leetcode: 63. 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.
#
# For example,
# There is one obstacle in the middle of a 3x3 grid as illustrated below.
#
# [
#     [0,0,0],
#     [0,1,0],
#     [0,0,0]
# ]
# The total number of unique paths is 2.
#
# Note: m and n will be at most 100.

与 Unique Paths I 有两点不同：

1. 当(i, j)有障碍时dp[i][j] = 0
2. dp[0][j]和dp[i][0]未必为1.
    dp[0][j] = obstacleGrid[0][j] ? 0 : dp[0][j-1]
    dp[i][0] = obstacleGrid[i][0] ? 0 : dp[i-1][0]
3. 当obstacleGrid [0][0] = 1时，return 0

class Solution():
    def uniquePathsWithObstacles(self, x):
        m, n = len(x[0]), len(x)
        ways = [0] * m
        ways[0] = 1
        for i in range(n):
            if x[i][0] == 1:
                ways[0] = 0
            for j in range(1, m):
                if x[i][j] == 1:
                    ways[j] = 0
                else:
                    ways[j] += ways[j-1]
        return ways[-1]


if __name__ == "__main__":
    x = [[0,0,0],
         [0,1,0],
         [0,0,0]]
    assert Solution().uniquePathsWithObstacles(x) == 2