Return a Shortest Path Through a Binary Grid

Question

The question asks the candidate to find the shortest path from the top-left corner to the bottom-right corner of a binary grid, where 0s represent open cells and 1s represent blocked cells.

Codemia · Accepted Answer

To solve the problem of finding the shortest path through a binary grid, we can treat the grid as a graph where each cell is a node. Our goal is to traverse from the top-left corner to the bottom-right corner, avoiding blocked cells represented by 1s. We will use a breadth-first search (BFS) approach since it is well-suited for finding the shortest path in an unweighted grid.

1. **Initialize the BFS**: Start by adding the top-left corner (0,0) to a queue. 
2. **Track visited nodes**: Use a set to keep track of visited nodes to avoid cycles. 
3. **Explore neighbors**: For each cell, explore its neighbors (up, down, left, right) that are within grid bounds and not blocked. 
4. **Count steps**: Maintain a step counter to track the number of moves taken to reach each cell.

Here’s a Python implementation of the BFS approach:
```python
from collections import deque

def shortest_path_binary_grid(grid):
    if not grid or grid[0][0] == 1 or grid[-1][-1] == 1:
        return -1
    n = len(grid)
    queue = deque([(0, 0, 1)])  # (row, column, steps)
    directions = [(0, 1), (1, 0), (0, -1), (-1, 0), (1, 1), (1, -1), (-1, 1), (-1, -1)]
    visited = set((0, 0))

while queue:
        x, y, steps = queue.popleft()
        if x == n - 1 and y == n - 1:
            return steps
        for dx, dy in directions:
            nx, ny = x + dx, y + dy
            if 0 <= nx < n and 0 <= ny < n and grid[nx][ny] == 0 and (nx, ny) not in visited:
                visited.add((nx, ny))
                queue.append((nx, ny, steps + 1))
    return -1
```
This code initializes a queue for BFS, explores all possible paths, and returns the number of steps taken to reach the bottom-right corner if a path exists.

The time complexity of this algorithm is O(N^2) in the worst case, where N is the number of rows (or columns) in the grid, as we may need to visit each cell. The space complexity is also O(N^2) due to the queue and visited set storing potentially all cells in the grid.

When implementing this solution, it is crucial to handle edge cases such as an empty grid or a grid where the start or end cells are blocked. Additionally, discussing alternative approaches, such as DFS, and their trade-offs can demonstrate a deeper understanding of pathfinding algorithms.

Return a Shortest Path Through a Binary Grid

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