LeetCode 64. Minimum Path Sum
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Given a m x n grid filled with non-negative numbers, find a path from top left to bottom right which minimizes the sum of all numbers along its path.
Note: You can only move either down or right at any point in time.
用一个dp二维数组标记当前方格的最小值0.当i == 0 && j == 0的时候,dp[i][j] = grid[i][j];1.对于i==0的时候,为最上面一排,当前方格只能由左边方格来,所以dp[i][j] = dp[i][j-1] + grid[i][j];2.对于j==0的时候,为最左边一排,当前方格只能由上边方格来,所以dp[i][j] = dp[i-1][j] + grid[i][j];3.其他情况下,dp[i][j] = min(dp[i-1][j], dp[i][j-1]) + grid[i][j];最后直到一直递推输出到终点(m-1, n-1)的时候return dp[m-1][n-1];
class Solution {public: int minPathSum(vector<vector<int>>& grid) { int n=grid.size(),m=grid[0].size(); int dp[n][m]; for(int i=0;i<n;i++){ for(int j=0;j<m;j++){ if(i==0&&j==0) dp[i][j]=grid[i][j]; else if(i==0)dp[i][j]=dp[i][j-1]+grid[i][j]; else if(j==0)dp[i][j]=dp[i-1][j]+grid[i][j]; else dp[i][j]=min(dp[i-1][j],dp[i][j-1])+grid[i][j]; } } return dp[n-1][m-1]; }};
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