LeetCode OJ：Minimum Path Sum（最小路径和）

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.

对m * n 的网格，求其左上角到右下角的最短路径和：

DP问题，计算式是：min(ret[i][j]) = min(ret[i - 1][j], ret[i][j - 1]) + input[i][j];

代码如下：

class Solution {
public:
    int minPathSum(vector<vector<int>>& grid) {
        if(grid.size() == 0 || grid[0].size() == 0) return 0;
        int szHor = grid.size();
        int szVer = grid[0].size();
        vector<vector<int>> ret = grid;
        ret[0][0] = grid[0][0]
        for(int i = 1; i < szHor; ++i){
            ret[i][0] = ret[i - 1][0] + grid[i][0];
        }

        for(int i = 1; i < szVer; ++i){
            ret[0][i] = ret[0][i - 1] + grid[0][i];
        }
        
        for(int i = 1; i < grid.size(); ++i){
            for(int j = 1; j < grid[0].size(); ++j){
                ret[i][j] = min(ret[i - 1][j], ret[i][j - 1]) + grid[i][j];
            }
        }
        return ret[szHor - 1][szVer - 1];
    }
};

 简单的DP问题，java版本代码如下所示：

public class Solution {
    public int minPathSum(int[][] grid) {
        if(grid.length == 0 || grid[0].length == 0)
            return 0;        
        int szRol = grid.length;
        int szCol = grid[0].length;
        int [][] ret = new int [szRol][szCol];
        ret[0][0] = grid[0][0];
        for(int i = 1; i < szRol; ++i){
            ret[i][0] = ret[i-1][0] + grid[i][0];
        }
        for(int i = 1; i < szCol; ++i){
            ret[0][i] = ret[0][i-1] + grid[0][i];  
        }
        for(int i = 1; i < szRol; ++i){
            for(int j = 1; j < szCol; ++j){
                ret[i][j] = Math.min(ret[i-1][j], ret[i][j-1]) + grid[i][j];       
            }
        }
        return ret[szRol-1][szCol-1];
    }
}