[LeetCode] Unique Paths 解题报告

最新推荐文章于 2019-05-17 11:15:21 发布

原创最新推荐文章于 2019-05-17 11:15:21 发布 · 184 阅读

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本文探讨了如何使用动态规划算法解决机器人从网格左上角移动到右下角的问题，仅能向下或向右移动。以一个具体的3x7网格为例，详细解释了计算所有可能的唯一路径数量的方法。

Ranking: **
A robot is located at the top-left corner of a m x n grid (marked ‘Start’ in the diagram below).

The robot can only move either down or right at any point in time. The robot is trying to reach the bottom-right corner of the grid (marked ‘Finish’ in the diagram below).

How many possible unique paths are there?

Above is a 3 x 7 grid. How many possible unique paths are there?

Note: m and n will be at most 100.

» Solve this problem

[解题思路]
一维DP。 Step[i][j] = Step[i-1][j] + Step[i][j-1];

[Code]

1:       int uniquePaths(int m, int n) {  
2:            vector<int> maxV(n,0);  
3:            maxV[0]=1;  
4:            for(int i =0; i< m; i++)  
5:            {  
6:                 for(int j =1; j<n; j++)  
7:                 {  
8:                      maxV[j] = maxV[j-1] + maxV[j];  
9:                 }  
10:            }  
11:            return maxV[n-1];  
12:       }