leetCode —— Unique Paths II [Dynamic Programming]

唯一路径问题II

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.

--

第一种方法(uniquePathsWithObstacles)为递归实现，但是会超时，最后一个case有16亿+条路径...递归方法会走每条路径，所以一定会超时。

第二种方法(uniquePathsWithObstaclesDP)为动态规划。

‘‘‘
Created on Nov 25, 2014

@author: ScottGu<[email protected], [email protected]>
‘‘‘
class Solution:
    def __init__(self):
        self.ways=0
        self.max_x=0
        self.max_y=0

    # @param obstacleGrid, a list of lists of integers
    # @return an integer
    def uniquePathsWithObstacles(self, obstacleGrid):
        if(obstacleGrid==None):return 0
        if(len(obstacleGrid)==0):return 0
        if(obstacleGrid[0][0] ==1): return 0

        self.__init__()
        self.max_x=len(obstacleGrid[0])-1
        self.max_y=len(obstacleGrid)-1
        self.find_ways(0,0, obstacleGrid)
        return self.ways

    def find_ways(self, x, y, grid):
        if(x==self.max_x and y==self.max_y):
            self.ways=self.ways+1

        if(x<self.max_x and grid[y][x+1]!=1):
            self.find_ways(x+1, y, grid)
        if(y<self.max_y and grid[y+1][x]!=1):
            self.find_ways(x, y+1, grid)

    def uniquePathsWithObstaclesDP(self, obstacleGrid):
        m = len(obstacleGrid)
        if(m ==0): return 0
        n = len(obstacleGrid[0])
        if(obstacleGrid[0][0] ==1): return 0

        maxV={}
        for x in range(n):maxV[x]=0

        maxV[0]=1;
        for i in range(m):
            for j in range(n):
                if(obstacleGrid[i][j] ==1):
                    maxV[j]=0
                else:
                    if(j >0):
                        maxV[j] = maxV[j-1]+maxV[j]
        return maxV[n-1];  

if __name__ == ‘__main__‘:
    sl=Solution()
    grid=[[0,0,0],
          [0,1,0],
          [0,0,0]]
    print sl.uniquePathsWithObstacles(grid)
    grid=[[0,0,0,0,0],
          [0,1,0,0,0],
          [0,1,0,0,0],
          [0,1,0,0,0],
          [0,0,0,0,0]]
    print sl.uniquePathsWithObstacles(grid)
    grid= [
               [0,0,0,0,0,0,0,0,0,0],
               [0,0,0,0,0,1,0,0,0,0],
               [0,0,0,1,0,0,0,0,0,0],
               [0,0,0,0,0,0,0,0,0,0],
               [0,1,0,1,0,0,0,0,0,0],
               [0,0,0,0,0,0,0,0,1,0],
               [0,1,0,1,0,0,0,0,0,0]
           ]

    print sl.uniquePathsWithObstacles(grid)
    grid=[
[0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1],
[0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0],
[1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,1,0,0,0,0,0,0,0,0,1,0,0,1],
[0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0],
[0,0,0,1,0,1,0,0,0,0,1,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,1,0],
[1,0,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0],
[0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,0,0,0,1,0,1,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,1,0],
[0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,1,0,0,0,0,0],
[0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0],
[1,0,1,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,1,0,1,0,0,0,1,0,1,0,0,0,0,1],
[0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,1,0,0,0,0,0,0,1,1,0,0,0,0,0],
[0,1,0,1,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,1,0,0,0,0,0],
[0,1,0,0,0,0,0,0,1,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,1,0,1],
[1,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,1,1,0,0,1,0,0,0,0,0,0],
[0,0,1,0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,0,0,0,0,0,1,1,0,1,0,0,0,0,1,1],
[0,1,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,1,0,1],
[1,1,1,0,1,0,0,0,0,1,0,0,0,0,0,0,1,0,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,1,1],
[0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,1,0,0,0,1,0,0,0]
]
    print sl.uniquePathsWithObstaclesDP(grid)