How do you solve Find a Safe Walk Through a Grid on LeetCode?

Find a Safe Walk Through a Grid (LeetCode #3286) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(n) space complexity. Key insight: Using BFS ensures we explore the shortest paths first, which is crucial for pathfinding problems.

What is the time complexity of Find a Safe Walk Through a Grid?

The optimal solution for Find a Safe Walk Through a Grid runs in O(n) time and uses O(n) space. The time complexity is O(n) as we explore each cell at most once. The space complexity is O(n) due to the queue used for BFS.

What is the brute force solution for Find a Safe Walk Through a Grid?

The brute force approach for Find a Safe Walk Through a Grid is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach involves exploring all possible paths from the start to the end of the grid. We can use a depth-first search (DFS) to check if there's a valid path that allows us to reach the destination while keeping our health above zero. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Find a Safe Walk Through a Grid?

Find a Safe Walk Through a Grid uses the following concepts: Array, Breadth-First Search, Graph Theory, Heap (Priority Queue), Matrix, Shortest Path. The recommended patterns to study are: Graph Traversal, Breadth-First Search, Depth-First Search.

What are the interview tips for Find a Safe Walk Through a Grid?

Always clarify the problem constraints and edge cases before diving into coding. Explain your thought process as you write code; it shows your understanding. Practice BFS and DFS problems to become comfortable with these traversal techniques.

What are common mistakes when solving Find a Safe Walk Through a Grid?

Not handling edge cases where health drops to zero immediately. Failing to mark cells as visited can lead to infinite loops.

#3286

Find a Safe Walk Through a Grid

Medium

ArrayBreadth-First SearchGraph TheoryHeap (Priority Queue)MatrixShortest PathGraph TraversalBreadth-First SearchDepth-First Search

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n)
Space	O(1)	O(n)

💡

Intuition

Time O(n)Space O(n)

The optimal solution uses a Breadth-First Search (BFS) approach with a queue to explore the grid. This allows us to find the shortest path while efficiently managing health points, ensuring we only explore viable paths.

⚙️

Algorithm

4 steps

1Step 1: Initialize a queue with the starting position (0, 0) and the initial health.
2Step 2: While the queue is not empty, dequeue an element and check if it's the bottom-right corner.
3Step 3: For each valid move (up, down, left, right), calculate the new health and enqueue the new position if health is still positive and not visited.
4Step 4: Continue until the queue is empty or the destination is reached.

solution.py24 lines

1# Full working Python code
2from collections import deque
3from typing import List
4
5def canReach(grid: List[List[int]], health: int) -> bool:
6    m, n = len(grid), len(grid[0])
7    queue = deque([(0, 0, health)])
8    visited = set()
9    directions = [(1, 0), (-1, 0), (0, 1), (0, -1)]
10
11    while queue:
12        x, y, h = queue.popleft()
13        if (x, y) == (m - 1, n - 1) and h >= 1:
14            return True
15        visited.add((x, y))
16
17        for dx, dy in directions:
18            nx, ny = x + dx, y + dy
19            if 0 <= nx < m and 0 <= ny < n and (nx, ny) not in visited:
20                next_health = h - grid[nx][ny]
21                if next_health > 0:
22                    queue.append((nx, ny, next_health))
23
24    return False

ℹ

Complexity note: The time complexity is O(n) as we explore each cell at most once. The space complexity is O(n) due to the queue used for BFS.

1Using BFS ensures we explore the shortest paths first, which is crucial for pathfinding problems.
2Tracking visited nodes prevents cycles and unnecessary re-exploration.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.