64-最小路径和

LeetCode 64. Minimum Path Sum

LeetCode-64

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.

Example 1:

Input: grid = [[1,3,1],[1,5,1],[4,2,1]]
Output: 7
Explanation: Because the path 1 → 3 → 1 → 1 → 1 minimizes the sum.

method

int minPathSum(vector<vector<int>>& grid) {
    int n = grid.size(), m = grid[0].size();
    vector<vector<int>> dp(n, vector<int>(m, 0));
    dp[0][0] = grid[0][0];
    for (int i = 1; i < n; i++) dp[i][0] = dp[i - 1][0] + grid[i][0];
    for (int j = 1; j < m; j++) dp[0][j] = dp[0][j - 1] + grid[0][j];
    for (int i = 1; i < n; i++) {
        for (int j = 1; j < m; j++) {
            dp[i][j] = min(dp[i - 1][j], dp[i][j - 1]) + grid[i][j];
        }
    }
    return dp[n - 1][m - 1];
}