Explanation of the 2018 AP CSA FRQ - Question 4 (Part B)

Prior Knowledge

Helper Methods in the Problem

• getColumn(int[][] arr2D, int c): Returns an array containing all elements in column c of a 2D array.

• containsDuplicates(int[] arr): Returns true if the array contains duplicate values.

• hasAllValues(int[] arr1, int[] arr2): Returns true if all elements in arr1 are present in arr2.
Latin Square Definition

• The first row has no duplicate values.

• All values in the first row appear in every row of the square.

• All values in the first row appear in every column of the square.
Preconditions

• The input array is guaranteed to be square (equal number of rows and columns).

• At least one row exists in the array.

Solution

```java

public static boolean isLatin(int[][] square) { if (containsDuplicates(square[0])) { return false; } for (int r = 1; r < square.length; r++) { if (!hasAllValues(square[0], square[r])) { return false; } }
for (int c = 0; c < square[0].length; c++) { if (!hasAllValues(square[0], getColumn(square, c))) { return false; }

}
return true;

}

Explanation of the Solution

Checking the First Row for Duplicates

• The method starts by using containsDuplicates(square[0]) to ensure that the first row contains no duplicate values. If duplicates are found, the square cannot be a Latin square.
Validating Rows and Columns Against the First Row

• The method checks that all the values in the first row appear in every other row and column. It uses hasAllValues(square[0], square[i]) for rows and hasAllValues(square[0], getColumn(square, i)) for columns to verify this.
Returning the Final Result

• If all checks pass, the method returns true, meaning the input is a Latin square. If any check fails, it returns false.

Meets the Latin Square Requirement

•	No duplicates in the first row.

•	All rows contain the same values as the first row.

•	All columns contain the same values as the first row.

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