Leetcode_UniquePath.cpp

/*
Problem No:-62

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) {
        if(m<=2){
            if(m==1) return 1;
            else return n;
        }
        if(n<=2){
            if(n==1) return 1;
            else return m;
        }
        vector<vector<int>> v(m,vector<int>(n));
        for(int i=0;i<m;i++){
            v[i][0]=1;
        }
        for(int i=0;i<n;i++){
            v[0][i]=1;
        }
        
        for(int i=1;i<m;i++)
            for(int j=1;j<n;j++)
                  v[i][j]=v[i-1][j]+v[i][j-1];
        
        return v[m-1][n-1];
    }
};