{"id":151548,"date":"2020-08-27T05:18:12","date_gmt":"2020-08-26T21:18:12","guid":{"rendered":"http:\/\/4563.org\/?p=151548"},"modified":"2020-08-27T05:18:12","modified_gmt":"2020-08-26T21:18:12","slug":"leetcode-lintcode-%e9%a2%98%e8%a7%a3-%e8%83%8c%e5%8c%85%e9%97%ae%e9%a2%98","status":"publish","type":"post","link":"http:\/\/4563.org\/?p=151548","title":{"rendered":"[leetcode\/lintcode \u9898\u89e3] \u80cc\u5305\u95ee\u9898"},"content":{"rendered":"
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[leetcode\/lintcode \u9898\u89e3] \u80cc\u5305\u95ee\u9898 <\/h1>\n

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\u8cc7\u6df1\u5927\u4f6c : hakunamatata11 <\/span> <\/i> 15<\/span> <\/div>\n
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\u5728 n \u4e2a\u7269\u54c1\u4e2d\u6311\u9009\u82e5\u5e72\u7269\u54c1\u88c5\u5165\u80cc\u5305\uff0c\u6700\u591a\u80fd\u88c5\u591a\u6ee1\uff1f\u5047\u8bbe\u80cc\u5305\u7684\u5927\u5c0f\u4e3a m\uff0c\u6bcf\u4e2a\u7269\u54c1\u7684\u5927\u5c0f\u4e3a A[i]\u3002<\/p>\n

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  • \u4f60\u4e0d\u53ef\u4ee5\u5c06\u7269\u54c1\u8fdb\u884c\u5207\u5272\u3002<\/li>\n<\/ul>\n
    \u6837\u4f8b 1:  \u8f93\u5165:  [3,4,8,5], backpack size=10  \u8f93\u51fa:  9  \u6837\u4f8b 2:  \u8f93\u5165:  [2,3,5,7], backpack size=12  \u8f93\u51fa:  12 <\/code><\/pre>\n
    \u7b97\u6cd5\uff1aDP<\/strong><\/p>\n
    \u4ece\u5df2\u77e5\u7684\u9898\u76ee\u4e2d\uff0c\u53ef\u4ee5\u603b\u7ed3\u51fa\u4ee5\u4e0b\u4e24\u70b9\uff1a<\/p>\n
      \n
    • \u6bcf\u4ef6\u7269\u54c1\u53ea\u6709\u4e00\u79cd<\/li>\n
    • \u6bcf\u4ef6\u7269\u54c1\u6700\u591a\u9009\u62e9\u4e00\u6b21<\/li>\n<\/ul>\n
      \u90a3\u4e48\u8003\u8651\u5bf9\u4e8e\u524d i \u4ef6\u7684\u7269\u54c1\u5728\u5bb9\u91cf\u4e3a w \u7684\u80cc\u5305\u4e0b\uff0c\u6700\u5927\u7684\u88c5\u8f7d\u91cf\u662f\u591a\u5c11\uff0c\u7531\u6b64\u53ef\u4ee5\u603b\u7ed3\u51fa\u5bf9\u5e94\u7684\u5b50\u7ed3\u6784\uff0c\u8fdb\u884c\u52a8\u6001\u89c4\u5212\u3002<\/p>\n
      \u7b97\u6cd5\u601d\u8def<\/strong><\/p>\n
      \u8bbe\u8ba1 dp \u6570\u7ec4 dp[n][m]\uff0c\u7528 dp[i][j]\u8868\u793a\u7b2c i \u4e2a\u7269\u54c1\u5728\u5bb9\u91cf\u4e3a j \u7684\u80cc\u5305\u4e0b\uff0c\u6700\u5927\u7684\u88c5\u8f7d\u91cf\u3002<\/p>\n
      \u5728\u8fd9\u4e2a\u95ee\u9898\u4e2d\uff0c\u82e5\u53ea\u8003\u8651\u7b2c i \u4ef6\u7269\u54c1\u7684\u7b56\u7565\uff08\u653e\u6216\u4e0d\u653e\uff09\uff0c\u90a3\u4e48\u5c31\u53ef\u4ee5\u8f6c\u5316\u4e3a\u4e00\u4e2a\u53ea\u7275\u626f\u524d i\u22121 \u4ef6\u7269\u54c1\u7684\u95ee\u9898\uff1a<\/p>\n
        \n
      • \u5982\u679c\u4e0d\u653e\u7b2c i \u4ef6\u7269\u54c1\uff0c\u53ef\u5f97 dp[i][j]=dp[i\u22121][j]<\/li>\n
      • \u5982\u679c\u653e\u4e86\u7b2c i \u4ef6\u7269\u54c1\uff0c\u53ef\u5f97 dp[i][j]=dp[i\u22121][j\u2212A[i]]+Ai<\/li>\n<\/ul>\n
        \u603b\u7ed3\u72b6\u6001\u8f6c\u4e49\u65b9\u7a0b\u4e3a\uff1adp[i][j]=max(dp[i\u22121][j],dp[i\u22121][j\u2212A[i]]+A[i])<\/p>\n
        \u590d\u6742\u5ea6\u5206\u6790<\/strong><\/p>\n
        n \u8868\u793a\u7269\u54c1\u4ef6\u6570\uff0cm \u8868\u793a\u80cc\u5305\u5bb9\u91cf<\/p>\n
          \n
        • \u65f6\u95f4\u590d\u6742\u5ea6\uff1aO(nm)<\/li>\n
        • \u7a7a\u95f4\u590d\u6742\u5ea6\uff1aO(nm)<\/li>\n<\/ul>\n
          \u7b97\u6cd5\u4f18\u5316\u89c2\u5bdf\u4e0a\u65b9\u7684\u72b6\u6001\u8f6c\u4e49\u65b9\u7a0b\uff0c\u53ef\u4ee5\u53d1\u73b0 dp[i][j]\u65b9\u7a0b\u7684\u4e24\u4e2a\u72b6\u6001\u90fd\u53ea\u548c dp[i-1]\u6709\u5173\uff0c\u663e\u7136\u901a\u8fc7 O(nm)\u7684\u7a7a\u95f4\u590d\u6742\u5ea6\uff0c\u96be\u514d\u4f1a\u6d6a\u8d39\u4e00\u4e9b\u7a7a\u95f4\u3002<\/p>\n
          \u53ef\u4ee5\u8003\u8651\u4f7f\u7528\u6eda\u52a8\u6570\u7ec4\u4f18\u5316\uff0c\u5efa\u7acb dp \u6570\u7ec4 dp[m]\uff0c\u4f7f\u7528 dp[j-A[i]]\u4ee3\u66ff dp[i-1][j-A[i]]\u3002\u4f18\u5316\u540e\u72b6\u6001\u8f6c\u4e49\u65b9\u7a0b\u4e3a dp[j]=max(dp[j],dp[j\u2212A[i]]+A[i])<\/p>\n
          \u4f18\u5316\u540e\u590d\u6742\u5ea6\u5206\u6790<\/strong><\/p>\n
          \u65f6\u95f4\u590d\u6742\u5ea6\uff1aO(nm) \u7a7a\u95f4\u590d\u6742\u5ea6\uff1aO(m)<\/p>\n
          \u4ee3\u7801\u601d\u8def\u5206\u6790<\/strong><\/p>\n
            \n
          • \u5efa\u7acb\u6570\u7ec4 dp[m]\u8868\u793a\u80cc\u5305\u5bb9\u91cf\u4e3a m \u7684\u60c5\u51b5\u4e0b\uff0c\u6700\u5927\u7684\u88c5\u8f7d\u91cf<\/li>\n
          • \u521d\u59cb\u5316 dp[0]=0<\/li>\n
          • \u6b63\u5e8f\u679a\u4e3e A[i]\uff0c\u5e76\u5012\u53d9\u679a\u4e3e j\uff0c\u8fd9\u6837\u6240\u9700\u8981\u7684 dp[j-A[i]]\u4e0d\u4f1a\u88ab\u63d0\u524d\u66f4\u65b0<\/li>\n
          • \u6700\u540e\u8fd4\u56de dp[m]\uff0c\u8868\u793a\u80cc\u5305\u5bb9\u91cf\u5728 m \u4e0b\u7684\u7b54\u6848<\/li>\n<\/ul>\n
            public class Solution {     \/**      * @param m: An integer m denotes the size of a backpack      * @param A: Given n items with size A[i]      * @return: The maximum size      *\/     public int backPack(int m, int[] A) {         \/\/ write your code here         \/\/ \u5982\u679c\u80cc\u5305\u5bb9\u91cf\u6216\u8005\u7269\u54c1\u6570\u91cf\u4e3a 0\uff0c\u5219\u76f4\u63a5\u8fd4\u56de         if (A.length == 0 || m == 0) {             return 0;         }         int n = A.length;         int[] dp = new int[m + 1];         for (int i = 0; i < n; i++) {             \/\/ \u6eda\u52a8\u6570\u7ec4\u4f18\u5316 \u5012\u5e8f\u679a\u4e3e j             for (int j = m; j >= A[i]; j--) {                 dp[j] = Integer.max(dp[j], dp[j - A[i]] + A[i]);             }         }         return dp[m];     } } <\/code><\/pre>\n
            \u66f4\u591a\u5927\u5382\u9762\u8bd5\u52a8\u6001\u89c4\u5212\u9898\u89e3\u53c2\u89c1\uff1ahttps:\/\/www.jiuzhang.com\/course\/76\/?utm_source=sc-v2ex-fks<\/p>\n
            \u5b57\u8282\u6296\u97f3\u7ec4\u5927\u725b 2 \u5c0f\u65f6\u5256\u6790\u76ee\u524d\u5927\u70ed\u7684 [\u79d2\u6740\u7cfb\u7edf\u548c\u8ba2\u5355\u7cfb\u7edf] \uff0c\u901a\u8fc7\u5206\u6790\u9ad8\u5e76\u53d1\u573a\u666f\u4e0b\u7684\u5e38\u89c1\u95ee\u9898\u4e86\u89e3\u6570\u636e\u4e00\u81f4\u6027\uff0c\u4ec0\u4e48\u662f\u52a8\u9759\u5206\u79bb\uff0c\u8bfb\u5199\u5206\u79bb\u5982\u4f55\u5b9e\u73b0\uff0c\u5982\u4f55\u9632\u6b62\u8d85\u5356\u7b49\u79d2\u6740\u7cfb\u7edf\u8bbe\u8ba1\u7684\u6838\u5fc3\u8003\u70b9\u3002<\/p>\n
            \u8bfe\u7a0b\u4eae\u70b9<\/h2>\n
            \u901a\u8fc7\u79d2\u6740\u7cfb\u7edf\u548c\u8ba2\u7968\u7cfb\u7edf\u4e86\u89e3\u5982\u4e0b\u5185\u5bb9\uff1a<\/p>\n
              \n
            • \u9ad8\u5e76\u53d1\u573a\u666f\u4e0b\u5f15\u53d1\u7684\u5e38\u89c1\u95ee\u9898<\/li>\n
            • \u4e86\u89e3\u6570\u636e\u4e00\u81f4\u6027<\/li>\n
            • \u4ec0\u4e48\u662f\u52a8\u9759\u5206\u79bb<\/li>\n
            • \u8bfb\u5199\u5206\u79bb\u5982\u4f55\u5b9e\u73b0<\/li>\n
            • \u5982\u4f55\u9632\u6b62\u8d85\u5356<\/li>\n<\/ul>\n
              \u8bb2\u5e08\u4ecb\u7ecd<\/h2>\n
              \u897f\u6bd2\u2014\u2014\u5c31\u804c\u4e8e\u56fd\u5185\u4e00\u7ebf\u4e92\u8054\u7f51\u4f01\u4e1a\uff0c\u670d\u52a1\u4e8e\u4ebf\u7ea7\u65e5\u6d3b\u7528\u6237\u3002\u64c5\u957f\u540e\u7aef\u670d\u52a1\u5f00\u53d1\u548c\u67b6\u6784\u8bbe\u8ba1\u3002\u540c\u65f6\u6709\u4e30\u5bcc\u7684\u9762\u8bd5\u7ecf\u9a8c\uff0c\u9762\u8bd5\u8fc7\u8fd1\u767e\u4f4d\u5019\u9009\u4eba\u3002<\/p>\n
              \u8bb2\u5ea7\u65f6\u95f4\uff1a8\/22 \uff08\u672c\u5468\u516d\uff09\u4e0a\u5348 10:00:00<\/h2>\n
              \u62a5\u540d\u65b9\u5f0f:<\/h2>\n
              \n
              \u6233\u6211\u5373\u53ef\u62a5\u540d<\/p>\n<\/blockquote><\/div>\n
               \u5927\u4f6c\u6709\u8a71\u8aaa<\/b> (0<\/span>)        <\/div>\n
               <\/div>\n<\/p><\/div>\n<\/p><\/div>\n
                \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\/151548"}],"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=151548"}],"version-history":[{"count":0,"href":"http:\/\/4563.org\/index.php?rest_route=\/wp\/v2\/posts\/151548\/revisions"}],"wp:attachment":[{"href":"http:\/\/4563.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=151548"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/4563.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=151548"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/4563.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=151548"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}