62. Unique Path Leetcode Python

hyperbolechi

于 2015-01-30 11:57:48 发布

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分类专栏： leetcode 文章标签： leetcode python DP

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本文介绍了一种计算机器人从网格左上角到右下角所有唯一路径数量的方法。提供了两种解决方案：一种是利用组合数学公式直接计算；另一种是采用动态规划逐步累加路径数。

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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?

这题有两种解法

1.直接的数学表达式 choose m-1 from m+n-2

class Solution:
    # @return an integer
    def fac(self,n):
        if n==1 or n==0:
            return 1
        return n*self.fac(n-1)
    def uniquePaths(self, m, n):
        if m==1 or n==1:
            return 1
        val1=self.fac(m+n-2)
        val2=self.fac(m-1)
        val3=self.fac(n-1)
        result=val1/(val2*val3)
        return result

2.动态规划，每一步都是相邻最近的格子的和。

代码如下

class Solution:
    # @return an integer
    def uniquePaths(self, m, n):
        dp=[[0 for index in range(n)] for index in range(m)]
        for row in range(m):
            dp[row][0]=1
        for col in range(n):
            dp[0][col]=1
        for row in range(1,m):
            for col in range(1,n):
                dp[row][col]=dp[row-1][col]+dp[row][col-1]
        return dp[m-1][n-1]