牛客网：NC59 矩阵的最小路径和

/**
 * @author xienl
 * @description 矩阵的最小路径和
 * @date 2022/7/6
 */

public class Solution {
    public static void main(String[] args) {
        Solution solution = new Solution();
        int[][] arr = {{1,3,2,9},{8,3,3,4},{5,0,6,1},{8,8,4,0}};
        System.out.println(solution.minPathSum(arr));

    }

    public int minPathSum (int[][] matrix) {
        // write code here
        int n = matrix.length;
        int m = matrix[0].length;
        int[][] dp = new int[n][m];
        dp[0][0] = matrix[0][0];

        // 初始化dp
        for (int i = 1; i < n; i++){
            dp[i][0] = matrix[i][0] + dp[i - 1][0] ;
        }

        for (int i = 1; i < m; i++){
            dp[0][i] = matrix[0][i] + dp[0][ i - 1];
        }
        for (int i = 1; i < n; i++){
            for (int j = 1; j < m; j++){
                dp[i][j] = Math.min(dp[i - 1][j], dp[i][j - 1]) + matrix[i][j];
            }
        }
        return dp[n - 1][m - 1];
    }
}