Shortest Bridge Between Islands: análisis del problema

How to solve the shortest bridge problem between islands?

The problem we are talking about is to find the most efficient way to create a bridge between two islands in a binary matrix. You are faced with a new challenge: finding the minimum distance needed to connect two islands, represented by groups of adjacent cells of ones, surrounded by cells of zeros representing water. Let's break down how you might approach this problem with your programming skills.

What is an island?

• An island is made up of adjacent cells of ones ('1') that form a block of land.
• They must be surrounded by cells of zeros ('0'), symbolizing water.
• They can have any shape, which makes it complex to find the optimal point for the bridge.

How to find the shortest distance to build the bridge?

The goal is to find the ends of the islands that are closest to each other, so as to minimize the "bridge" of cells of zeros needed to connect the islands. I invite you to think about how you can use previous solutions. In particular, you could reuse elements of the code used to identify the number of islands and adapt it to this new context.

Practical example

Imagine a ring formed by an island surrounding another central island. Here, since each boundary point of the outer island is equidistant from the inner one, several solutions can be equally valid. We can consider these situations:

1. Equal distances: when the islands are equidistant at all points, the result would be 1, since any bridge will have the same minimum length.
2. Irregular shapes: You might be faced with unusually shaped islands, where you need to identify the optimal points for the bridge, often involving more computational complexity.

How do you reuse parts of the code from the previous problem?

Moving forward, consider how you used search algorithms in the 'number of islands' problem. You could:

• Employ Depth First Search (DFS) or Breadth First Search (BFS) to identify islands.
• Modify these methods to search the shortest possible distance between island edges.

In implementing these concepts, I share a code snippet you might consider:

# Example for BFS in Pythonfrom collections import deque
def bfs_shortest_bridge(grid): # Initialize queue for BFS and apply initial search for an island queue = deque() for i in range(len(grid)): for j in range(len(grid[0])): if grid[i][j] == 1:
                dfs_mark_island(grid, i, j, queue) break if queue: break    
 # Expand the bridge using BFS steps = 0 directions = [(-1, 0), (1, 0), (0,-1), (0, 1)] while queue: size = len(queue) for _ in range(size): x, y = queue.popleft() for dx, dy in directions: nx, ny = x + dx, y + dy if 0 <= nx < len(grid) and 0 <= ny < len(grid[0]): if grid[nx][ny] == 1: return steps elif grid[nx][ny] == 0: grid[nx][ny] =-1 # Mark the expanded water queue.append((nx, ny)) steps += 1 return-1
def dfs_mark_island(grid, i, j, queue): if i < 0 or i >= len(grid) or j < 0 or j >= len(grid[0]) or grid[i][j] != 1: return grid[i][j] =-1 # Mark as visited queue.append((i, j)) for di, dj in [(-1, 0), (1, 0), (0,-1), (0, 1)]: dfs_mark_island(grid, i + di, j + dj, queue)

This snippet illustrates how to identify an island and then use BFS to find the minimum bridge distance. By running the code, you find the shortest path between islands, improving the efficiency of materials needed to build it.

Motivate yourself to solve the problem

If you already have an idea, I encourage you to try to solve it yourself. Use what you have learned above, adapt the code to your needs and share your experiences and solutions in the comments section - keep learning and improving your skills!