":"dijkstra%e7%ae%97%e6%b3%95%e8%af%a6%e8%a7%a3","status":"publish","type":"post","link":"https:\/\/www.yesybl.com\/?p=520","title":{"rendered":"Dijkstra\u7b97\u6cd5\u8be6\u89e3"},"content":{"rendered":"

Dijkstra\u7b97\u6cd5\uff0c\u4e2d\u6587\u7ffb\u8bd1\u4e3a\u8fea\u6770\u65af\u7279\u62c9\u7b97\u6cd5\uff0c\u662f\u5728\u5e26\u6743\u6709\u5411\u56feG = (V, W) \uff08V\u662f\u8282\u70b9\u7684\u96c6\u5408\uff0cW\u662f\u8fb9\u4e0a\u6743\u503c\u7684\u96c6\u5408\uff0c\u5728\u96c6\u5408W\u4e2d\uff0c\u4e0d\u76f4\u63a5\u76f8\u8fde\u7684\u8282\u70b9\u95f4\u7684\u8ddd\u79bb\u6807\u8bb0\u4e3a\u65e0\u7a77\u5927\uff09\u4e2d\u6c42\u67d0\u4e2a\u8282\u70b9\u5230\u5176\u4f59\u8282\u70b9\u4e4b\u95f4\u6700\u77ed\u8def\u5f84\u7684\u7ecf\u5178\u7b97\u6cd5\u3002\u8be5\u7b97\u6cd5\u7684\u6838\u5fc3\u601d\u60f3\u662f\u5c06\u56fe\u4e2d\u6240\u6709\u7684\u8282\u70b9\u5212\u5206\u4e3a2\u4e2a\u96c6\u5408\uff0c\u96c6\u5408S\u5305\u542b\u5df2\u7ecf\u627e\u5230\u6700\u77ed\u8def\u5f84\u7684\u8282\u70b9\uff0c\u96c6\u5408U\u5305\u542b\u5c1a\u672a\u627e\u5230\u6700\u77ed\u8def\u5f84\u7684\u8282\u70b9\u7684\u8ddd\u79bb\uff08\u521d\u59cb\u503c\u5168\u90e8\u8bbe\u5b9a\u4e3a\u65e0\u7a77\u5927\uff09\u3002\u4ece\u67d0\u4e00\u70b9v\u5f00\u59cb\u91c7\u7528\u5e7f\u5ea6\u4f18\u5148\u904d\u5386\u601d\u60f3\u5bf9\u56fe\u8fdb\u884c\u904d\u5386\uff0c\u6bcf\u627e\u5230\u4e00\u4e2a\u8282\u70b9\u7684\u6700\u77ed\u8def\u5f84\uff0c\u5c31\u5c06\u8be5\u8282\u70b9\u4ece\u96c6\u5408U\u4e2d\u79fb\u9664\uff0c\u5e76\u52a0\u5165\u5230\u96c6\u5408S\u4e2d\uff0c\u76f4\u5230\u6700\u540eU\u53d8\u4e3a\u7a7a\u96c6\uff0cS\u5305\u542b\u56fe\u4e2d\u6240\u6709\u7684\u8282\u70b9\u5230\u51fa\u53d1\u70b9\u7684\u6700\u5c0f\u8ddd\u79bb\u3002\u5728\u52a0\u5165\u7684\u8fc7\u7a0b\u4e2d\uff0c\u603b\u4fdd\u6301\u4ece\u6e90\u70b9v\u5230S\u4e2d\u5404\u9876\u70b9\u7684\u6700\u77ed\u8def\u5f84\u957f\u5ea6\u4e0d\u5927\u4e8e\u4ece\u6e90\u70b9v\u5230U\u4e2d\u4efb\u4f55\u9876\u70b9\u7684\u6700\u77ed\u8def\u5f84\u957f\u5ea6\u3002<\/span>\n\t<\/p>\n

Dijkstra\u7b97\u6cd5\u7684\u8fc7\u7a0b\uff1a\n<\/p>\n

    \n
  1. \u9009\u53d6\u67d0\u4e2a\u8282\u70b9v\u4f5c\u4e3a\u51fa\u53d1\u70b9\uff0c\u4ece\u51fa\u53d1\u70b9\u5230\u51fa\u53d1\u70b9\u8ddd\u79bb\u4e3a0\uff0c\u5373\u627e\u5230\u6700\u5c0f\u8def\u5f84\u3002\u5c06\u8be5\u51fa\u53d1\u70b9\u4ece\u96c6\u5408U\u4e2d\u79fb\u9664\u5e76\u52a0\u5165\u5230\u96c6\u5408S\u4e2d\u3002\n<\/li>\n
  2. \u5728\u96c6\u5408W\u4e2d\u67e5\u770b\u51fa\u53d1\u70b9v\u5230\u96c6\u5408U\u4e2d\u5404\u4e2a\u8282\u70b9\u7684\u8ddd\u79bb\u3002\u627e\u51fa\u8ddd\u79bb\u6700\u5c0f\u7684\u8282\u70b9k\uff08\u5230k\u7684\u6700\u77ed\u8def\u5f84\u627e\u5230\uff09\uff0c\u5c06k\u4ece\u96c6\u5408U\u4e2d\u79fb\u9664\u5e76\u52a0\u5165\u5230\u96c6\u5408S\u4e2d\u3002\n<\/li>\n
  3. \u4ee5k\u4f5c\u4e3a\u4e2d\u95f4\u70b9\uff0c\u5728W\u4e2d\u67e5\u770b\u4ecek\u5230U\u4e2d\u8282\u70b9m\u7684\u8ddd\u79bb\uff0c\u5982\u679cm\u5728W\u4e2d\u7684\u503c\u5c0f\u4e8em\u5728U\u4e2d\u7684\u503c\uff08k\u548cm\u76f4\u63a5\u8fde\u63a5\uff09\uff0c\u5c06m\u5728W\u4e2d\u7684\u503c\u4e0ek\u5728U\u4e2d\u7684\u503c\u76f8\u52a0\uff08\u4ecev\u51fa\u53d1\u7ecf\u8fc7k\u5230\u8fbem\u7684\u8ddd\u79bb\uff09\uff0c\u518d\u5c06\u76f8\u52a0\u7ed3\u679c\u4e0eW\u4e2dv\u5230m\u7684\u503c(v\u4e0d\u7ecf\u8fc7\u4e2d\u95f4\u70b9\u5230m\u7684\u8ddd\u79bb)\u5bf9\u6bd4\u5927\u5c0f\uff0c\u9009\u53d6\u8f83\u5c0f\u7684\u503c\u8ddf\u65b0k\u5728U\u4e2d\u7684\u6570\u636e\u3002\n<\/li>\n
  4. \u5728U\u4e2d\u627e\u51fa\u6570\u503c\u6700\u5c0f\u7684\u8282\u70b9n\uff0c\u8be5\u503c\u5373\u4e3av\u5230n\u7684\u6700\u77ed\u8def\u5f84\u3002\u5c06n\u4ece\u96c6\u5408U\u4e2d\u79fb\u9664\u5e76\u52a0\u5165\u5230\u96c6\u5408S\u4e2d\u3002\u628an\u4f5c\u4e3a\u4e2d\u95f4\u70b9\u91cd\u590d\u7b2c3\u30014\u6b65\uff0c\u76f4\u5230U\u4e2d\u6240\u6709\u7684\u8282\u70b9\u90fd\u79fb\u52a8\u5230S\u4e2d\u3002\n<\/li>\n<\/ol>\n

    \"\"\/\n\t<\/p>\n

    \u56fe1\n<\/p>\n

    Dijkstra\u7b97\u6cd5\u7684\u624b\u7b97\u65b9\u6cd5\n<\/p>\n

    \u5982\u56fe1\uff0c\u4ece\u8282\u70b9A\u5f00\u59cb\u3002\u9996\u5148\u6211\u4eec\u521b\u5efa\u4e00\u4e2a\u8868\uff0c\u7528\u8be5\u8868\u8bb0\u5f55\u6bcf\u6b21\u8fd0\u7b97\u7684\u503c\u3002\u8be5\u8868\u8868\u5934\u4ee3\u8868\u4e86\u96c6\u5408U\u4e2d\u5305\u542b\u7684\u8282\u70b9\uff08\u672a\u627e\u51fa\u6700\u77ed\u8def\u5f84\u8282\u70b9\uff1aA\u3001B\u3001C\u3001D\uff09\u3002\u7b2c\uff12\u884c\u5c06\u5404\u8282\u70b9\u7684\u8ddd\u79bb\uff0c\u521d\u59cb\u5316\u4e3a\u65e0\u7a77\u5927\uff0c\u7528INF\u8868\u793a\u3002<\/p>\n

    \n\n\n\n\n\n\n<\/colgroup>\n\n\n\n
    \u00a0<\/td>\n\n

    A<\/p>\n<\/td>\n

    		\n

    B<\/p>\n<\/td>\n

    		\n

    C<\/p>\n<\/td>\n

    		\n

    D<\/p>\n<\/td>\n<\/tr>\n

    \u00a0<\/td>\n\n

    INF<\/p>\n<\/td>\n

    		\n

    INF<\/p>\n<\/td>\n

    		\n

    INF<\/p>\n<\/td>\n

    		\n

    INF<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

    \n\u00a0<\/p>\n

    \u70b9A\u662f\u51fa\u53d1\u70b9\uff0c\u81ea\u8eab\u5230\u81ea\u8eab\u7684\u8def\u5f84\u6700\u77ed\uff0c\u4e3a0\uff0c\u5373A\u5230\uff21\u7684\u6700\u77ed\u8def\u5f84\u627e\u5230\u3002\u5728\uff21\u5217\u7684\u7b2c\uff12\u884c\u8f93\u5165\uff10\uff0c\u5e76\u7528\u4e0b\u5212\u7ebf\u6807\u51fa\uff0c\u8868\u660e\u5c06\uff21\u4ece\uff35\u4e2d\u79fb\u9664\u3002\u5728\u8868\u7684\u7b2c\uff12\u884c\u6700\u5de6\u4fa7\u5199A\uff0c\u8868\u793a\u5c06A\u52a0\u5165\u96c6\u5408S\u3002<\/p>\n

    \n\n\n\n\n\n\n<\/colgroup>\n\n\n\n
    \u00a0<\/td>\n\n

    A\u00a0<\/p>\n<\/td>\n

    		\n

    B<\/p>\n<\/td>\n

    		\n

    C<\/p>\n<\/td>\n

    		\n

    D<\/p>\n<\/td>\n<\/tr>\n

    \n

    A\u00a0<\/p>\n<\/td>\n

    		\n

    0<\/span><\/p>\n<\/td>\n

    		\n

    INF<\/p>\n<\/td>\n

    		\n

    INF<\/p>\n<\/td>\n

    		\n

    INF<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

    \u5efa\u7acb\u8868\u683c\u7b2c3\u884c\u3002\u6b64\u65f6\u96c6\u5408U\u4e2d\u5305\u542b{B\u3001C\u3001D}\uff0c\u7531\u56fe\u53ef\u77e5A->B\u7684\u8ddd\u79bb\u4e3a1\uff08\u67e5\u8be2\u96c6\u5408W\uff09\uff0c\u66f4\u65b0B\u5217\u7684\u6570\u503c\uff0c\u5199\u5165\u7b2c3\u884c\u3002\u7531\u56fe\u53ef\u77e5A->C\u7684\u8ddd\u79bb\u4e3a5\uff0c\u66f4\u65b0B\u5217\u7684\u6570\u503c\uff0c\u5199\u5165\u7b2c3\u884c\u3002\u7531\u56fe\u53ef\u77e5A->D\u4e0d\u53ef\u76f4\u8fbe\uff0c\u6807\u8bb0\u4e3aINF\u3002\u5728\u8868\u7b2c3\u884c\u4e2d\u5bf9\u96c6\u5408U\u4e2d\u6240\u62e5\u6709\u7684\u5143\u7d20{1\uff0c5\uff0cINF}\u6c42\u6700\u5c0f\u503c\uff0c\u5f97\u5230B\uff0c\u6b64\u65f6B\u5217\u7b2c3\u884c\u6570\u636e\u5373\u4e3aA->B\u7684\u6700\u5c0f\u8def\u5f84\u3002\u5bf9B\u5217\u7b2c3\u884c\u6570\u636e\u52a0\u4e0b\u5212\u7ebf\u6807\u8bc6\u51fa\uff0c\u5373\u5c06B\u79fb\u51fa\u96c6\u5408U\u3002\u540c\u65f6\u5728\u7b2c3\u884c\u6700\u5de6\u7aef\u5199B\uff0c\u5373\u5c06B\u52a0\u5165\u96c6\u5408S\u4e2d\u3002<\/p>\n

    \n\n\n\n\n\n\n<\/colgroup>\n\n\n\n\n
    \u00a0<\/td>\n\n

    A<\/p>\n<\/td>\n

    		\n

    B<\/p>\n<\/td>\n

    		\n

    C<\/p>\n<\/td>\n

    		\n

    D<\/p>\n<\/td>\n<\/tr>\n

    \n

    A\u00a0<\/p>\n<\/td>\n

    		\n

    0<\/span><\/p>\n<\/td>\n

    		\n

    INF<\/p>\n<\/td>\n

    		\n

    INF<\/p>\n<\/td>\n

    		\n

    INF<\/p>\n<\/td>\n<\/tr>\n

    \n

    B\u00a0<\/p>\n<\/td>\n

    		\n

    0<\/span><\/p>\n<\/td>\n

    		\n

    1<\/span><\/p>\n<\/td>\n

    		\n

    5<\/p>\n<\/td>\n

    		\n

    INF<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

    \u5efa\u7acb\u8868\u683c\u7b2c4\u884c\u3002\u6b64\u65f6\u96c6\u5408U\u4e2d\u5305\u542b{C\u3001D}\uff0c\u8282\u70b9B\u4e3a\u4e2d\u95f4\u70b9\u3002\u7531\u56fe\u53ef\u77e5B->C\u7684\u8ddd\u79bb\u4e3a1\uff0c\u800cA->B\u7684\u8ddd\u79bb\u4fdd\u5b58\u5728\u8868B\u5217\u4e2d\uff0c\u662f1\uff0c\u5219A->B->C\u7684\u8ddd\u79bb\u4e3a1+1=2\u3002\u7531\u8868C\u5217\u7b2c3\u884c\u6570\u636e\u53ef\u77e5\u76ee\u524d\u5230\u8fbeC\u7684\u8ddd\u79bb\u4e3a5\uff08A\u76f4\u63a5\u5230\u8fbeC\uff09\u3002\u6c42\u4e24\u6761\u8def\u5f84\u7684\u6700\u5c0f\u503cmin(5,1+1)=2;\u66f4\u65b0C\u5217\u6570\u636e\uff0c\u5c062\u5199\u5165C\u5217\u7b2c4\u884c\u3002\u7531\u56fe\u53ef\u77e5B->D\u70b9\u7684\u8ddd\u79bb\u4e3a1\uff0c\u5219A->B->D\u7684\u8ddd\u79bb\u4e3a1+1=2\uff0c\u800cA->D\u4e0d\u53ef\u76f4\u63a5\u62b5\u8fbe\uff0c\u6545\u800c\u53d6\u503c\u65e0\u7a77\u5927INF\uff08\u8be5\u503c\u8bb0\u5f55\u5728\u96c6\u5408W\u4e2d\uff0c\u6b64\u65f6\u8be5\u503c\u7b49\u4e8e\u8868\u4e2dD\u5217\u6570\u636e\uff09\u3002\u6c42\u4e24\u6761\u8def\u5f84\u7684\u6700\u5c0f\u503cmin(INF\uff0c1+1)=2\u3002\u66f4\u884cD\u5217\u6570\u636e\uff0c\u5c062\u5199\u5165\u5230D\u5217\u7b2c4\u884c\u3002\u5bf9\u96c6\u5408U\u4e2d\u7684\u6570\u636e\u53d6\u6700\u5c0f\u503c\uff0cC\u548cD\u5747\u4e3a2\uff0c\u4efb\u9009\u4e00\u4e2a\uff0c\u8be5\u8282\u70b9\u5230A\u7684\u6700\u77ed\u8ddd\u79bb\u5373\u88ab\u8ba1\u7b97\u51fa\u6765\u3002\u6bd4\u5982\u9009C\u3002\u5bf9C\u8fdb\u884c\u6807\u8bb0\u3002<\/p>\n

    \n\n\n\n\n\n\n<\/colgroup>\n\n\n\n\n\n
    \u00a0<\/td>\n\n

    A<\/p>\n<\/td>\n

    		\n

    B<\/p>\n<\/td>\n

    		\n

    C<\/p>\n<\/td>\n

    		\n

    D<\/p>\n<\/td>\n<\/tr>\n

    \n

    A<\/p>\n<\/td>\n

    		\n

    0<\/span><\/p>\n<\/td>\n

    		\n

    INF<\/p>\n<\/td>\n

    		\n

    INF<\/p>\n<\/td>\n

    		\n

    INF<\/p>\n<\/td>\n<\/tr>\n

    \n

    B<\/p>\n<\/td>\n

    		\n

    0<\/span><\/p>\n<\/td>\n

    		\n

    1<\/span><\/p>\n<\/td>\n

    		\n

    5<\/p>\n<\/td>\n

    		\n

    INF<\/p>\n<\/td>\n<\/tr>\n

    \n

    C<\/p>\n<\/td>\n

    		\n

    0<\/span><\/p>\n<\/td>\n

    		\n

    1<\/span><\/p>\n<\/td>\n

    		\n

    2<\/span><\/p>\n<\/td>\n

    		\n

    2<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

    \u91cd\u590d\u4e0a\u9762\u7684\u64cd\u4f5c\uff0c\u5efa\u7acb\u8868\u683c\u7b2c5\u884c\u3002\u6b64\u65f6\u96c6\u5408U\u4e2d\u53ea\u5305\u542b{D}\uff0c\u8282\u70b9C\u4e3a\u4e2d\u95f4\u70b9\u3002\u7531\u56fe\u53ef\u77e5C->D\u7684\u8ddd\u79bb\u4e3a1\u3002\u800cA->C\u7684\u6700\u77ed\u8ddd\u79bb\u5df2\u7ecf\u6c42\u51fa\uff0c\u5728\u4e0a\u8868\u4e2dC\u5217\u7b2c4\u884c\uff0c\u4e3a2\uff08\u7ecf\u8fc7\u8282\u70b9B\uff09\u3002\u6545A->B->C->D\u7684\u8ddd\u79bb\u4e3a2+1=3\u3002\u8868\u4e2dD\u5217\u7b2c4\u884c\u8bb0\u5f55\u5230\u8fbeD\u70b9\u7684\u6700\u5c0f\u8def\u5f84\u4e3a2\uff08\u901a\u8fc7B\u70b9\uff09\uff0c\u6c42\u4e24\u6761\u8def\u5f84\u7684\u6700\u5c0f\u503cmin(2,2+1)=2\u3002\u5373D\u70b9\u7684\u6700\u5c0f\u8def\u5f84\u4e3a2\uff0c\u5c062\u5199\u5165D\u5217\u7b2c5\u884c\u5e76\u5bf9D\u5217\u7b2c5\u884c\u8fdb\u884c\u6807\u8bb0\u3002\u6b64\u65f6\u96c6\u5408U\u4e3a\u7a7a\u96c6\uff0c\u96c6\u5408S\u4e2d\u7684\u5143\u7d20\u4e3a{A\u3001B\u3001C\u3001D}\uff0c\u8ba1\u7b97\u5b8c\u6bd5\u3002\u8868\u4e2d\u7b2c5\u884c\u6240\u8bb0\u5f55\u6570\u636e\u5373\u4e3aA\u70b9\u5230\u5404\u70b9\u7684\u6700\u5c0f\u8def\u5f84\u503c\u3002<\/p>\n

    \n\n\n\n\n\n\n<\/colgroup>\n\n\n\n\n\n\n
    \u00a0<\/td>\n\n

    A<\/p>\n<\/td>\n

    		\n

    B<\/p>\n<\/td>\n

    		\n

    C<\/p>\n<\/td>\n

    		\n

    D<\/p>\n<\/td>\n<\/tr>\n

    \n

    A<\/p>\n<\/td>\n

    		\n

    0<\/span><\/p>\n<\/td>\n

    		\n

    INF<\/p>\n<\/td>\n

    		\n

    INF<\/p>\n<\/td>\n

    		\n

    INF<\/p>\n<\/td>\n<\/tr>\n

    \n

    B<\/p>\n<\/td>\n

    		\n

    0<\/span><\/p>\n<\/td>\n

    		\n

    1<\/span><\/p>\n<\/td>\n

    		\n

    5<\/p>\n<\/td>\n

    		\n

    INF<\/p>\n<\/td>\n<\/tr>\n

    \n

    C<\/p>\n<\/td>\n

    		\n

    0<\/span><\/p>\n<\/td>\n

    		\n

    1<\/span><\/p>\n<\/td>\n

    		\n

    2<\/span><\/p>\n<\/td>\n

    		\n

    2<\/p>\n<\/td>\n<\/tr>\n

    \n

    D<\/p>\n<\/td>\n

    		\n

    0<\/span><\/p>\n<\/td>\n

    		\n

    1<\/span><\/p>\n<\/td>\n

    		\n

    2<\/span><\/p>\n<\/td>\n

    		\n

    2<\/span><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

    \n\u00a0<\/p>\n

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