Minimum Path Sum

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.

 用DP实现

找出递推关系和边界条件

public class Solution {
    public int minPathSum(int[][] grid) {
        if(1 == grid.length && 1 == grid[0].length)
            return grid[0][0];
        int result[][] = new int[grid.length + 1][grid[0].length + 1];
        
            
            for(int i = 1; i <= grid.length; i++){
                for(int j = 1; j <= grid[0].length; j++){
                    if(i == 1){
                        result[i][j] = result[i][j - 1]; 
                    }
                    else if(j == 1)
                        result[i][j] = result[i - 1][j];
                    else
                        result[i][j] = result[i - 1][j] <= result[i][j - 1] ? result[i - 1][j] : result[i][j - 1];
                    result[i][j] += grid[i - 1][j - 1];
                }
            }

            return result[grid.length][grid[0].length];
    }
}