[leetcode]Unique Paths

新博文地址：[leetcode]Unique Paths

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.

只能向右或者向下走，即说明，要到达重点(m,n)要么经过（m-1,n）要么经过（m,n-1），很典型的斐波那契数列好吗？path[m][n] = path[m-1][n]+path[m][n-1]，可以用递归，但是最好用迭代。线性时间复杂度。 

不罗嗦

    public int uniquePaths(int m, int n) {
		int[][] path = new int[m][n];
		int max = m > n ? m : n;
		for (int i = 0; i < max; i++) {
			if (i < n) {
				path[0][i] = 1;
			}
			if (i < m) {
				path[i][0] = 1;
			}
		}
		for (int i = 1; i < m; i++) {
			for (int j = 1; j < n; j++) {
				path[i][j] = path[i-1][j] + path[i][j-1];
			}
		}
		return path[m-1][n-1];
    }