62. Unique Paths - medium
문제
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?
제한사항
- m and n will be at most 100.
입출력 예
1
2
3
4
5
6
7
8
9
10
11
12
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
풀이
- DP
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
class Solution {
public:
int uniquePaths(int m, int n) {
if(m == 1 || n == 1)
return 1;
vector<vector<int>> item(m, vector<int>(n, 1));
for(auto i = 1 ; i < m ; ++i){
for(auto j = 1 ; j < n ; ++j){
item[i][j] = item[i-1][j] + item[i][j-1];
}
}
return item[m-1][n-1];
}
};