64. Minimum Path Sum

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本文介绍了一种寻找矩阵中从左上角到右下角路径的算法，该路径上的数值之和最小。采用动态规划的方法，通过逐步更新矩阵中的每个元素来实现。此算法仅允许向右或向下移动。

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Minimum Path Sum

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.

思路

同样使用动态规划类似于上几题

public class Solution {
    public int minPathSum(int[][] grid) {
        int m = grid.length;
        int n = grid[0].length;
        for(int i = 0; i < m; i++){
            for(int j = 0; j < n; j++){
                if(i == 0 && j == 0){
                    grid[i][j] = grid[i][j]; //初始
                }else if(i == 0 && j != 0){
                    grid[i][j] = grid[i][j] + grid[i][j-1]; //第一行的初始化 应为只能向右走
                }else if(i != 0 && j == 0){
                    grid[i][j] = grid[i][j] + grid[i-1][j]; //第一列的初始化 应为只能向下走
                }else{
                    grid[i][j] = Math.min(grid[i-1][j] , grid[i][j-1]) + grid[i][j];
                }
            }
        }
        return grid[m - 1][n - 1];
    }
}