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() ==  || grid[].size() == ) return ;
         int szHor = grid.size();
         int szVer = grid[].size();
         vector<vector<int>> ret = grid;
         ret[][] = grid[][]
         for(int i = ; i < szHor; ++i){
             ret[i][] = ret[i - ][] + grid[i][];
         }

         for(int i = ; i < szVer; ++i){
             ret[][i] = ret[][i - ] + grid[][i];
         }

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

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];
     }
 }