Title

the problem link

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?

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

二维vector声明：

std::vector<std::vector<int>> dp(n, std::vector<int>(m, 0));

Solution

//cpp:
class Solution {
public:

	int uniquePaths(int m, int n) {
		vector<vector<int>> v;
		v.resize(n);
		for (int i = 0; i < v.size(); i++) {
			v[i].resize(m);
		}
		v[0][0] = 1;
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < m; j++) {
				if (i > 0) {
					v[i][j] += v[i - 1][j];
				}
				if (j > 0) {
					v[i][j] += v[i][j - 1];
				}
				cout << v[i][j] << " ";
			}
			cout << endl;
		}
		return v[n-1][m-1];
	}
};