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:
1. Right -> Down -> Down
2. Down -> Down -> Right
3. Down -> Right -> Down
Constraints:
- 1 <= m, n <= 100
class Solution {
public int uniquePaths(int m, int n) {
int[][] dp = new int[m+1][n+1];
dp[1][1] = 1;
for(int i=2;i<=m;i++){
dp[i][1] = dp[i-1][1];
}
for(int j=2;j<=n;j++){
dp[1][j] = dp[1][j-1];
}
for(int i=2;i<=m;i++){
for(int j=2;j<=n;j++){
dp[i][j] = dp[i-1][j]+dp[i][j-1];
}
}
return dp[m][n];
}
}