CollegeBoard FRQ

This question involves reasoning about one-dimensional and two-dimensional arrays of integers. You will write three static methods, all of which are in a single enclosing class, named DiverseArray (not shown). The first method returns the sum of the values of a one-dimensional array; the second method returns an array that represents the sums of the rows of a two-dimensional array; and the third method analyzes row sums.

In part (a), the instructions are to Write a static method arraySum that calculates and returns the sum of the entries in a specified one-dimensional array.

public static int arraySum (int[] arr1) {
  int sum = 0;
  for (int i = 0; i<arr1.length; i++) {
    sum += arr1[i];
  }
  return sum;
}

Here we can test the method with the example array which is [1, 3, 2, 7, 3], which should have a sum of 16.

int[] arrayTest = {1, 3, 2, 7, 3};
System.out.println(arraySum(arrayTest));

16

Part (b) asks to Write a static method rowSums that calculates the sums of each of the rows in a given two dimensional array and returns these sums in a one-dimensional array. The method has one parameter, a two dimensional array arr2D of int values. The array is in row-major order: arr2D[r][c] is the entry at row r and column c. The method returns a one-dimensional array with one entry for each row of arr2D such that each entry is the sum of the corresponding row in arr2D.

public static int[] rowSums(int[][] arr2D) {
  int[] sums = new int[arr2D.length]; //elements initialize to 0
  for (int i = 0; i < arr2D.length; i++) {
    for (int j = 0; j < arr2D[i].length; j++) {
      sums[i] += arr2D[i][j];
    }
  }
  return sums;
}

Now we can test with the example:
1   3   2   7   3
10  10  4   6   2
5   3   5   9   6
7   6   4   2   1

The expected output here is {16, 32, 28, 20}.

int[][] arrayTest2D = {
  {1, 3, 2, 7, 3},
  {10, 10, 4, 6, 2},
  {5, 3, 5, 9, 6},
  {7, 6, 4, 2, 1}
};
int[] sums = rowSums(arrayTest2D);
for (int i = 0; i<sums.length; i++) {
  System.out.println(sums[i]);
}

16
32
28
20

Part (c) asks us to Write a static method isDiverse that determines whether or not a given two-dimensional array is diverse. The method has one parameter: a two-dimensional array arr2D of int values. The method should return true if all the row sums in the given array are unique; otherwise, it should return false

public static boolean isDiverse (int[][] arr2D) {
  int[] sums = rowSums(arr2D);
  for (int i = 0; i < sums.length; i++) {
    for (int j = i + 1; j < sums.length; j++) {
      if (sums[i] == sums[j]) return false; // returns false if two elements are the same
    }
  }

  //if end is reached all elements have passed uniqueness test
  return true;
}

We can test with the two provided examples which are diverse and not diverse.

This example is diverse:
1   3   2   7   3
10  10  4   6   2
5   3   5   9   6
7   6   4   2   1

This example is not diverse:
1   1   5   3   4
12  7   6   1   9
8   11  10  2   5
3   2   3   0   6

int[][] arrayTestDiverse = {
  {1, 3, 2, 7, 3},
  {10, 10, 4, 6, 2},
  {5, 3, 5, 9, 6},
  {7, 6, 4, 2, 1}
};
int[][] arrayTestNotDiverse = {
  {1, 1, 5, 3, 4},
  {12, 7, 6, 1, 9},
  {8, 11, 10, 2, 5},
  {3, 2, 3, 0, 6}
};
System.out.println(isDiverse(arrayTestDiverse));
System.out.println(isDiverse(arrayTestNotDiverse));

true
false