[LeetCode]题解（python）：063-Unique path II

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题目来源

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https://leetcode.com/problems/unique-paths-ii/

Follow up for "Unique Paths":

Now consider if some obstacles are added to the grids. How many unique paths would there be?

An obstacle and empty space is marked as 1 and 0 respectively in the grid.

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题意分析

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Input:a matrix as list[list[int]]

Output:the number of path

Conditions:从左上角走到左下角，注意有障碍不能通过

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题目思路

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上一题是用数学方法直接解，这一题用动态规划吧，因为每一步都会基于上一格或者是左一格，动态方程为dp[i][j] = dp[i][j-1] + dp[i-1][j]

注意初始化的时候如果遇到障碍，后面的位置不能初始化为0了

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AC代码（Python）

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class Solution(object):
    def uniquePathsWithObstacles(self, obstacleGrid):
        """
        :type obstacleGrid: List[List[int]]
        :rtype: int
        """
        m = len(obstacleGrid)
        n = len(obstacleGrid[0])
        dp = [[0 for i in range(n)] for j in range(m)]
        for i in range(n):
            if obstacleGrid[0][i] == 1:
                break
            else:
                dp[0][i] = 1
        
        for i in range(m):
            if obstacleGrid[i][0] == 1:
                break
            else:
                dp[i][0] = 1
        
        for i in range(1, m):
            for j in range(1, n):
                if obstacleGrid[i][j] == 0:
                    dp[i][j] = dp[i - 1][j] + dp[i][j - 1]
        
        return dp[m - 1][n - 1]