LeetCode 64. Minimum Path Sum
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【题目】
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.
【题解】
这是一道典型的动态规划题目,令sum[i][j]为走到第i行第j列的格子时沿路上所有数字和最小的值,其动态转移方程为
sum[i][j]=min(sum[i-1][j], sum[i][j-1])+grid[i][j]
其中grid[i][j]为第i行第j列的格子上的数字,最后返回的结果为sum[m-1][n-1],m为行数,n为列数
【代码】
int minPathSum(vector<vector<int>>& grid){ int m = grid.size(); int n = grid[0].size(); vector<vector<int>> sum(m, vector<int>(n, grid[0][0])); for (int i = 1; i < m; i++) sum[i][0] = sum[i - 1][0] + grid[i][0]; for (int j = 1; j < n; j++) sum[0][j] = sum[0][j - 1] + grid[0][j]; for (int i = 1; i < m; i++) for (int j = 1; j < n; j++) sum[i][j] = min(sum[i - 1][j], sum[i][j - 1]) + grid[i][j]; return sum[m - 1][n - 1]; }
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