{"id":44,"date":"2025-03-22T12:32:39","date_gmt":"2025-03-22T04:32:39","guid":{"rendered":"http:\/\/m.qzcy2.top\/?p=44"},"modified":"2025-03-23T01:20:29","modified_gmt":"2025-03-22T17:20:29","slug":"%e5%8a%a8%e6%80%81%e8%a7%84%e5%88%92dp%e7%bb%8f%e5%85%b8%e6%a8%a1%e6%9d%bf","status":"publish","type":"post","link":"https:\/\/m.qzcy2.top\/index.php\/2025\/03\/22\/%e5%8a%a8%e6%80%81%e8%a7%84%e5%88%92dp%e7%bb%8f%e5%85%b8%e6%a8%a1%e6%9d%bf\/","title":{"rendered":"\u52a8\u6001\u89c4\u5212dp\u7ecf\u5178\u6a21\u677f(\u57fa\u7840)"},"content":{"rendered":"

\u58f0\u660e\uff1a<\/h1>\n

\u672c\u6587\u4ec5\u4e3a\u4f5c\u8005\u4e3a\u4e86\u590d\u4e60\u800c\u5199\uff0c\u5e76\u975e\u4f5c\u4e3a\u6559\u7a0b\u4f7f\u7528\uff01<\/span><\/p>\n

\n

\u6590\u6ce2\u90a3\u5951\u7c7b\u578b<\/strong><\/h1>\n

\u901a\u5e38\u662f\u7ebf\u6027\u7684\uff0c\u72b6\u6001\u8f6c\u79fb\u4e3a\u76f8\u90bb\u5143\u7d20\u6216\u53d7\u5230\u9650\u5236\u7684\u90bb\u5143\u7d20<\/span><\/p>\n

1.\u4f7f\u7528\u6700\u5c0f\u82b1\u8d39\u722c\u697c\u68af<\/strong><\/h2>\n

n<=2 \u7279\u6b8a\u5904\u7406 \u5f53\u524d\u697c\u68af\u9636\u5c42\u53ef\u7531i-1\u6216i-2\u800c\u6765 \u63a8\u51fa\u72b6\u6001\u8f6c\u79fb\u65b9\u7a0b \uff1a\u00a0 f[i] = min(f[i - 1] + cost[i - 1] , f[i - 2] + cost[i - 2])<\/span><\/p>\n

\u9898\u76ee\u63cf\u8ff0\uff1a<\/p>\n

\u7ed9\u4f60\u4e00\u4e2a\u6574\u6570\u6570\u7ec4\u00a0cost<\/code>\u00a0\uff0c\u5176\u4e2d\u00a0cost[i]<\/code>\u00a0\u662f\u4ece\u697c\u68af\u7b2c\u00a0i<\/code>\u00a0\u4e2a\u53f0\u9636\u5411\u4e0a\u722c\u9700\u8981\u652f\u4ed8\u7684\u8d39\u7528\u3002\u4e00\u65e6\u4f60\u652f\u4ed8\u6b64\u8d39\u7528\uff0c\u5373\u53ef\u9009\u62e9\u5411\u4e0a\u722c\u4e00\u4e2a\u6216\u8005\u4e24\u4e2a\u53f0\u9636\u3002<\/p>\n

\u4f60\u53ef\u4ee5\u9009\u62e9\u4ece\u4e0b\u6807\u4e3a\u00a00<\/code>\u00a0\u6216\u4e0b\u6807\u4e3a\u00a01<\/code>\u00a0\u7684\u53f0\u9636\u5f00\u59cb\u722c\u697c\u68af\u3002<\/p>\n

\u8bf7\u4f60\u8ba1\u7b97\u5e76\u8fd4\u56de\u8fbe\u5230\u697c\u68af\u9876\u90e8\u7684\u6700\u4f4e\u82b1\u8d39\u3002<\/p>\n

\u793a\u4f8b\uff1a<\/span>\r\n\u8f93\u5165\uff1acost = [1,100,1,1,1,100,1,1,100,1]\r\n\u8f93\u51fa\uff1a6\r\n\u89e3\u91ca\uff1a\u4f60\u5c06\u4ece\u4e0b\u6807\u4e3a 0 \u7684\u53f0\u9636\u5f00\u59cb\u3002\r\n- \u652f\u4ed8 1 \uff0c\u5411\u4e0a\u722c\u4e24\u4e2a\u53f0\u9636\uff0c\u5230\u8fbe\u4e0b\u6807\u4e3a 2 \u7684\u53f0\u9636\u3002\r\n- \u652f\u4ed8 1 \uff0c\u5411\u4e0a\u722c\u4e24\u4e2a\u53f0\u9636\uff0c\u5230\u8fbe\u4e0b\u6807\u4e3a 4 \u7684\u53f0\u9636\u3002\r\n- \u652f\u4ed8 1 \uff0c\u5411\u4e0a\u722c\u4e24\u4e2a\u53f0\u9636\uff0c\u5230\u8fbe\u4e0b\u6807\u4e3a 6 \u7684\u53f0\u9636\u3002\r\n- \u652f\u4ed8 1 \uff0c\u5411\u4e0a\u722c\u4e00\u4e2a\u53f0\u9636\uff0c\u5230\u8fbe\u4e0b\u6807\u4e3a 7 \u7684\u53f0\u9636\u3002\r\n- \u652f\u4ed8 1 \uff0c\u5411\u4e0a\u722c\u4e24\u4e2a\u53f0\u9636\uff0c\u5230\u8fbe\u4e0b\u6807\u4e3a 9 \u7684\u53f0\u9636\u3002\r\n- \u652f\u4ed8 1 \uff0c\u5411\u4e0a\u722c\u4e00\u4e2a\u53f0\u9636\uff0c\u5230\u8fbe\u697c\u68af\u9876\u90e8\u3002\r\n\u603b\u82b1\u8d39\u4e3a 6 \u3002<\/pre>\n
class Solution {\r\npublic:\r\n    int minCostClimbingStairs(vector<int>& cost) {\r\n        int n = cost.size();\r\n        vector<int> f(n + 1 , 0x3f);\r\n\r\n        f[0] = f[1] = 0;\r\n        for (int i = 2 ; i <= n ; i ++ )\r\n        {\r\n            f[i] = min(f[i - 1] + cost[i - 1] , f[i - 2] + cost[i - 2]);\r\n        }\r\n\r\n        return f[n];\r\n\r\n    }\r\n};<\/pre>\n
2.\u6253\u5bb6\u52ab\u820d<\/h2>\n
n<=2\u7279\u6b8a\u5904\u7406 \u5f53\u524d\u623f\u95f4\u9009\u62e9\u5077\u6216\u4e0d\u5077\uff0c\u82e5\u4e3a\u5077\u5219f[i] = f[i - 2] + nums[i]\uff0c\u82e5\u4e3a\u4e0d\u5077\u5219f[i] = f[i - 1]<\/span><\/p>\n
\u9898\u76ee\u63cf\u8ff0\uff1a<\/p>\n
\u4f60\u662f\u4e00\u4e2a\u4e13\u4e1a\u7684\u5c0f\u5077\uff0c\u8ba1\u5212\u5077\u7a83\u6cbf\u8857\u7684\u623f\u5c4b\u3002\u6bcf\u95f4\u623f\u5185\u90fd\u85cf\u6709\u4e00\u5b9a\u7684\u73b0\u91d1\uff0c\u5f71\u54cd\u4f60\u5077\u7a83\u7684\u552f\u4e00\u5236\u7ea6\u56e0\u7d20\u5c31\u662f\u76f8\u90bb\u7684\u623f\u5c4b\u88c5\u6709\u76f8\u4e92\u8fde\u901a\u7684\u9632\u76d7\u7cfb\u7edf\uff0c\u5982\u679c\u4e24\u95f4\u76f8\u90bb\u7684\u623f\u5c4b\u5728\u540c\u4e00\u665a\u4e0a\u88ab\u5c0f\u5077\u95ef\u5165\uff0c\u7cfb\u7edf\u4f1a\u81ea\u52a8\u62a5\u8b66<\/strong>\u3002<\/p>\n
\u7ed9\u5b9a\u4e00\u4e2a\u4ee3\u8868\u6bcf\u4e2a\u623f\u5c4b\u5b58\u653e\u91d1\u989d\u7684\u975e\u8d1f\u6574\u6570\u6570\u7ec4\uff0c\u8ba1\u7b97\u4f60\u00a0\u4e0d\u89e6\u52a8\u8b66\u62a5\u88c5\u7f6e\u7684\u60c5\u51b5\u4e0b\u00a0<\/strong>\uff0c\u4e00\u591c\u4e4b\u5185\u80fd\u591f\u5077\u7a83\u5230\u7684\u6700\u9ad8\u91d1\u989d\u3002<\/p>\n
\u793a\u4f8b\uff1a<\/span>\r\n\r\n\u8f93\u5165\uff1a[2,7,9,3,1] \u8f93\u51fa\uff1a12 \u89e3\u91ca\uff1a\u5077\u7a83 1 \u53f7\u623f\u5c4b (\u91d1\u989d = 2), \u5077\u7a83 3 \u53f7\u623f\u5c4b (\u91d1\u989d = 9)\uff0c\u63a5\u7740\u5077\u7a83 5 \u53f7\u623f\u5c4b (\u91d1\u989d = 1)\u3002 \u5077\u7a83\u5230\u7684\u6700\u9ad8\u91d1\u989d = 2 + 9 + 1 = 12 \u3002<\/pre>\n
class Solution {\r\npublic:\r\n    int rob(vector<int>& nums) {\r\n        int n = nums.size();\r\n        if (!n) return 0;\r\n\r\n        vector<int> f(n , 0);\r\n\r\n        f[0] = nums[0];\r\n        if (n == 1) return nums[0];\r\n\r\n        f[1] = max(f[0] , nums[1]);\r\n        if (n == 2) return max(nums[0] , nums[1]);\r\n\r\n\r\n        for (int i = 2 ; i < n ; i ++ )\r\n        {\r\n            f[i] = max(f[i - 2] + nums[i] , f[i - 1]);\r\n        }\r\n\r\n        return f[n - 1];\r\n    }\r\n};<\/pre>\n
\u77e9\u9635<\/strong><\/h1>\n
\u901a\u5e38\u4e3a\u6709\u9650\u5236\u7684\u4ece\u4e00\u4e2a\u6216\u8005\u591a\u4e2a\u65b9\u5411\u8f6c\u79fb\u800c\u6765\uff0c\u9700\u8981\u6ce8\u610f\u8fb9\u754c\u95ee\u9898<\/span><\/p>\n
1.\u4e09\u89d2\u5f62\u6700\u5c0f\u8def\u5f84\u548c\uff08\u6570\u5b57\u4e09\u89d2\u5f62\uff09<\/h2>\n
\u9700\u8981\u6ce8\u610f\u5f53j(\u5217) \u8fb9\u754c(0)\u7684\u65f6\u5019\uff0c\u53ea\u80fd\u4ece\u4e0a\u65b9\u800c\u6765\uff0c\u5f53i=j(\u5bf9\u89d2\u7ebf\u4f4d\u7f6e)\u8fb9\u754c\u7684\u65f6\u5019\uff0c\u53ea\u80fd\u4ece\u5de6\u4e0a\u65b9\u800c\u6765\u3002\u5bf9\u4e8e\u5176\u4ed6\u4f4d\u7f6e\u5219\u53ef\u63a8\u51fa\u72b6\u6001\u8f6c\u79fb\u65b9\u7a0b\uff1af[i][j] = min(f[i - 1][j] , f[i - 1][j - 1]) + triangle[i][j];<\/span><\/p>\n
\u7ed9\u5b9a\u4e00\u4e2a\u4e09\u89d2\u5f62 triangle \uff0c\u627e\u51fa\u81ea\u9876\u5411\u4e0b\u7684\u6700\u5c0f\u8def\u5f84\u548c\u3002
\n\u6bcf\u4e00\u6b65\u53ea\u80fd\u79fb\u52a8\u5230\u4e0b\u4e00\u884c\u4e2d\u76f8\u90bb\u7684\u7ed3\u70b9\u4e0a\u3002\u76f8\u90bb\u7684\u7ed3\u70b9 \u5728\u8fd9\u91cc\u6307\u7684\u662f \u4e0b\u6807 \u4e0e \u4e0a\u4e00\u5c42\u7ed3\u70b9\u4e0b\u6807 \u76f8\u540c\u6216\u8005\u7b49\u4e8e \u4e0a\u4e00\u5c42\u7ed3\u70b9\u4e0b\u6807 + 1 \u7684\u4e24\u4e2a\u7ed3\u70b9\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u5982\u679c\u6b63\u4f4d\u4e8e\u5f53\u524d\u884c\u7684\u4e0b\u6807 i \uff0c\u90a3\u4e48\u4e0b\u4e00\u6b65\u53ef\u4ee5\u79fb\u52a8\u5230\u4e0b\u4e00\u884c\u7684\u4e0b\u6807 i \u6216 i + 1 \u3002<\/p>\n
\u793a\u4f8b\uff1a\r\n\u8f93\u5165\uff1atriangle = [[2],[3,4],[6,5,7],[4,1,8,3]]\r\n\u8f93\u51fa\uff1a11\r\n\u89e3\u91ca\uff1a\u5982\u4e0b\u9762\u7b80\u56fe\u6240\u793a\uff1a\r\n2\r\n3 4\r\n6 5 7\r\n4 1 8 3\r\n\u81ea\u9876\u5411\u4e0b\u7684\u6700\u5c0f\u8def\u5f84\u548c\u4e3a 11\uff08\u5373\uff0c2 + 3 + 5 + 1 = 11\uff09\u3002<\/pre>\n
class Solution {\r\npublic:\r\n    int minimumTotal(vector<vector<int>>& triangle) {\r\n        int n = triangle.size();\r\n        vector<vector<int> > f(n , vector<int>(n , 0x3f));\r\n\r\n        f[0][0] = triangle[0][0];\r\n\r\n        for (int i = 1 ; i < n ; i ++ )\r\n        {\r\n            f[i][0] = f[i - 1][0] + triangle[i][0];\r\n            for (int j = 1 ; j < i ; j ++ )\r\n                f[i][j] = min(f[i - 1][j - 1] , f[i - 1][j]) + triangle[i][j];\r\n            f[i][i] = f[i - 1][i - 1] + triangle[i][i];\r\n        }\r\n\r\n        int ans = 0x3f3f3f3f;\r\n        for (int i = 0 ; i < n ; i ++ ) ans = min(ans , f[n - 1][i]);\r\n        return ans ;\r\n\r\n    }\r\n};<\/pre>\n
2.\u6700\u5927\u6b63\u65b9\u5f62<\/h2>\n
\u6ce8\u610f\u8fb9\u754c\u5f53i=0\u6216j=0\u65f6\uff0c\u6700\u591a\u9762\u79ef\u53ea\u80fd\u4e3a1\u3002\u5c06\u5f53\u524d\u4f4d\u7f6e\u4f5c\u4e3a\u6b63\u65b9\u5f62\u7684\u53f3\u4e0b\u89d2\uff0c\u5219\u4e00\u5b9a\u6ee1\u8db3\u4ee5\u6b64\u53f3\u4e0b\u89d2\u4e3a\u6b63\u65b9\u5f62\u7684\u8fb9\u957f\u4e00\u5b9a\u4e3a\u5176min(\u4e0a\u65b9\u3001\u5de6\u65b9\u3001\u5de6\u4e0a\u65b9\u4e09\u4e2a\u4f4d\u7f6e\u4e3a\u53f3\u4e0b\u89d2\u7684\u6b63\u65b9\u5f62\u7684\u8fb9\u957f) + 1\u3002\u5373\u53ef\u63a8\u51fa\u72b6\u6001\u8f6c\u79fb\u65b9\u7a0b\u4e3a\uff1af[i][j] = min(min(f[i - 1][j] , f[i][j - 1]) , f[i - 1][j - 1]) + 1;<\/span><\/p>\n
\u9898\u76ee\u63cf\u8ff0\uff1a<\/p>\n
\u5728\u4e00\u4e2a\u7531\u00a0'0'<\/code>\u00a0\u548c\u00a0'1'<\/code>\u00a0\u7ec4\u6210\u7684\u4e8c\u7ef4\u77e9\u9635\u5185\uff0c\u627e\u5230\u53ea\u5305\u542b\u00a0'1'<\/code>\u00a0\u7684\u6700\u5927\u6b63\u65b9\u5f62\uff0c\u5e76\u8fd4\u56de\u5176\u9762\u79ef\u3002<\/p>\n
\u8be6\u7ec6\u9898\u76ee\u63cf\u8ff0https:\/\/leetcode.cn\/problems\/maximal-square\/?envType=study-plan-v2&envId=dynamic-programming<\/a><\/p>\n
class Solution {\r\npublic:\r\n    int maximalSquare(vector<vector<char>>& matrix) {\r\n        int n = matrix.size();\r\n        int m = matrix[0].size();\r\n\r\n        vector<vector<int> > f(n , vector<int>(m , 0));\r\n\r\n        int ans = 0;\r\n        for (int i = 0 ; i < n ; i ++ )\r\n        {\r\n            for (int j = 0 ; j < m ; j ++ )\r\n            {\r\n                if (matrix[i][j] == '1')\r\n                {\r\n                    if (!i || !j) f[i][j] = 1;\r\n                    else f[i][j] = min(min(f[i - 1][j] , f[i - 1][j - 1]) , f[i][j - 1]) + 1;\r\n                }\r\n                ans = max(ans , f[i][j]);\r\n            }\r\n        }\r\n        return ans * ans ;\r\n    }\r\n};<\/pre>\n
\u6700\u957f\u9012\u589e\u5b50\u5e8f\u5217<\/h1>\n
\u901a\u5e38\u662f\u6839\u636e\u4e00\u4e9b\u7279\u5b9a\u7684\u6761\u4ef6\u786e\u5b9a\u72b6\u6001\u8f6c\u79fb\u7684\u4e0a\u4e00\u4e2a\u4f4d\u7f6e \u5982\u9012\u589e\uff0c\u4e0d\u4e0b\u964d\uff0c\u5b9a\u5dee\uff0c\u591a\u5143\u7ec4\u7b49\u601d\u8def\u6bd4\u8f83\u7b80\u5355<\/span><\/p>\n
1.\u6700\u957f\u4e0a\u5347\u5b50\u5e8f\u5217<\/h2>\n
\u53ea\u8981\u6ee1\u8db3\u5728\u5f53\u524d\u5143\u7d20\u4e4b\u524d\u4e14\u5c0f\u4e8e\u5f53\u524d\u5143\u7d20\uff0c\u5373\u4e3a\u8f6c\u79fb\u76ee\u6807\u3002\u72b6\u6001\u8f6c\u79fb\u65b9\u7a0b\uff1af[i] = max(f[i] , f[j - 1] + 1);<\/span><\/p>\n
\u9898\u76ee\u63cf\u8ff0\uff1a<\/p>\n
\u7ed9\u4f60\u4e00\u4e2a\u6574\u6570\u6570\u7ec4\u00a0nums<\/code>\u00a0\uff0c\u627e\u5230\u5176\u4e2d\u6700\u957f\u4e25\u683c\u9012\u589e\u5b50\u5e8f\u5217\u7684\u957f\u5ea6\u3002<\/p>\n
\u5b50\u5e8f\u5217\u00a0<\/strong>\u662f\u7531\u6570\u7ec4\u6d3e\u751f\u800c\u6765\u7684\u5e8f\u5217\uff0c\u5220\u9664\uff08\u6216\u4e0d\u5220\u9664\uff09\u6570\u7ec4\u4e2d\u7684\u5143\u7d20\u800c\u4e0d\u6539\u53d8\u5176\u4f59\u5143\u7d20\u7684\u987a\u5e8f\u3002\u4f8b\u5982\uff0c[3,6,2,7]<\/code>\u00a0\u662f\u6570\u7ec4\u00a0[0,3,1,6,2,2,7]<\/code> \u7684\u5b50\u5e8f\u5217\u3002<\/p>\n
\u793a\u4f8b\uff1a\r\n\u8f93\u5165\uff1anums = [10,9,2,5,3,7,101,18]\r\n\u8f93\u51fa\uff1a4\r\n\u89e3\u91ca\uff1a\u6700\u957f\u9012\u589e\u5b50\u5e8f\u5217\u662f [2,3,7,101]\uff0c\u56e0\u6b64\u957f\u5ea6\u4e3a 4 \u3002<\/pre>\n
class Solution {\r\npublic:\r\n    int lengthOfLIS(vector<int>& nums) {\r\n        int n = nums.size();\r\n        vector<int> f(n + 1 , 1);\r\n\r\n        int res = 1;\r\n        for (int i = 0 ; i < n ; i ++ )\r\n        {\r\n            for (int j = 0 ; j < i ; j ++ )\r\n            {\r\n                if (nums[j] < nums[i]) f[i] = max(f[i] , f[j] + 1);\r\n                res = max(f[i] , res);\r\n            }\r\n        }\r\n        return res;\r\n    }\r\n};<\/pre>\n
2.\u6700\u957f\u4e0a\u5347\u5b50\u5e8f\u5217\u7684\u4e2a\u6570<\/h2>\n
\u6b64\u9898\u4e3a1\u9898\u7684\u53d8\u5f0f\uff0c\u72b6\u6001\u8f6c\u79fb\u76f8\u540c\u3002\u9700\u8981\u6ce8\u610f\u7684\u662f\u9898\u610f\u662f\u7edf\u8ba1\u6700\u957f\u4e0a\u5347\u5b50\u5e8f\u5217\u7684\u4e2a\u6570\uff0c\u5373\u957f\u5ea6\u76f8\u540c\u4e14\u6700\u957f\u3002\u4e3a\u6bcf\u4e2a\u4e0b\u6807\u4f4d\u7f6e\u5b58\u4e0b\u4ee5\u8be5\u4e0b\u6807\u7ed3\u5c3e\u7684\u5b50\u5e8f\u5217\u7684\u4e2a\u6570(\u6700\u957f)\uff0c\u9700\u8981\u6dfb\u52a0\u53c2\u7167(\u5982maxLen)\u786e\u4fdd\u6bcf\u6b21\u66f4\u65b0\u7684\u662f\u5426\u4e3a\u6700\u957f\u5e8f\u5217\u4e2a\u6570\u3002<\/span><\/p>\n
\u9898\u76ee\u63cf\u8ff0\uff1a<\/p>\n
\u7ed9\u5b9a\u4e00\u4e2a\u672a\u6392\u5e8f\u7684\u6574\u6570\u6570\u7ec4 nums \uff0c \u8fd4\u56de\u6700\u957f\u9012\u589e\u5b50\u5e8f\u5217\u7684\u4e2a\u6570 \u3002<\/p>\n
\u6ce8\u610f \u8fd9\u4e2a\u6570\u5217\u5fc5\u987b\u662f \u4e25\u683c \u9012\u589e\u7684\u3002<\/p>\n
\u793a\u4f8b\uff1a\r\n\u8f93\u5165: [1,3,5,4,7]\r\n\u8f93\u51fa: 2\r\n\u89e3\u91ca: \u6709\u4e24\u4e2a\u6700\u957f\u9012\u589e\u5b50\u5e8f\u5217\uff0c\u5206\u522b\u662f [1, 3, 4, 7] \u548c[1, 3, 5, 7]\u3002<\/pre>\n
class Solution {\r\npublic:\r\n    int findNumberOfLIS(vector<int>& nums) {\r\n        int n = nums.size();\r\n        vector<int> f(n + 1 , 1) , cnt(n + 1 , 1);\r\n\r\n        int res = 0 , maxLen = 0;\r\n        for (int i = 0 ; i < n ; i ++ )\r\n        {\r\n            for (int j = 0 ; j < i ; j ++ )\r\n            {\r\n                if (nums[j] < nums[i])\r\n                {\r\n                    if (f[i] < f[j] + 1)\r\n                    {\r\n                        f[i] = f[j] + 1;\r\n                        cnt[i] = cnt[j];\r\n                    }\r\n                    else if (f[i] == f[j] + 1) cnt[i] += cnt[j];\r\n                }\r\n            }\r\n            if (f[i] > maxLen)\r\n            {\r\n                maxLen = f[i];\r\n                res = cnt[i];\r\n            }\r\n            else if (f[i] == maxLen)\r\n                res += cnt[i];\r\n        }\r\n\r\n        return res;\r\n    }\r\n};<\/pre>\n
3.\u6700\u957f\u5b9a\u5dee\u5b50\u5e8f\u5217<\/h2>\n
\u9898\u76ee\u6240\u7ed9\u7684\u5b9a\u5dee\u5728\u72b6\u6001\u8f6c\u79fb\u8fc7\u7a0b\u4e2d\u53ef\u80fd\u5b58\u5728\u8ba9\u6211\u4eec\u7684\u4e2d\u95f4\u72b6\u6001\u7684\u4e0b\u6807\u4e3a\u8d1f\u6570\u7684\u60c5\u51b5\uff0c\u800c\u4f7f\u7528unordered_map\u5c31\u53ef\u4ee5\u5f88\u597d\u7684\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\u3002\u4f7f\u7528\u4e00\u7ef4\u4ee3\u8868\u503c\u4e3ai\u7684\u65f6\u5019\u5176\u5dee\u4e3adifference\u7684\u5e8f\u5217\u957f\u5ea6\uff0c\u5219\u6709\u72b6\u6001\u8f6c\u79fb\u65b9\u7a0b\u4e3a\uff1af[i] = f[i - difference] + 1;<\/span><\/p>\n
\u9898\u76ee\u63cf\u8ff0\uff1a<\/p>\n
\u7ed9\u4f60\u4e00\u4e2a\u6574\u6570\u6570\u7ec4\u00a0arr<\/code>\u00a0\u548c\u4e00\u4e2a\u6574\u6570\u00a0difference<\/code>\uff0c\u8bf7\u4f60\u627e\u51fa\u5e76\u8fd4\u56de\u00a0arr<\/code>\u00a0\u4e2d\u6700\u957f\u7b49\u5dee\u5b50\u5e8f\u5217\u7684\u957f\u5ea6\uff0c\u8be5\u5b50\u5e8f\u5217\u4e2d\u76f8\u90bb\u5143\u7d20\u4e4b\u95f4\u7684\u5dee\u7b49\u4e8e\u00a0difference<\/code>\u00a0\u3002<\/p>\n
\u5b50\u5e8f\u5217<\/strong>\u00a0\u662f\u6307\u5728\u4e0d\u6539\u53d8\u5176\u4f59\u5143\u7d20\u987a\u5e8f\u7684\u60c5\u51b5\u4e0b\uff0c\u901a\u8fc7\u5220\u9664\u4e00\u4e9b\u5143\u7d20\u6216\u4e0d\u5220\u9664\u4efb\u4f55\u5143\u7d20\u800c\u4ece\u00a0arr<\/code>\u00a0\u6d3e\u751f\u51fa\u6765\u7684\u5e8f\u5217\u3002<\/p>\n
\u793a\u4f8b\uff1a\r\n\u8f93\u5165\uff1aarr = [1,5,7,8,5,3,4,2,1], difference = -2\r\n\u8f93\u51fa\uff1a4\r\n\u89e3\u91ca\uff1a\u6700\u957f\u7684\u7b49\u5dee\u5b50\u5e8f\u5217\u662f [7,5,3,1]\u3002<\/pre>\n
class Solution {\r\npublic:\r\n    int longestSubsequence(vector<int>& arr, int difference) {\r\n        int n = arr.size();\r\n        if (!n) return 0;\r\n\r\n        unordered_map<int , int> f;\r\n\r\n        int res = 0;\r\n\r\n        for (int i : arr)\r\n        {\r\n            f[i] = f[i - difference] + 1;\r\n            res = max(res , f[i]);\r\n        }\r\n        return res;\r\n    }\r\n};<\/pre>\n
3.\u6700\u957f\u7b49\u5dee\u5e8f\u5217<\/h2>\n
\u6574\u4f53\u601d\u8def\u540c2\u9898\uff0c\u4f46\u662f\u7b49\u5dee\u5e8f\u5217\u5b58\u5728\u591a\u4e2a\u4e0d\u4e00\u6837\u7684d(\u516c\u5dee)\uff0c\u56e0\u6b64\u9700\u8981\u4f7f\u7528\u4e8c\u7ef4\u6765\u8bb0\u5f55\u4e0d\u540c\u7684d(\u516c\u5dee)\u7684\u5e8f\u5217\u957f\u5ea6\u3002f[i][d]\u8868\u793a\u4ee5\u7b2ci\u4e2a\u5143\u7d20\u7ed3\u5c3e\u7684\u516c\u5dee\u4e3ad\u7684\u5e8f\u5217\u7684\u957f\u5ea6\u3002\u5219\u72b6\u6001\u8f6c\u79fb\u65b9\u7a0b\u4e3a:f[i][d] = f[j][d];\u6b64\u5904\u7684i,j\u548c1\u9898\u5177\u6709\u76f8\u540c\u610f\u4e49\u3002<\/span><\/p>\n
\u9898\u76ee\u63cf\u8ff0\uff1a<\/p>\n
\u7ed9\u4f60\u4e00\u4e2a\u6574\u6570\u6570\u7ec4\u00a0nums<\/code>\uff0c\u8fd4\u56de\u00a0nums<\/code>\u00a0\u4e2d\u6700\u957f\u7b49\u5dee\u5b50\u5e8f\u5217\u7684\u957f\u5ea6<\/strong>\u3002<\/p>\n
\u56de\u60f3\u4e00\u4e0b\uff0cnums<\/code>\u00a0\u7684\u5b50\u5e8f\u5217\u662f\u4e00\u4e2a\u5217\u8868\u00a0nums[i<\/code>1<\/sub>], nums[i<\/code>2<\/sub>], ..., nums[i<\/code>k<\/sub>]<\/code>\u00a0\uff0c\u4e14\u00a00 <= i<\/code>1<\/sub> < i<\/code>2<\/sub> < ... < i<\/code>k<\/sub> <= nums.length - 1<\/code>\u3002\u5e76\u4e14\u5982\u679c\u00a0seq[i+1] - seq[i]<\/code>(\u00a00 <= i < seq.length - 1<\/code>) \u7684\u503c\u90fd\u76f8\u540c\uff0c\u90a3\u4e48\u5e8f\u5217\u00a0seq<\/code>\u00a0\u662f\u7b49\u5dee\u7684\u3002<\/p>\n
\u793a\u4f8b\uff1a\r\n\u8f93\u5165\uff1anums = [9,4,7,2,10]\r\n\u8f93\u51fa\uff1a3\r\n\u89e3\u91ca\uff1a\u6700\u957f\u7684\u7b49\u5dee\u5b50\u5e8f\u5217\u662f [4,7,10]\u3002<\/pre>\n
class Solution {\r\npublic:\r\n    int longestArithSeqLength(vector<int>& nums) {\r\n        int n = nums.size();\r\n        int res = 0;\r\n        vector<unordered_map<int , int> > f(n);\r\n\r\n        for (int i = 1 ; i < n ; i ++ )\r\n        {\r\n            for (int j = 0 ; j < i ; j ++ )\r\n            {\r\n                int d = nums[i] - nums[j];\r\n                f[i][d] = f[j][d] + 1;\r\n                res = max(res , f[i][d]);\r\n            }\r\n           \r\n        }\r\n\r\n        return res + 1;\r\n    }\r\n};<\/pre>\n
4.\u4fc4\u7f57\u65af\u5957\u5a03\u4fe1\u5c01\u95ee\u9898<\/h2>\n
\u9700\u8981\u8003\u8651\u4fe1\u5c01\u7684\u957f\u3001\u5bbd\u5747\u5c0f\u4e8e\u624d\u80fd\u5957\u5a03\u8fdb\u53bb\u3002\u4f7f\u7528\u00a0Lambda \u8868\u8fbe\u5f0f<\/strong>\u81ea\u5b9a\u4e49\u6392\u5e8f\u89c4\u5219\u3002\u72b6\u6001\u8f6c\u79fb\u7684\u601d\u8def\u540c1.\u9898 \u5373f[i] = max(f[i] , f[j] + 1);<\/span><\/p>\n
\u9898\u76ee\u63cf\u8ff0\uff1a<\/p>\n
\u7ed9\u4f60\u4e00\u4e2a\u4e8c\u7ef4\u6574\u6570\u6570\u7ec4 envelopes \uff0c\u5176\u4e2d envelopes[i] = [wi, hi] \uff0c\u8868\u793a\u7b2c i \u4e2a\u4fe1\u5c01\u7684\u5bbd\u5ea6\u548c\u9ad8\u5ea6\u3002<\/p>\n
\u5f53\u53e6\u4e00\u4e2a\u4fe1\u5c01\u7684\u5bbd\u5ea6\u548c\u9ad8\u5ea6\u90fd\u6bd4\u8fd9\u4e2a\u4fe1\u5c01\u5927\u7684\u65f6\u5019\uff0c\u8fd9\u4e2a\u4fe1\u5c01\u5c31\u53ef\u4ee5\u653e\u8fdb\u53e6\u4e00\u4e2a\u4fe1\u5c01\u91cc\uff0c\u5982\u540c\u4fc4\u7f57\u65af\u5957\u5a03\u4e00\u6837\u3002<\/p>\n
\u8bf7\u8ba1\u7b97 \u6700\u591a\u80fd\u6709\u591a\u5c11\u4e2a \u4fe1\u5c01\u80fd\u7ec4\u6210\u4e00\u7ec4\u201c\u4fc4\u7f57\u65af\u5957\u5a03\u201d\u4fe1\u5c01\uff08\u5373\u53ef\u4ee5\u628a\u4e00\u4e2a\u4fe1\u5c01\u653e\u5230\u53e6\u4e00\u4e2a\u4fe1\u5c01\u91cc\u9762\uff09\u3002<\/p>\n
\u6ce8\u610f\uff1a\u4e0d\u5141\u8bb8\u65cb\u8f6c\u4fe1\u5c01\u3002<\/p>\n
\u793a\u4f8b\uff1a\r\n\u8f93\u5165\uff1aenvelopes = [[5,4],[6,4],[6,7],[2,3]]\r\n\u8f93\u51fa\uff1a3\r\n\u89e3\u91ca\uff1a\u6700\u591a\u4fe1\u5c01\u7684\u4e2a\u6570\u4e3a 3, \u7ec4\u5408\u4e3a: [2,3] => [5,4] => [6,7]\u3002\r\n<\/pre>\n
class Solution {\r\npublic:\r\n    int maxEnvelopes(vector<vector<int>>& envelopes) {\r\n        int n = envelopes.size();\r\n\r\n        sort(envelopes.begin(), envelopes.end(), [](const auto& e1, const auto& e2) {\r\n            return e1[0] < e2[0] || (e1[0] == e2[0] && e1[1] > e2[1]);\r\n        });\r\n        int res = 1;\r\n        vector<int> f(n + 1 , 1);\r\n        for (int i = 0 ; i < n ; i ++ )\r\n        {\r\n            for (int j = 0 ; j < i ; j ++ )\r\n            {\r\n                if (envelopes[i][1] > envelopes[j][1] && envelopes[i][0] > envelopes[j][0])\r\n                {\r\n                    f[i] = max(f[i] , f[j] + 1);\r\n                }\r\n\r\n                res = max(res , f[i]);\r\n            }\r\n        }\r\n\r\n        return res;\r\n    }\r\n};<\/pre>\n
\u4e8c\u5206\u4f18\u5316<\/h3>\n
\u4f46\u662f\u4ee5\u4e0a\u8fd9\u4e2a\u505a\u6cd5\u5728\u6570\u636e\u8f83\u5927\u7684\u65f6\u5019\u4e0d\u80fd\u901a\u8fc7\u9898\u76eeO(n\u00b2)\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u3002\u6240\u4ee5\u4f7f\u7528\u4e8c\u5206\u67e5\u627e\u7684\u65b9\u5f0f\u51cf\u5c0f\u65f6\u95f4\u590d\u6742\u5ea6O(nlogn);<\/span><\/span><\/p>\n
class Solution {\r\npublic:\r\n    int maxEnvelopes(vector<vector<int>>& envelopes) {\r\n        if (envelopes.empty()) {\r\n            return 0;\r\n        }\r\n        \r\n        int n = envelopes.size();\r\n        sort(envelopes.begin(), envelopes.end(), [](const auto& e1, const auto& e2) {\r\n            return e1[0] < e2[0] || (e1[0] == e2[0] && e1[1] > e2[1]);\r\n        });\r\n\r\n        vector<int> f = {envelopes[0][1]};\r\n        for (int i = 1; i < n; ++i) {\r\n            if (int num = envelopes[i][1]; num > f.back()) {\r\n                f.push_back(num);\r\n            }\r\n            else {\r\n                auto it = lower_bound(f.begin(), f.end(), num);\r\n                *it = num;\r\n            }\r\n        }\r\n        return f.size();\r\n    }\r\n};\r\n<\/pre>\n
\u6700\u957f\u516c\u5171\u5b50\u5e8f\u5217<\/h1>\n
\u901a\u5e38\u4e3a\u8003\u8651\u4e24\u4e2a\u5e8f\u5217\u4e92\u76f8\u4e3a\u53c2\u7167\u7269\u4ece\u7279\u5b9a\u7684\u4f4d\u7f6e\u72b6\u6001\u8f6c\u79fb\u8fc7\u6765\u7684max\u503c\u3002\u5728\u67d0\u4e9b\u7279\u6b8a\u60c5\u51b5\u4e0b\uff0c\u56de\u6587\u4e32\u7684\u5bfb\u627e\u4e5f\u53ef\u4ee5\u8f6c\u6362\u4e3a\u6700\u957f\u516c\u5171\u5b50\u5e8f\u5217\u95ee\u9898\u3002<\/span><\/p>\n
1.\u6700\u957f\u516c\u5171\u5b50\u5e8f\u5217<\/h2>\n
\u6bcf\u6b21\u5230\u4e00\u4e2a\u65b0\u7684\u4f4d\u7f6e\u7684\u65f6\u5019\u5148\u521d\u59cb\u5316\u5f53\u524d\u4f4d\u7f6e\u7684\u6700\u957f\u503c\u4e3amax(1\u5e8f\u5217\u4ee5\u4e0a\u4e00\u4e2a\u5b57\u7b26\u7ed3\u5c3e\u6700\u957f\u503c \uff0c 2\u5e8f\u5217\u4ee5\u4e0a\u4e00\u4e2a\u5b57\u7b26\u7ed3\u5c3e\u7684\u6700\u957f\u503c)(\u6216\u8005\u7406\u89e3\u4e3a\u5f53\u524d\u4f4d\u7f6e\u4e24\u4e2a\u5e8f\u5217\u7684\u5b57\u7b26\u4e0d\u76f8\u540c\u7684\u60c5\u51b5)<\/span>,\u5982\u679c\u76f8\u540c\u5219\u6709\u72b6\u6001\u8f6c\u79fb:f[i][j] = max(f[i - 1][j - 1] + 1 , f[i][j])\uff1b<\/span><\/p>\n
\u9898\u76ee\u63cf\u8ff0\uff1a
\n\u7ed9\u5b9a\u4e24\u4e2a\u5b57\u7b26\u4e32 text1 \u548c text2\uff0c\u8fd4\u56de\u8fd9\u4e24\u4e2a\u5b57\u7b26\u4e32\u7684\u6700\u957f \u516c\u5171\u5b50\u5e8f\u5217 \u7684\u957f\u5ea6\u3002\u5982\u679c\u4e0d\u5b58\u5728 \u516c\u5171\u5b50\u5e8f\u5217 \uff0c\u8fd4\u56de 0 \u3002
\n\u4e00\u4e2a\u5b57\u7b26\u4e32\u7684 \u5b50\u5e8f\u5217 \u662f\u6307\u8fd9\u6837\u4e00\u4e2a\u65b0\u7684\u5b57\u7b26\u4e32\uff1a\u5b83\u662f\u7531\u539f\u5b57\u7b26\u4e32\u5728\u4e0d\u6539\u53d8\u5b57\u7b26\u7684\u76f8\u5bf9\u987a\u5e8f\u7684\u60c5\u51b5\u4e0b\u5220\u9664\u67d0\u4e9b\u5b57\u7b26\uff08\u4e5f\u53ef\u4ee5\u4e0d\u5220\u9664\u4efb\u4f55\u5b57\u7b26\uff09\u540e\u7ec4\u6210\u7684\u65b0\u5b57\u7b26\u4e32\u3002
\n\u4f8b\u5982\uff0c\"ace\" \u662f \"abcde\" \u7684\u5b50\u5e8f\u5217\uff0c\u4f46 \"aec\" \u4e0d\u662f \"abcde\" \u7684\u5b50\u5e8f\u5217\u3002
\n\u4e24\u4e2a\u5b57\u7b26\u4e32\u7684 \u516c\u5171\u5b50\u5e8f\u5217 \u662f\u8fd9\u4e24\u4e2a\u5b57\u7b26\u4e32\u6240\u5171\u540c\u62e5\u6709\u7684\u5b50\u5e8f\u5217\u3002<\/p>\n
\u793a\u4f8b\uff1a\r\n\u8f93\u5165\uff1atext1 = \"abcde\", text2 = \"ace\" \r\n\u8f93\u51fa\uff1a3 \r\n\u89e3\u91ca\uff1a\u6700\u957f\u516c\u5171\u5b50\u5e8f\u5217\u662f \"ace\" \uff0c\u5b83\u7684\u957f\u5ea6\u4e3a 3 \u3002<\/pre>\n
class Solution {\r\npublic:\r\n    int longestCommonSubsequence(string text1, string text2) {\r\n       int n = text1.size();\r\n       int m = text2.size();\r\n       text1 = \" \" + text1;\r\n       text2 = \" \" + text2;\r\n\r\n       vector<vector<int>> f(n + 1 , vector<int>(m + 1 , 0));   \r\n       int res = 0;\r\n       for (int i = 1 ; i <= n ; i ++ )\r\n       {\r\n            for (int j = 1 ; j <= m ; j ++ )\r\n            {\r\n                f[i][j] = max(f[i - 1][j] , f[i][j - 1]);\r\n                if (text1[i] == text2[j]) f[i][j] = max(f[i - 1][j - 1] + 1 , f[i][j]);\r\n\r\n                res = max(f[i][j] , res);\r\n            }\r\n       }\r\n\r\n       return res;\r\n    }\r\n};<\/pre>\n
2.\u8ba9\u5b57\u7b26\u4e32\u6210\u4e3a\u56de\u6587\u4e32\u7684\u6700\u5c0f\u63d2\u5165\u6b21\u6570<\/h2>\n
\u524d\u6587\u63d0\u5230\u8fc7\uff0c\u53ef\u4ee5\u901a\u8fc7\u5c06\u56de\u6587\u4e32\u95ee\u9898\u8f6c\u5316\u4e3a\u6700\u5c0f\u516c\u5171\u5b50\u5e8f\u5217\u95ee\u9898\uff0c\u5373\u4e00\u4e2a\u5e8f\u5217\u4e8e\u4ed6\u76f8\u53cd\u7684\u5e8f\u5217(reverse)\u7684\u6700\u957f\u516c\u5171\u5b50\u5e8f\u5217\u7684\u957f\u5ea6\u5373\u4e3a\u6700\u957f\u56de\u6587\u4e32\u7684\u957f\u5ea6\u3002<\/span><\/p>\n
\u9898\u76ee\u63cf\u8ff0\uff1a<\/p>\n
\u7ed9\u4f60\u4e00\u4e2a\u5b57\u7b26\u4e32 s \uff0c\u6bcf\u4e00\u6b21\u64cd\u4f5c\u4f60\u90fd\u53ef\u4ee5\u5728\u5b57\u7b26\u4e32\u7684\u4efb\u610f\u4f4d\u7f6e\u63d2\u5165\u4efb\u610f\u5b57\u7b26\u3002<\/p>\n
\u8bf7\u4f60\u8fd4\u56de\u8ba9 s \u6210\u4e3a\u56de\u6587\u4e32\u7684 \u6700\u5c11\u64cd\u4f5c\u6b21\u6570 \u3002<\/p>\n
\u300c\u56de\u6587\u4e32\u300d\u662f\u6b63\u8bfb\u548c\u53cd\u8bfb\u90fd\u76f8\u540c\u7684\u5b57\u7b26\u4e32\u3002<\/p>\n
\u793a\u4f8b\uff1a\r\n\u8f93\u5165\uff1as = \"mbadm\"\r\n\u8f93\u51fa\uff1a2\r\n\u89e3\u91ca\uff1a\u5b57\u7b26\u4e32\u53ef\u53d8\u4e3a \"mbdadbm\" \u6216\u8005 \"mdbabdm\" \u3002<\/pre>\n
class Solution {\r\npublic:\r\n    int minInsertions(string s) {\r\n        int n = s.size();\r\n        auto rs = s;\r\n        reverse(rs.begin() , rs.end());\r\n        rs = \" \" + rs;\r\n        s = \" \" + s;\r\n\r\n        int res = 0;\r\n        vector<vector<int> > f(n + 1 , vector<int>(n + 1 , 0) );\r\n\r\n        for (int i = 1 ; i <= n ; i ++ )\r\n        {\r\n            for (int j = 1 ; j <= n ; j ++ )\r\n            {\r\n                f[i][j] = max(f[i - 1][j] , f[i][j - 1]);\r\n                if (s[i] == rs[j])\r\n                    f[i][j] = max(f[i - 1][j - 1] + 1 , f[i][j]);\r\n\r\n                res = max(f[i][j] , res);\r\n            }\r\n        }\r\n\r\n        return n - res;\r\n    }\r\n};<\/pre>\n
\u80cc\u5305\u95ee\u9898<\/h1>\n
\u80cc\u5305\u95ee\u9898\u662f\u4e00\u4e2a\u5f88\u7ecf\u5178\u7684dp\u901a\u5e38\u4e3a\u4e8c\u7ef4\uff0c\u53ef\u6839\u636e\u9898\u76ee\u8981\u6c42\u4f18\u5316\u5230\u4e00\u7ef4\u3002\u6838\u5fc3\u662f\u63a8\u5bfc\u8f6c\u79fb\u65b9\u7a0b\uff1a\u4ee5\u524di\u4e2a\u7269\u54c1\u7ed3\u5c3e\u7684\u4e0d\u8d85\u8fc7j\u7684\u4ee3\u4ef7\u6240\u83b7\u5f97\u7684\u6700\u5927\/\u6700\u5c0f\u4ef7\u503c<\/span><\/p>\n
1.01\u80cc\u5305\u95ee\u9898<\/h2>\n
f[i][j] \u8868\u793a\u524di\u4e2a\u7269\u54c1\u5728\u4f7f\u7528\u80cc\u5305\u5bb9\u79ef\u4e0d\u8d85\u8fc7j\u7684\u6700\u5927\u4ef7\u503c\u3002\u5206\u4e3a\u9009or\u4e0d\u9009 \u4e0d\u9009\u7684\u65f6\u5019\u5f53\u524d\u7684\u6700\u5927\u4ef7\u503c\u5c31\u662f\u4e0a\u4e00\u4e2a(i -\u00a0 1)\u4e2a\u7269\u54c1\u7684\u6700\u5927\u4ef7\u503c \uff1a f[i][j] = f[i - 1][j]; \u9009\u7684\u65f6\u5019\uff1af[i][j] = max(f[i][j] , f[i - 1][j - v] + w);<\/span><\/p>\n
\u9898\u76ee\u63cf\u8ff0\uff1a<\/strong>
\n\u6709 N \u4ef6\u7269\u54c1\u548c\u4e00\u4e2a\u5bb9\u91cf\u662f V \u7684\u80cc\u5305\u3002\u6bcf\u4ef6\u7269\u54c1\u53ea\u80fd\u4f7f\u7528\u4e00\u6b21\u3002
\n\u7b2c i \u4ef6\u7269\u54c1\u7684\u4f53\u79ef\u662f vi\uff0c\u4ef7\u503c\u662f wi\u3002
\n\u6c42\u89e3\u5c06\u54ea\u4e9b\u7269\u54c1\u88c5\u5165\u80cc\u5305\uff0c\u53ef\u4f7f\u8fd9\u4e9b\u7269\u54c1\u7684\u603b\u4f53\u79ef\u4e0d\u8d85\u8fc7\u80cc\u5305\u5bb9\u91cf\uff0c\u4e14\u603b\u4ef7\u503c\u6700\u5927\u3002
\n\u8f93\u51fa\u6700\u5927\u4ef7\u503c\u3002<\/p>\n
\u793a\u4f8b\uff1a\r\n\u8f93\u5165\uff1a[[4,5],[1,2],[2,4],[3,4],[4,5]] \r\n\u8f93\u51fa\uff1a8\r\n\u89e3\u91ca\uff1a\r\n\u5728\u8fd9\u4e2a\u6837\u4f8b\u4e2d\uff0c\u80cc\u5305\u5bb9\u91cf\u4e3a 5\uff0c\u7269\u54c1\u4fe1\u606f\u5982\u4e0b\uff1a\r\n\u7269\u54c1 1\uff1a\u4f53\u79ef 1\uff0c\u4ef7\u503c 2\r\n\u7269\u54c1 2\uff1a\u4f53\u79ef 2\uff0c\u4ef7\u503c 4\r\n\u7269\u54c1 3\uff1a\u4f53\u79ef 3\uff0c\u4ef7\u503c 4\r\n\u7269\u54c1 4\uff1a\u4f53\u79ef 4\uff0c\u4ef7\u503c 5\r\n\u53ef\u4ee5\u9009\u62e9\u7269\u54c1 2 \u548c\u7269\u54c1 3\uff0c\u603b\u4f53\u79ef\u4e3a 5\uff0c\u603b\u4ef7\u503c\u4e3a 8\uff0c\u8fd9\u662f\u6700\u5927\u4ef7\u503c\u3002<\/pre>\n
class Solution {\r\npublic :\r\n    int o1BagQusetionSolve(int n , int m , vector<int>& v , vector<int>& w)\r\n    {\r\n        vector<vector<int> > f(n + 1 , vector<int>(m + 1 , 0));\r\n\r\n        for (int i = 1 ; i <= n ; i ++ )\r\n        {\r\n            for (int j = 0 ; j <= m ; j ++ )\r\n            {\r\n                f[i][j] = f[i - 1][j];\r\n                if (j >= v[i]) f[i][j] = max(f[i][j] , f[i - 1][j - v[i]] + w[i]);\r\n            }\r\n        }\r\n\r\n        return f[n][m];\r\n    }\r\n};<\/pre>\n
01\u80cc\u5305\u7684\u7a7a\u95f4\u4f18\u5316O(n)<\/h3>\n
\u4e8c\u7ef4\u80cc\u5305\u7684\u8f6c\u79fb\u65b9\u7a0b\u4e2d\u7684i\u59cb\u7ec8\u662f\u7531i - 1\u800c\u6765\u7684\uff0c\u53ef\u4ee5\u5c1d\u8bd5\u53bb\u6389i - 1\u3002\u5012\u53d9\u904d\u5386\u662f\u56e0\u4e3a\u6b63\u5e8f\u4f1a\u5bfc\u81f4\u67d0\u4e9b\u72b6\u6001\u88ab\u4f7f\u7528\u591a\u6b21\u3002<\/span><\/p>\n
class Solution {\r\npublic :\r\n    int o1BagQusetionSolve(int n , int m , vector<int>& v , vector<int>& w)\r\n    {\r\n        vector<int> f(m + 1 , 0);\r\n\r\n        for (int i = 1 ; i <= n ; i ++ )\r\n        {\r\n            for (int j = m ; j >= v[i] ; j -- )\r\n            {\r\n                f[j] = max(f[j] , f[j - v[i]] + w[i]);\r\n            }\r\n        }\r\n\r\n        return f[m];\r\n    }\r\n};\r\n<\/pre>\n
2.\u5b8c\u5168\u80cc\u5305<\/h2>\n
\u9898\u76ee\u63cf\u8ff0\uff1a
\n\u6709 N \u79cd\u7269\u54c1\u548c\u4e00\u4e2a\u5bb9\u91cf\u662f V \u7684\u80cc\u5305\uff0c\u6bcf\u79cd\u7269\u54c1\u90fd\u6709\u65e0\u9650\u4ef6\u53ef\u7528\u3002
\n\u7b2c i \u79cd\u7269\u54c1\u7684\u4f53\u79ef\u662f vi\uff0c\u4ef7\u503c\u662f wi\u3002
\n\u6c42\u89e3\u5c06\u54ea\u4e9b\u7269\u54c1\u88c5\u5165\u80cc\u5305\uff0c\u53ef\u4f7f\u8fd9\u4e9b\u7269\u54c1\u7684\u603b\u4f53\u79ef\u4e0d\u8d85\u8fc7\u80cc\u5305\u5bb9\u91cf\uff0c\u4e14\u603b\u4ef7\u503c\u6700\u5927\u3002
\n\u8f93\u51fa\u6700\u5927\u4ef7\u503c\u3002<\/p>\n
\u793a\u4f8b\uff1a\r\n\u8f93\u5165\u6837\u4f8b\uff1a[[4,5][1,2],[2,4],[3,4],[4,5]];\r\n\u8f93\u51fa\u6837\u4f8b\uff1a10\r\n\u89e3\u91ca\uff1a\r\n\u7269\u54c1 2 \u653e\u5165\u80cc\u5305 5 \u6b21\uff0c\u603b\u4f53\u79ef\u4e3a 5\uff0c\u603b\u4ef7\u503c\u4e3a 10\u3002\r\n\u7269\u54c1 3 \u653e\u5165\u80cc\u5305 2 \u6b21\uff0c\u603b\u4f53\u79ef\u4e3a 4\uff0c\u603b\u4ef7\u503c\u4e3a 8\u3002\r\n\u7269\u54c1 4 \u653e\u5165\u80cc\u5305 2 \u6b21\uff0c\u603b\u4f53\u79ef\u4e3a 6\uff0c\u603b\u4ef7\u503c\u4e3a 8\u3002\r\n\u7269\u54c1 1 \u653e\u5165\u80cc\u5305 2 \u6b21\uff0c\u603b\u4f53\u79ef\u4e3a 8\uff0c\u603b\u4ef7\u503c\u4e3a 10\u3002\r\n\u7269\u54c1 5 \u653e\u5165\u80cc\u5305 2 \u6b21\uff0c\u603b\u4f53\u79ef\u4e3a 8\uff0c\u603b\u4ef7\u503c\u4e3a 10\u3002<\/pre>\n
class Solution {\r\npublic :\r\n    int completeBagQuestionSolve(int n , int m , vector<int>& v , vector<int>& w)\r\n    {\r\n        vector<vector<int> > f(n + 1 , vector<int>(m + 1 , 0));\r\n\r\n        for (int i = 1 ; i <= n ; i ++ )\r\n        {\r\n            for (int j = 0 ; j <= m ; j ++ )\r\n            {\r\n                if (j >= v[i]) f[i][j] = max(f[i - 1][j] , f[i][j - v[i]] + w[i]);\r\n                else f[i][j] = f[i - 1][j];\r\n            }\r\n        }\r\n\r\n        return f[n][m];\r\n    }\r\n};<\/pre>\n
\u5b8c\u5168\u80cc\u5305\u7684\u7a7a\u95f4\u4f18\u5316\r\n\u539f\u7406\u548c01\u80cc\u5305\u7a7a\u95f4\u4f18\u5316\u7c7b\u4f3c\uff0c\u4f46\u662f\u9700\u8981\u91cd\u590d\u4f7f\u7528\u72b6\u6001\u6240\u4ee5\u6b63\u5e8f\u904d\u5386\u3002\r\n<\/span><\/pre>\n
class Solution {\r\npublic :\r\n    int completeBagQuestionSolve(int n , int m , vector<int>& v , vector<int>& w)\r\n    {\r\n        vector<int> f(m + 1 , 0);\r\n\r\n        for (int i = 1 ; i <= n ; i ++ )\r\n        {\r\n            for (int j = v[i] ; j <= m ; j ++ )\r\n            {\r\n                f[j] = max(f[j] , f[j - v[i]] + w[i]);\r\n            }\r\n        }\r\n\r\n        return f[m];\r\n    }\r\n};<\/pre>\n
\u591a\u91cd\u80cc\u5305\u7c7b\u4f3c\u3001\u6df7\u5408\u80cc\u5305\u7c7b\u4f3c\u5199\u6cd5\u7701\u7565\u3002<\/span><\/pre>\n
 <\/p>\n
\u5b8c\u7ed3\u6492\u82b1<\/span><\/h1>\n
(\u6682\u65f6)<\/del><\/span><\/p>\n
 <\/p>\n
\u7ed9\u65f6\u5149\u4ee5\u751f\u547d\uff0c\u7ed9\u5c81\u6708\u4ee5\u6587\u660e\u3002<\/p><\/blockquote>\n","protected":false},"excerpt":{"rendered":"
\u58f0\u660e\uff1a \u672c\u6587\u4ec5\u4e3a\u4f5c\u8005\u4e3a\u4e86\u590d\u4e60\u800c\u5199\uff0c\u5e76\u975e\u4f5c\u4e3a\u6559\u7a0b\u4f7f\u7528\uff01 \u6590\u6ce2\u90a3\u5951\u7c7b\u578b \u901a\u5e38\u662f\u7ebf\u6027\u7684\uff0c\u72b6\u6001\u8f6c\u79fb\u4e3a\u76f8\u90bb\u5143\u7d20\u6216\u53d7\u5230\u9650\u5236\u7684\u90bb\u5143\u7d20 1.\u4f7f\u7528\u6700 …<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"emotion":"","emotion_color":"","title_style":"","license":"","footnotes":""},"categories":[7],"tags":[12,8,9,10,11],"class_list":{"0":"post-44","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"hentry","6":"category-algorithm","7":"tag-algorithm","8":"tag-dp","9":"tag-9","11":"tag-11"},"_links":{"self":[{"href":"https:\/\/m.qzcy2.top\/index.php\/wp-json\/wp\/v2\/posts\/44","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/m.qzcy2.top\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/m.qzcy2.top\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/m.qzcy2.top\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/m.qzcy2.top\/index.php\/wp-json\/wp\/v2\/comments?post=44"}],"version-history":[{"count":46,"href":"https:\/\/m.qzcy2.top\/index.php\/wp-json\/wp\/v2\/posts\/44\/revisions"}],"predecessor-version":[{"id":103,"href":"https:\/\/m.qzcy2.top\/index.php\/wp-json\/wp\/v2\/posts\/44\/revisions\/103"}],"wp:attachment":[{"href":"https:\/\/m.qzcy2.top\/index.php\/wp-json\/wp\/v2\/media?parent=44"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/m.qzcy2.top\/index.php\/wp-json\/wp\/v2\/categories?post=44"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/m.qzcy2.top\/index.php\/wp-json\/wp\/v2\/tags?post=44"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}