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.
public class Solution {
public int UniquePaths(int m, int n) {
var T = new int[m,n];
for(int i=0;i<m;i++){
T[i,0]=1;
}
for(int i=0;i<n;i++){
T[0,i]=1;
}
for(int i=1;i<m;i++){
for(int j=1;j<n;j++){
T[i,j]=T[i-1,j] + T[i,j-1];
}
}
return T[m-1,n-1];
}
}
Time Complexity: O(m*n)
Space Complexity: O(m*n)