Finding the Maximum Sum of Islands in a 2D Array Using Recursion

Discover how to calculate the maximum sum of islands within a 2D array leveraging recursion to navigate through the grid structure efficiently.
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How to Find the Maximum Sum of Islands in a 2D Array Using Recursion

When working with 2D arrays, one intriguing problem you may encounter is calculating the maximum sum of islands. In this context, an island is defined as a contiguous cluster of positive integers surrounded by zeroes (or water). In this guide, we will explore the problem in detail and demonstrate how to tackle it using recursion in Java.

Understanding the Problem

Imagine you have an N x M grid where:

Each cell contains either a 0 (indicating water) or a positive integer (indicating land).

We need to find all contiguous groups of land (i.e., islands) and determine the maximum sum of their values.

The Challenge

Given a method called maxValueIsland, which scans through the grid, we need to implement another method, getIslandValue, that will recursively calculate the sum of each island. The method maxValueIsland then returns the maximum value found among all islands.

The Approach

To solve this problem effectively, we will break it down as follows:

Step 1: The Main Method - maxValueIsland

This method will iterate through the 2D array and initiate the calculation for each unvisited land cell.

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Step 2: The Recursive Method - getIslandValue

This method will calculate the sum of the island by traversing through adjacent cells recursively.

Key Points:

Adjust the current cell to 0 (mark it as visited) to avoid counting it again.

Recursively call the method for all four directions (up, down, left, right).

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Step 3: Testing the Solution

We can test our solution using a sample grid. The following code initializes a grid and outputs the maximum island value:

[[See Video to Reveal this Text or Code Snippet]]

Expected Output

When you run the above test code, you should see the output indicating the maximum sum of islands:

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This output suggests that the sum of the values in the connected cells of the highest value island equals 8.

Conclusion

Finding the maximum sum of islands in a 2D array involves a systematic traversal of the grid with recursion. By implementing the maxValueIsland and getIslandValue methods, we can efficiently compute the desired values. Recursion allows us to explore the grid in an elegant manner, making it easy to handle this type of problem.

By keeping our approach organized and clear, we can solve complex problems like this one with confidence and precision.