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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.
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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<gu.kai.66@gmail.com, 150316990@qq.com>‘‘‘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)
leetCode —— Unique Paths II [Dynamic Programming]
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