LeetCode 62. Unique Paths 题解
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题目描述:
62. Unique Paths
- Total Accepted: 106575
- Total Submissions: 279213
- Difficulty: Medium
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.
解题思路:
首先到达一个结点(x,y)(x>1.y>1),有两种方法,即从(x-1,y),(x,y-1),所以到(x,y)的路径数即为到(x-1,y)和(x,y-1)之和。搜索过程中,将已经走过的点的路径数记录下来,避免重复计算,从而提高运算效率。
代码展示:
//代码一// 复杂度 O(n*n) class Solution {public: int uniquePaths(int m, int n) { res = vector<vector<int> >(m,vector<int>(n,0)); res[0][0]=1; return dfs(m-1,n-1); }private: //res 已搜索过的结点的路径数 vector<vector<int> > res; int dfs(int x,int y) { if(x<0||y<0) return 0; if(x==0&&y==0) return 1; //如果未搜索过点x,y if(!res[x][y]) { res[x][y]=dfs(x-1,y)+dfs(x,y-1); return res[x][y]; } //若已求出到该点路径数,直接返回 else return res[x][y]; } };
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