m*n从左上角到右下角路径，路径数字总和最小

Question

m*n从左上角到右下角路径，每次只能向下或向右移动一步路径数字总和最小

Answer 1

可以使用动态规划来解决

public class MinimumPathSum {
    public int minPathSum(int[][] grid) {
        int m = grid.length;
        int n = grid[0].length;
        int[][] dp = new int[m][n];
        dp[0][0] = grid[0][0];
        // 初始化第一行和第一列
        for (int i = 1; i < m; i++) {
            dp[i][0] = dp[i - 1][0] + grid[i][0];
        }
        for (int j = 1; j < n; j++) {
            dp[0][j] = dp[0][j - 1] + grid[0][j];
        }
        // 动态规划
        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];
    }

    public static void main(String[] args) {
        int[][] grid = {{1, 3, 1}, {1, 5, 1}, {4, 2, 1}};
        MinimumPathSum solution = new MinimumPathSum();
        System.out.println(solution.minPathSum(grid)); 
    }
}