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Step-by-Step Explanation for Magic Squares Code

This section provides a step-by-step explanation of how the algorithm for finding 3x3 magic squares in a grid works, using C++, Java, JavaScript, Python, and Go.

C++ Code Explanation

  1. Grid Dimensions: The code begins by determining the number of rows and columns in the grid.
  2. Count Initialization: A counter count is initialized to keep track of the number of magic squares found.
  3. Lambda Function Definition: A lambda function isMagicSquare is defined to check if a 3x3 grid is a magic square.
    • Number Validation: The function first checks if the numbers in the 3x3 grid are between 1 and 9 and ensures no number is repeated.
    • Sum Validation: It then checks if the sum of the numbers in each row, column, and diagonal equals 15.
  4. Grid Traversal: The grid is traversed to check each possible 3x3 subgrid using the isMagicSquare function.
  5. Return Count: Finally, the total count of magic squares found is returned.

Java Code Explanation

  1. Grid Dimensions: The number of rows and columns in the grid is calculated.
  2. Count Initialization: A counter count is initialized to keep track of the magic squares.
  3. Grid Traversal: The code loops through the grid but stops 2 rows and 2 columns before the end to leave space for a 3x3 square.
  4. Magic Square Check: A helper method isMagicSquare is called to check each 3x3 subgrid.
    • Number Validation: The method ensures that numbers 1-9 appear exactly once.
    • Sum Validation: It checks if the sums of the rows, columns, and diagonals are all equal to 15.
  5. Return Count: The total count of magic squares found is returned.

JavaScript Code Explanation

  1. Grid Dimensions: The number of rows and columns in the grid is calculated using grid.length.
  2. Count Initialization: A variable count is initialized to keep track of the magic squares.
  3. Helper Function: A helper function isMagicSquare is defined to determine if a 3x3 grid is a magic square.
    • Number Validation: The function ensures that the numbers in the grid are between 1 and 9, with no duplicates.
    • Sum Validation: It checks that the sums of the rows, columns, and diagonals are 15.
  4. Grid Traversal: The grid is traversed to check all possible 3x3 subgrids using the isMagicSquare function.
  5. Return Count: The final count of magic squares is returned.

Python Code Explanation

  1. Helper Function: A helper function isMagicSquare is defined to check if a 3x3 grid is a magic square.
    • Number Validation: The function validates that numbers 1-9 appear exactly once.
    • Sum Validation: It checks that the sums of rows, columns, and diagonals equal 15.
  2. Grid Dimensions: The number of rows and columns in the grid is determined.
  3. Count Initialization: A counter count is initialized to track the number of magic squares.
  4. Grid Traversal: The grid is traversed, and each possible 3x3 subgrid is checked using isMagicSquare.
  5. Return Count: The total count of magic squares found is returned.

Go Code Explanation

  1. Grid Dimensions: The number of rows and columns in the grid is determined.
  2. Count Initialization: A counter count is initialized to track the magic squares found.
  3. Magic Square Check: A function isMagicSquare is defined to validate a 3x3 subgrid.
    • Number Validation: It checks that numbers 1-9 appear exactly once and are within the valid range.
    • Sum Validation: It verifies that the sums of rows, columns, and diagonals are 15.
  4. Grid Traversal: The grid is looped through to check every possible 3x3 subgrid using the isMagicSquare function.
  5. Return Count: The final count of magic squares found is returned.