Pablo73 / MagicSquareConversion

Creating a Magic Square with Minimal Cost

This Java code demonstrates how to create a magic square with the lowest possible cost. A magic square is a square matrix where the sum of all rows, columns, and diagonals is equal to the same constant value known as the magic constant. The code calculates and explains the cost of converting an input matrix into a magic square.

Code Overview

• Import necessary Java classes.
• Create a class named MagicSquareConversion.
• In the main method:
  • Define an input matrix s as a List<List>. You can replace this matrix with your desired input.
• Call the minimalCost function to find the minimal cost of converting the input matrix into a magic square.
• Display the minimum cost.
• The minimalCost function:
  • Generates all possible 3x3 magic squares.
  • Iterates through each generated magic square.
  • Calculates the cost of converting the input matrix into that magic square.
  • Keeps track of the minimum cost found.
• The generateMagicSquares function should be filled with all possible 3x3 magic squares. These can be hard-coded or generated algorithmically. For brevity, we've skipped this part.
• The calculateCost function computes the cost of converting the input matrix s into a magic square. It calculates the absolute difference between corresponding elements.

How to Use

• Compile and run the Java code.
• Define your input matrix s as a List<List>.
• The code will find and display the minimum cost of converting your input matrix into a magic square.
• You can customize the input matrix with any 3x3 matrix of integers within the specified range.

Cost Calculation

The cost of converting the input matrix into a magic square is calculated as follows:

• For each element in the input matrix, calculate the absolute difference between the corresponding element in the target magic square.
• Sum up these absolute differences for all elements in the matrix.

Example Output

Running the code with your input matrix will display the minimum cost of converting it into a magic square.

Feel free to use and adapt this code to find the minimal cost of converting your input matrix into a magic square. You can customize the input matrix with your own data to explore different scenarios.