64. 最小路径和

动态规划

class Solution {
    public int minPathSum(int[][] grid) {

        int m = grid.length;
        int n = grid[0].length;

        /**
         * dp[i][j]定义为从起点出发到当前这个点的最小路径和
         * 初始值dp[0][0] == grid[0][0]
         */
        int[][] dp = new int[m][n];
        dp[0][0] = grid[0][0];

        for (int i = 1; i < n; i++) {
            dp[0][i] = dp[0][i - 1] + grid[0][i];
        }

        for (int i = 1; i < m; i++) {
            dp[i][0] = dp[i - 1][0] + grid[i][0];
        }

        for (int i = 1; i < m; i++) {

            for (int j = 1; j < n; j++) {
                dp[i][j] = Math.min(dp[i - 1][j], dp[i][j - 1]) + grid[i][j];
            }
        }

        return dp[m - 1][n - 1];
    }
}

/**
 * 时间复杂度 O(m*n)
 * 空间复杂度 O(m*n)
 */

https://leetcode-cn.com/problems/minimum-path-sum/