[LeetCode] 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.

開一個f[m][n]的數組，f[i][j] = f[i-1][j] + f[i][j-1]，空間時間復雜度O(m*n)。用滾動數組空間復雜度可降為O(n)

class Solution {
public:
    int uniquePaths(int m, int n) {
        // Start typing your C/C++ solution below
        // DO NOT write int main() function
        vector<vector<int> > f(m, vector<int>(n));
        
        for(int i = 0; i < n; i++)
            f[0][i] = 1;
            
        for(int i = 0; i < m; i++)
            f[i][0] = 1;
            
        for(int i = 1; i < m; i++)
            for(int j = 1; j < n; j++)
                f[i][j] = f[i-1][j] + f[i][j-1];
                
        return f[m-1][n-1];
    }
};