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### by Sumit Chourasia | Oct 31, 2020 | Category :coding | Tags : algorithmarraydata-structureleetcodemedium #### Unique Paths - Array - Medium - LeetCode

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)