The MatrixManipulator practice problem is intended as practice with 2D arrays and with the nested loops commonly used to traverse them.

The MatrixManipulator practice problem requires extensive manipulation of 2D arrays of integers, including declaration, traversal and partial traversal. You must declare new 2D arrays with the correct dimensions and fill them with the correct values.

MatrixManipulator is not intended to simulate an AP style free response question and should not be used as part of a practice test or for practicing timing.

Arrays.deepToString is a method to quickly produce formatted output. It is not covered on the AP CS A Exam. The format of the output below has been adjusted for readability.

The Java files below include skeleton code for each method and a JUnit3 tester for each method.

MatrixManipulator.java
MatrixManipulatorTest.java

addable method

/**
 * Determines if (first + second) is defined where +
 * indicates matrix addition.
 * @return true if matrix addition is defined, false otherwise.
 */
public static boolean addable(int[][] first, int[][] second)

addable explanation

first and second are addable if first has the same number of rows as second and first has the same number of columns as second.

addable examples

int[][] mat1 = {
    {1, 2, 3, 4, 5},
    {6, 7, 8, 9, 10}
};

int[][] mat2 = {
    {11, 12, 13, 14, 15},
    {16, 17, 18, 19, 20}
};

System.out.println(MatrixManipulator.addable(mat1, mat2)); // prints true

mat2 = new int[][] {
    {11, 12, 13, 14, 15, 21},
    {16, 17, 18, 19, 20, 22}
};

System.out.println(MatrixManipulator.addable(mat1, mat2)); // prints false

add method

/**
 * Performs (first + second) where + indicates matrix addition.
 * Precondition: addable(first, second)
 * @return the result of first + second.
 */
public static int[][] add(int[][] first, int[][] second)

add explanation

The sum of 2 matrices is a matrix with the same number of rows and columns as both operands. Each position in the result matrix is the sum of the values at the same position in each of the operands.

add example

int[][] mat1 = {
    {1, 2, 3, 4, 5},
    {6, 7, 8, 9, 10}
};

int[][] mat2 = {
    {11, 12, 13, 14, 15},
    {16, 17, 18, 19, 20}
};

int[][] result = MatrixManipulator.add(mat1, mat2);

System.out.println(Arrays.deepToString(result)); // prints:
// [[12, 14, 16, 18, 20]
//  [22, 24, 26, 28, 30]]

multiplyByScalar method

/**
 * Performs (scalar * matrix) where * indicates
 * scalar multiplication of a matrix.
 * Precondition: matrix.length > 0 && matrix[0].length > 0
 * @return the result of scalar * matrix.
 */
public static int[][] multiplyByScalar(int scalar, int[][] matrix)

multiplyByScalar explanation

The result of multiplying a matrix by a scalar is a matrix with the same number of rows and columns. Each value in the result matrix is the result of multiplying the value at the corresponding position in the original matrix by the scalar.

multiplyByScalar example

int[][] mat = {
    {1, 2, 3, 4, 5},
    {6, 7, 8, 9, 10}
};

int scalar = 2;

int[][] result = MatrixManipulator.multiplyByScalar(scalar, mat);

System.out.println(Arrays.deepToString(result)); // prints:
// [[2, 4, 6, 8, 10],
//  [12, 14, 16, 18, 20]]

multipliable method

/**
 * Determines if (first * second) is defined where *
 * indicates matrix multiplication.
 * @return true if matrix multiplication is defined, false otherwise.
 */
public static boolean multipliable(int[][] first, int[][] second)

multipliable explanation

first and second are multipliable if the number of columns in first is equal to the number of rows in second.

multipliable example

int[][] mat1 = {
    {20, 21, 22, 23},
    {24, 25, 26, 27},
    {28, 29, 30, 31}
};

int[][] mat2 = {
    {32, 33},
    {34, 35},
    {36, 37},
    {38, 39}
};

System.out.println(MatrixManipulator.multipliable(mat1, mat2)); // prints true

mat2 = new int[][]{
    {32, 33, 36},
    {34, 35, 37},
    {36, 37, 38},
    {38, 39, 39}
};

System.out.println(MatrixManipulator.multipliable(mat1, mat2)); // prints true

mat2 = new int[][]{
    {32, 33, 36},
    {34, 35, 37},
    {36, 37, 38},
    {38, 39, 39},
    {40, 41, 42}
};

System.out.println(MatrixManipulator.multipliable(mat1, mat2)); // prints false

multiply(int[][], int, int[][], int) method

/**
 * Multiplies the specified row of first by the specified column of second.
 * Precondition: first[row].length > 0 && first[row].length == second.length
 * @return the result of multiplying the specified row and column.
 */
public static int multiply(int[][] first, int row, int[][] second, int col)

multiply(int[][], int, int[][], int) explanation

Multiplying a row of one matrix by a column of another matrix results in a single int. The value is calculated as the sum of the products of the corresponding values in the row of the first matrix and the column of the second matrix.

In the example below, the result of multiplying row 0 of mat1 by column 0 of mat2 is calculated as:
20 * 32 + 21 * 34 + 22 * 36 + 23 * 38 is 3020

The result of multiplying row 0 of mat1 by column 1 of mat2 is calculated as:
20 * 33 + 21 * 35 + 22 * 37 + 23 * 39 is 3106

multiply(int[][], int, int[][], int) examples

int[][] mat1 = {
    {20, 21, 22, 23},
    {24, 25, 26, 27},
    {28, 29, 30, 31}
};

int[][] mat2 = {
    {32, 33},
    {34, 35},
    {36, 37},
    {38, 39}
};

int row = 0, col = 0;
System.out.println(MatrixManipulator.multiply(mat1, row, mat2, col)); // prints 3020

row = 0; col = 1;
System.out.println(MatrixManipulator.multiply(mat1, row, mat2, col)); // prints 3106

row = 1; col = 0;
System.out.println(MatrixManipulator.multiply(mat1, row, mat2, col)); // prints 3580

row = 1; col = 1;
System.out.println(MatrixManipulator.multiply(mat1, row, mat2, col)); // prints 3682

multiply(int[][], int[][]) method

/**
 * Performs (first * second) where * indicates matrix multiplication.
 * Precondition: multipliable(first, second)
 * @return the result of first * second.
 */
public static int[][] multiply(int[][] first, int[][] second)

multiply(int[][], int[][]) explanation

The result of multiplying mat1 by mat2 is a new matrix with the same number of rows as mat1 and the same number of columns as mat2. Each value in the product matrix is obtained by multiplying the corresponding row from mat1 by the corresponding column from mat2.

In the example below, result[0][1], 3106, was obtained by multiplying row 0 in mat1 by column 1 in mat2.

result[2][1], 4258, was obtained by multiplying row 2 in mat1 by column 1 in mat2.

multiply(int[][], int[][]) example

int[][] mat1 = {
    {20, 21, 22, 23},
    {24, 25, 26, 27},
    {28, 29, 30, 31}
};

int[][] mat2 = {
    {32, 33},
    {34, 35},
    {36, 37},
    {38, 39}
};

int[][] result = MatrixManipulator.multiply(mat1, mat2);

System.out.println(Arrays.deepToString(result)); // prints:
// [[3020, 3106],
//  [3580, 3682],
//  [4140, 4258]]

Solution & comments

See the MatrixManipulator solution or review it with AP CS Tutor Brandon Horn.

Comment on MatrixManipulator

Additional 2D array resources