[leetcode]Unique Paths @ Python

原題地址：https://oj.leetcode.com/problems/unique-paths/

題意：

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.

解題思路：這道題和climbing stairs很像，可以用動態規划解決。狀態轉移方程為dp[i][j]=dp[i-1][j]+dp[i][j-1]。

代碼：

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]