There is a robot on an m x n grid. The robot is initially located at the top-left corner (i.e., grid[0][0]). The robot tries to move to the bottom-right corner (i.e., grid[m - 1][n - 1]). The robot can only move either down or right at any point in time.
Given the two integers m and n, return the number of possible unique paths that the robot can take to reach the bottom-right corner.
The test cases are generated so that the answer will be less than or equal to 2 * 109.
Example 1:
Input: m = 3, n = 7 Output: 28
Example 2:
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:
- Right → Down → Down
- Down → Down → Right
- Down → Right → Down
Constraints:
1 <= m, n <= 100
Code
class Solution {
public:
int uniquePaths(int m, int n) {
vector<int> dp(n, 1);
for(int i = 1; i < m; i++) {
for(int j = 1; j < n; j++) {
dp[j] += dp[j - 1];
}
}
return dp[n - 1];
}
};