Leetcode #490: The Maze
In this guide, we solve Leetcode #490 The Maze in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
Problem Statement
There is a ball in a maze with empty spaces (represented as 0) and walls (represented as 1). The ball can go through the empty spaces by rolling up, down, left or right, but it won't stop rolling until hitting a wall.
Quick Facts
- Difficulty: Medium
- Premium: Yes
- Tags: Depth-First Search, Breadth-First Search, Array, Matrix
Intuition
We need to explore a structure deeply before backing up, which suits DFS.
DFS keeps local context on the call stack and is easy to implement recursively.
Approach
Define a recursive DFS that carries the necessary state.
Combine child results as the recursion unwinds.
Steps:
- Define a recursive DFS with state.
- Visit children and combine results.
- Return the final aggregation.
Example
Input: maze = [[0,0,1,0,0],[0,0,0,0,0],[0,0,0,1,0],[1,1,0,1,1],[0,0,0,0,0]], start = [0,4], destination = [4,4]
Output: true
Explanation: One possible way is : left -> down -> left -> down -> right -> down -> right.
Python Solution
class Solution:
def hasPath(
self, maze: List[List[int]], start: List[int], destination: List[int]
) -> bool:
def dfs(i, j):
if vis[i][j]:
return
vis[i][j] = True
if [i, j] == destination:
return
for a, b in [[0, -1], [0, 1], [1, 0], [-1, 0]]:
x, y = i, j
while 0 <= x + a < m and 0 <= y + b < n and maze[x + a][y + b] == 0:
x, y = x + a, y + b
dfs(x, y)
m, n = len(maze), len(maze[0])
vis = [[False] * n for _ in range(m)]
dfs(start[0], start[1])
return vis[destination[0]][destination[1]]
Complexity
The time complexity is O(V+E). The space complexity is O(V).
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.