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.

原题链接：https://oj.leetcode.com/problems/unique-paths/

求m*n矩阵的(0,0)到(m,n)有多少种唯一走法，其中每次只能向右或向下走一步。

动态规划状态转移方程：dp[m][n] = dp[m][n-1] + dp[m-1][n]，其中dp[m][n]表示到达坐标[m][n]时有多少条唯一的路径

public class UniquePaths {
	public int uniquePaths(int m, int n) {
		if (m == 0 || n == 0)
			return 1;
		int dp[][] = new int[m][n];
		for (int r = 0; r < m; r++)
			dp[r][0] = 1;
		for (int c = 0; c < n; c++)
			dp[0][c] = 1;
		for (int r = 1; r < m; r++) {
			for (int c = 1; c < n; c++)
				dp[r][c] = dp[r - 1][c] + dp[r][c - 1];
		}
		return dp[m - 1][n - 1];
	}
}

LeetCode——Unique Paths