0062. Unique Paths

// 简单动归题
1062. 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 7 x 3 grid. How many possible unique paths are there?

Note: m and n will be at most 100.

Example 1:

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 -> Right -> Down
2. Right -> Down -> Right
3. Down -> Right -> Right
Example 2:

Input: m = 7, n = 3
Output: 28

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
class Solution {
public:
    int uniquePaths(int m, int n) {
        vector<vector<int> > ans(m, vector<int>(n, 1)); //int[][] f = new int[m][n]需要初始化
        for(int i = 1; i < m; i++){
            for(int j=1; j < n; j++){
                ans[i][j] = ans[i-1][j] + ans[i][j-1];// 其实不需要二维数组
            }
        }
        return ans[m-1][n-1];
    }
};

class Solution {
public:
    int uniquePaths(int m, int n) {
        vector<int> ans(n, 1);
        for(int i=1; i<m; i++){
            for(int j=1; j<n; j++){
                ans[j] += ans[j-1];
            }
        }
        return ans[n-1];
    }
};