[leetcode]Unique Paths @ Python

原题地址：https://oj.leetcode.com/problems/unique-paths/

题意：

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.

解题思路：这道题和climbing stairs很像，可以用动态规划解决。状态转移方程为dp[i][j]=dp[i-1][j]+dp[i][j-1]。

代码：

class Solution:

    # @return an integer

    def uniquePaths(self, m, n):

        if m == 1 and n == 1:

            list = [[1]]

        elif m == 1 and n > 1:

            list = [[1 for i in range(n)]]

        elif m > 1 and n == 1:

            list = [[1] for i in range(m)]

        else:

            list = [[0 for i in range(n)] for i in range(m)]

            for i in range(0, n):

                list[0][i] = 1

            for i in range(0, m):

                list[i][0] = 1

            for i in range(1, m):

                for j in range(1, n):

                    list[i][j] = list[i-1][j] + list[i][j-1]

        return list[m-1][n-1]