62_UniquePaths.py

# coding: utf8


"""
    题目链接: https://leetcode.com/problems/unique-paths/description.
    题目描述:

    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.

"""


class Solution(object):
    def uniquePaths(self, m, n):
        """
        :type m: int
        :type n: int
        :rtype: int
        """
        if m <= 1 or n <= 1:
            return 1

        return self.dynamic_unique_paths(m, n)

    # 常规dp
    def dynamic_unique_paths(self, m, n):
        dp = [[0 for _ in range(n)] for _ in range(m)]
        for i in range(m):
            dp[i][0] = 1
        for j in range(n):
            dp[0][j] = 1
        for i in range(1, m):
            for j in range(1, n):
                dp[i][j] = dp[i][j - 1] + dp[i - 1][j]

        return dp[m - 1][n - 1]