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[12/31] 980. Unique Paths III
본문
You are given an m x n
integer array grid
where grid[i][j]
could be:
1
representing the starting square. There is exactly one starting square.2
representing the ending square. There is exactly one ending square.0
representing empty squares we can walk over.-1
representing obstacles that we cannot walk over.
Return the number of 4-directional walks from the starting square to the ending square, that walk over every non-obstacle square exactly once.
Example 1:
Input: grid = [[1,0,0,0],[0,0,0,0],[0,0,2,-1]] Output: 2 Explanation: We have the following two paths: 1. (0,0),(0,1),(0,2),(0,3),(1,3),(1,2),(1,1),(1,0),(2,0),(2,1),(2,2) 2. (0,0),(1,0),(2,0),(2,1),(1,1),(0,1),(0,2),(0,3),(1,3),(1,2),(2,2)
Example 2:
Input: grid = [[1,0,0,0],[0,0,0,0],[0,0,0,2]] Output: 4 Explanation: We have the following four paths: 1. (0,0),(0,1),(0,2),(0,3),(1,3),(1,2),(1,1),(1,0),(2,0),(2,1),(2,2),(2,3) 2. (0,0),(0,1),(1,1),(1,0),(2,0),(2,1),(2,2),(1,2),(0,2),(0,3),(1,3),(2,3) 3. (0,0),(1,0),(2,0),(2,1),(2,2),(1,2),(1,1),(0,1),(0,2),(0,3),(1,3),(2,3) 4. (0,0),(1,0),(2,0),(2,1),(1,1),(0,1),(0,2),(0,3),(1,3),(1,2),(2,2),(2,3)
Example 3:
Input: grid = [[0,1],[2,0]] Output: 0 Explanation: There is no path that walks over every empty square exactly once. Note that the starting and ending square can be anywhere in the grid.
Constraints:
m == grid.length
n == grid[i].length
1 <= m, n <= 20
1 <= m * n <= 20
-1 <= grid[i][j] <= 2
- There is exactly one starting cell and one ending cell.
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class Solution:
def uniquePathsIII(self, grid: List[List[int]]) -> int:
ROW, COL = len(grid), len(grid[0])
path = set()
start = (0,0)
goal = (0,0)
obstacles = 0
for row in range(ROW):
for col in range(COL):
if grid[row][col] == 2:
goal = (row, col)
elif grid[row][col] == -1:
obstacles += 1
elif grid[row][col] == 1:
start = (row, col)
res = 0
directions = [(0,1),(1,0),(-1,0),(0,-1)]
def dfs(r, c):
path.add((r,c))
if len(path) == ROW*COL - obstacles and (r,c) == goal:
nonlocal res
res += 1
else:
for rd, cd in directions:
nr, nc = r+rd, c+cd
if 0<=nr<ROW and 0<=nc<COL and grid[nr][nc] != -1 and (nr, nc) not in path:
dfs(nr, nc)
path.remove((r,c))
dfs(start[0], start[1])
return res