63 leetcode - Unique Paths

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于 2016-12-27 20:41:17 发布

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本文介绍了一个经典的算法问题——独特路径。该问题要求计算机器人从网格左上角到右下角的不同路径数量，机器人只能向下或向右移动。通过动态规划的方法解决此问题，并提供了Python实现代码。

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#!/usr/bin/python
# -*- coding: utf-8 -*-
'''
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?
'''
class Solution(object):
    def uniquePaths(self, m, n):
        """
        :type m: int
        :type n: int
        :rtype: int
        """
        if m == 0 or n == 0:
            return 0

        dp = [[0] * n  for i in range(m)]
        for i in range(n):
            dp[0][i] = 1
        for i in range(m):
            dp[i][0] = 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]

if __name__ == "__main__":
    s = Solution()
    print s.uniquePaths(2,2)