62. 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?

题意：从方格的左上角到右下角，每次只能向右或向下，问有多少种走法。

思路：每个方格可以有左边或上边走过来，故dp[m][n] = dp[m-1][n] + dp[m][n-1];

class Solution {
public:
	int uniquePaths(int m, int n) {
		if (m == 0 || n == 0)
			return 0;
		vector<vector<int>> dp(m, vector<int>(n, 1));

		for (int i = 1; i < m; i++){
			for (int j = 1; j < n; j++){
				dp[i][j] = dp[i][j - 1] + dp[i - 1][j];
			}
		}
		return dp[m-1][n-1];
		
	}
};