Introduction
In this blog post, we will discuss the problem of finding the shortest bridge between two islands in a grid. We will explore an algorithmic approach to solve this problem efficiently.
Problem Statement
Given a grid consisting of 0s and 1s, where 0 represents water and 1 represents land, we need to find the shortest bridge that connects two islands. An island is formed by connecting adjacent land cells horizontally or vertically. The shortest bridge is the minimum number of steps required to reach from one island to the other.
Data Structure used
To solve this problem, we will use a queue to perform breadth-first search (BFS) traversal on the grid. We will also utilize a 2D grid to represent the island and track visited cells.
Algorithmic approach
The algorithm to find the shortest bridge between two islands in a grid is as follows:
Find the first island and change its type to 2. This can be done by iterating through the grid and finding the first land cell.
Push the coordinates of the newly found island cells into a queue.
Perform a breadth-first search (BFS) on the grid using the queue:
Increment the change variable by 1.
Process each cell in the queue and explore its neighboring cells.
If a neighboring cell is water (0), mark it as part of the island (type 2) and push its coordinates into the queue.
If a neighboring cell is another island (type 1), return the current change value - 1, as it represents the shortest bridge length.
If no bridge is found, return 0.
Time Complexity
The time complexity of this algorithm depends on the size of the grid. We need to traverse the grid to find the first island, which takes O(R C) time, where R is the number of rows and C is the number of columns. The BFS traversal also visits each cell once, resulting in a total time complexity of O(R C).
Space Complexity
The space complexity of this algorithm is determined by the queue, which can store up to O(R C) cells in the worst case. Therefore, the space complexity is O(R C).
Conclusion
In this blog post, we discussed the problem of finding the shortest bridge between two islands in a grid. By utilizing a breadth-first search (BFS) approach, we can efficiently traverse the grid and find the shortest path between the islands. Understanding the problem requirements and implementing the algorithmic approach allows us to determine the shortest bridge length.
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