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by Sumit Chourasia | Oct 31, 2020 | Category :coding | Tags : algorithm array data-structure leetcode medium

Unique Paths - Array - Medium - LeetCode

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)