题目
Given an n x n
binary matrix grid
, return the length of the shortest clear path in the matrix. If there is no clear path, return -1
.
A clear path in a binary matrix is a path from the top-left cell (i.e., (0, 0)
) to the bottom-right cell (i.e., (n - 1, n - 1)
) such that:
- All the visited cells of the path are
0
. - All the adjacent cells of the path are 8-directionally connected (i.e., they are different and they share an edge or a corner).
The length of a clear path is the number of visited cells of this path.
Example 1:
Input: grid = [[0,1],[1,0]]
Output: 2
Example 2:
Input: grid = [[0,0,0],[1,1,0],[1,1,0]]
Output: 4
Example 3:
Input: grid = [[1,0,0],[1,1,0],[1,1,0]]
Output: -1
Constraints:
n == grid.length
n == grid[i].length
1 <= n <= 100
grid[i][j] is 0 or 1
思路
dfs超时,而bfs却能够顺利通过,看来遇到迷宫题还是优先bfs为好。由于bfs遍历顺利永远是从近到远,不用判断到终点的距离是否最近,第一个到终点的就是距离最短的路径。
代码
python版本:
# dfs,超时
class Solution:
def shortestPathBinaryMatrix(self, grid: List[List[int]]) -> int:
def dfs(i, j):
if i < 0 or i >= len(grid) or j < 0 or j >= len(grid[0]) or grid[i][j] == 1:
return 99999999
if i == len(grid)-1 and j == len(grid[0])-1:
return 1
res = 99999999
for x, y in [[1, 0], [-1, 0], [0, 1], [0, -1], [1, 1], [1, -1], [-1, 1], [-1, -1]]:
grid[i][j] = 1
res = min(res, dfs(i+x, j+y))
grid[i][j] = 0
return 1+res
res = dfs(0, 0)
return res if res < 99999999 else -1
# bfs
class Solution:
def shortestPathBinaryMatrix(self, grid: List[List[int]]) -> int:
q = [(0, 0, 1)]
for i, j, d in q:
if i < 0 or i >= len(grid) or j < 0 or j >= len(grid[0]) or grid[i][j] == 1:
continue
if i == len(grid)-1 and j == len(grid[0])-1:
return d
grid[i][j] = 1
for x, y in ((0, 1), (0, -1), (1, 0), (-1, 0), (1, 1), (1, -1), (-1, 1), (-1, -1)):
q.append((i+x, j+y, d+1))
return -1