[LeetCode]: 64: Minimum Path Sum

题目：

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：动态规划

整个序列的最小路径= 上一个节点的最小路径+当前路径的节点值

依次往前看，第一个点的最小序列等于其本身

代码：

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

        if(grid.length == 0){
            return 0;
        }
        
        int[][] intResult = new int[grid.length][grid[0].length];

        for(int i = 0;i<grid.length;i++){
            for(int j = 0;j<grid[i].length;j++){
                if(i==0 && j==0){
                    intResult[i][j] = grid[i][j];
                }else if(i == 0 && j!=0){
                    intResult[i][j] = intResult[i][j-1] + grid[i][j];
                }
                else if(j== 0 && i!= 0){
                    intResult[i][j] = intResult[i-1][j] + grid[i][j];
                }
                else{
                    int intX = intResult[i][j-1] + grid[i][j];
                    int intY = intResult[i-1][j] + grid[i][j];
                    
                    if(intX > intY){
                        intResult[i][j] = intY;
                    }
                    else{
                        intResult[i][j] = intX;
                    }
                }
            }
        }
        
        return intResult[grid.length-1][grid[0].length-1];
    }