# LeetCode62. Unique Paths（动态规划）

## LeetCode62. Unique Paths（动态规划）

• Medium
• Accepted：270,453
• Submissions：577,298

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

Note: m and n will be at most 100.

Example 1:

Input: m = 3, n = 2
Output: 3
Explanation:
From the top-left corner, there are a total of 3 ways to reach the bottom-right corner:
1. Right -> Right -> Down
2. Right -> Down -> Right
3. Down -> Right -> Right

Example 2:

Input: m = 7, n = 3
Output: 28

### 链接

https://leetcode.com/problems/unique-paths

### 代码

• Runtime: 8 ms, faster than 11.52% of C++ online submissions for Unique Paths.
• Memory Usage: 8.6 MB, less than 45.22% of C++ online submissions for Unique Paths.
class Solution {
public:
int uniquePaths(int m, int n) {
vector <int> v(m + 1, 1);
for (int i = 2; i <= n; ++i)
{
for (int j = 2; j <= m; ++j)
v[j] = v[j - 1] + v[j];
}
return v[m];
}
};

The end.
2019年4月1日 星期一