Coding Project 6 Solution

Matrix Addition

A matrix is a rectangular array of mathematical values. Two matrices of the same dimension can be added. Dimension is defined as number of rows by number of columns.

Your assignment is to write the code for three methods: isSame(), addMatrix(), and printMatrix().

Here is the base program.

class Main {
  public static boolean isSame(int[][] a, int[][] b) {
    // return true if a and b have same dimension
    // else return false
    // dimension is defined as number of rows and number of columns
  }
  public static void addMatrix(int[][] a, int[][] b) {
    // precondition: a and b have same dimension
    // calculate: a = a + b
  }
  public static void printMatrix(int[][] a) {
    // output matrix by rows and columns, each value separated by a space
    // a1 a2 a3
    // a4 a5 a6
  }
  
  public static void main(String[] args) {
    int[][] m1 = {{1,2,3}, {4,5,6}};
    int[][] m2 = {{10,10,10}, {20,20,20}};

    System.out.println("-- m1 --");
    printMatrix(m1);
    System.out.println("-- m2 --");
    printMatrix(m2);
    
    if (isSame(m1,m2)) {
      addMatrix(m1, m2);
      System.out.println("-- m1 + m2 --");
      printMatrix(m1);
    } else {
      System.out.println("m1 and m2 have different dimensions.");
    }
  }
}

Solution

Step 1 – Write isSame() method.

public static boolean isSame(int[][] a, int[][] b) {
  // return true if a and b have same dimension
  // else return false
  // dimension is defined as number of rows and number of columns
}

Matrices a and b are arrays of arrays. In this example, matrix a has 2 elements. Each element of matrix a is also an array, containing 3 elements.

For any matrix a, the number of elements is retrieved by a.length. For any array element a[0], the number of elements is retrieved by a[0].length.

Two matrices have the same dimension if they have same number of rows and columns.

matrices a == b
if a.length == b.length         // same number of rows
and a[0].length == b[0].length  // same number of columns
and a[1].length == b[1].length
. . .
for every element a[n] and b[n]

Here is the code for isSame() method.

public static boolean isSame(int[][] a, int[][] b) {
  boolean result = true;
  if (a.length != b.length) {
    result = false;
  } else {
    for (int i=0; i<a.length; i++) {
      if (a[i].length != b[i].length) {
        result = false;
        break;
      }
    }
  }
  return result;
}

Line 3 – if a and b have different number of rows, return false.
Line 6 – iterate each element of a (and b)
Line 7 – if a[i] and b[i] have different number of elements, it means the columns don’t match. Return false.

You can test the method with a sample program.

public static void main(String[] args) {
  int[][] m1 = {{1,2,3}, {4,5,6}};
  int[][] m2 = {{10,10,10}, {20,20,20}};
  System.out.println(isSame(m1, m2));	// true

  int[][] a1 = {{1,2,3}, {4,5,6}, {7,8,9}};
  int[][] a2 = {{10,10,10}, {20,20,20}};
  System.out.println(isSame(a1, a2));	// false
    
  int[][] b1 = {{1,2,3,4}, {5,6,7,8}};
  int[][] b2 = {{10,10,10}, {20,20,20}};
  System.out.println(isSame(b1, b2));	// false
}

m1 and m2 have same dimension.
a1 has more rows than a2.
b1 has more columns than b2.

Step 2 – Write addMatrix() method.

public static void addMatrix(int[][] a, int[][] b) {
  // precondition: a and b have same dimension
  // calculate: a = a + b
}

To add matrices a and b, we add an element of a to the element of b in the matching [x][y] position.

In other words,
a[i][j] + b[i][j]
where i iterates the rows and j iterates the columns.

The sum is stored in the matrix a.
a[i][j] = a[i][j] + b[i][j]

Here is the code for addMatrix() method.

public static void addMatrix(int[][] a, int[][] b) {
  // a = a + b
  for (int i=0; i<a.length; i++) {
    for (int j=0; j<a[0].length; j++) {
      a[i][j] = a[i][j] + b[i][j];
    }
  }
}

Step 3 – Write printMatrix() method.

public static void printMatrix(int[][] a) {
  // output matrix by rows and columns, 
  // each value separated by a space
  // a1 a2 a3
  // a4 a5 a6
}

Where i iterates the rows and j iterates the columns,
print a[i][j] + " " for every j
and move the cursor to new line for very i.

Here is the code for printMatrix() method.

public static void printMatrix(int[][] a) {
  for (int i=0; i<a.length; i++) {
    for (int j=0; j<a[0].length; j++) {
      System.out.print(a[i][j] + " ");
    }
    System.out.println();
  }
}

Putting it all together, here is the complete program.

class Main {
  public static boolean isSame(int[][] a, int[][] b) {
    boolean result = true;
    if (a.length != b.length) {
      result = false;
    } else {
      for (int i=0; i<a.length; i++) {
        if (a[i].length != b[i].length) {
          result = false;
          break;
        }
      }
    }
    return result;
  }
  public static void addMatrix(int[][] a, int[][] b) {
    // a = a + b
    for (int i=0; i<a.length; i++) {
      for (int j=0; j<a[0].length; j++) {
        a[i][j] = a[i][j] + b[i][j];
      }
    }
  }
  public static void printMatrix(int[][] a) {
    for (int i=0; i<a.length; i++) {
      for (int j=0; j<a[0].length; j++) {
        System.out.print(a[i][j] + " ");
      }
      System.out.println();
    }
  }
  
  public static void main(String[] args) {
    int[][] m1 = {{1,2,3}, {4,5,6}};
    int[][] m2 = {{10,10,10}, {20,20,20}};
    
    System.out.println("-- m1 --");
    printMatrix(m1);
    System.out.println("-- m2 --");
    printMatrix(m2);
    
    if (isSame(m1,m2)) {
      addMatrix(m1, m2);
      System.out.println("-- m1 + m2 --");
      printMatrix(m1);
    } else {
      System.out.println("m1 and m2 have different dimensions.");
    }
  }
}