leetcode 9: Unique Paths

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?

Above is a 3 x 7 grid. How many possible unique paths are there?

Note: m and n will be at most 100.

 

class Solution {
    template <class T> 
    T swap( T& t1, T& t2) {
        T temp;
        temp = t1;
        t1 = t2;
        t2 = temp;
    }
    
public:
    int uniquePaths(int m, int n) {
        // Start typing your C/C++ solution below
        // DO NOT write int main() function
        
        if(m<=1 || n<=1) return 1;
        
        vector<int> r(n,0);
        vector< vector<int> > dp(m, r);
        
        for( int i=0; i<n; ++i) {
            dp[0][i] = 1;
        }
        
        for( int i=0; i<m; ++i) {
            dp[i][0] = 1;
        }
        
        for( int i=1; i<m; ++i) {
            for(int j=1; j<n; ++j) {
                dp[i][j] = dp[i-1][j] + dp[i][j-1];
            }
        }
        
        return dp[m-1][n-1];
    }
};