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?
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
Example 3:
Input: m = 7, n = 3
Output: 28
Example 4:
Input: m = 3, n = 3
Output: 6
Constraints:
- 1 <= m, n <= 100
- It's guaranteed that the answer will be less than or equal to 2 * 109.
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];
}
}