[LeetCode]64.Minimum Path Sum

【题目】

Given amxngrid filled with non-negative numbers, find a path from top left to bottom right whichminimizesthe sum of all numbers along its path.

Note:You can only move either down or right at any point in time.

【思路】

设sum[i][j] 到位置（i,j）时路径最小和

状态转移方程：

sum[i][j] = min(sum[i][j-1] ,sum[i-1][j]) + grid[i][j]

优化（空间轮转）：

sum[j] = min(sum[j],sum[j-1]) + grid[i][j]

【代码】

    /*------------------------------------
    *   日期：2015-02-04
    *   作者：SJF0115
    *   题目: 64.Minimum Path Sum
    *   网址：https://oj.leetcode.com/problems/minimum-path-sum/
    *   结果：AC
    *   来源：LeetCode
    *   博客：
    ---------------------------------------*/
    #include <iostream>
    #include <vector>
    #include <cstring>
    #include <algorithm>
    using namespace std;

    class Solution {
    public:
        int minPathSum(vector<vector<int> > &grid) {
            if(grid.empty()){
                return 0;
            }//if
            int row = grid.size();
            int col = grid[0].size();
            vector<int> sum(grid[0]);
            // 第一行 只能从左边过来
            for(int i = 1;i < col;++i){
                sum[i] += sum[i-1];
            }//for
            // 动态规划
            // sum[j] = min(sum[j],sum[j-1]) + grid[i][j]
            for(int i = 1;i < row;++i){
                sum[0] += grid[i][0];
                for(int j = 1;j < col;++j){
                    sum[j] = min(sum[j],sum[j-1]) + grid[i][j];
                }//for
            }//for
            return sum[col-1];
        }
    };

    int main(){
        Solution s;
        vector<vector<int> > grid = {{1,5,3,7},{2,6,4,1},{5,4,6,5}};
        int result = s.minPathSum(grid);
        // 输出
        cout<<result<<endl;
        return 0;
    }