Binary Matrix Shortest Path

Find the shortest clear path from top-left to bottom-right using 8-directional BFS

Binary Matrix

Current Cell

Distance

Queue Size

Shortest Path

BFS Queue

Empty

Click "Step" or "Play" to find the shortest path from (0,0) to (n-1,n-1)

Blocked (1)

Clear (0)

Start

Goal

Current

Visited

Path

Python Code - BFS Approach

                if grid[0][0] != 0 or grid[n-1][n-1] != 0:
            
                    return -1
            
                queue = deque([(0, 0, 1)]) # (row, col, distance)
            
                while len(queue) > 0:
            
                    i, j, dist = queue.popleft()
            
                    if in_bounds and grid[i][j] == 0 and not visited[i][j]:
            
                        visited[i][j] = True
            
                        if i == n-1 and j == n-1: return dist
            
                        for di, dj in directions: # 8 directions
            
                            queue.append((i+di, j+dj, dist+1))
            
                return -1 # no path found