Double Dimensional Arrays: Rows, Columns and Diagonals (ICSE Class 10 Java)

Understand Double Dimensional Arrays: Row, Column and Diagonal Sums

int[][] m = new int[3][4];          // 3 rows, 4 columns, all elements 0
int[][] t = {{1, 2, 3}, {4, 5, 6}}; // initialised: 2 rows, 3 columns

Scanner in = new Scanner(System.in);
for (int i = 0; i < r; i++)
    for (int j = 0; j < c; j++)
        m[i][j] = in.nextInt();

for (int i = 0; i < r; i++) {
    for (int j = 0; j < c; j++)
        System.out.print(m[i][j] + " ");
    System.out.println();
}

Double Dimensional Arrays: Row, Column and Diagonal Sums: key facts

Size of a 2D array

Rows	m.length
Columns	m[0].length
Elements	rows multiplied by columns
Last element	m[rows - 1][columns - 1]

Indices start at 0.

Element access

• •m[i][j]: row i, column j
• •i from 0 to rows - 1
• •j from 0 to columns - 1

Row first, column second.

Diagonals of an n by n matrix

Left diagonal	m[i][i]
Right diagonal	m[i][n - 1 - i]
Right diagonal	i + j = n - 1

Only for square matrices.

Row and column sums

• •Row sum: outer loop i, inner loop j
• •Column sum: outer loop j, inner loop i
• •Reset the sum to 0 each time

Swap the loops for columns.

How to answer Double Dimensional Arrays: Row, Column and Diagonal Sums questions

1. 1Write the matrix as a grid with row and column indices.
2. 2Decide the loop order: row sums and display use rows outside; column sums use columns outside.
3. 3Pick the elements asked for with the index rule (i equals j, or i + j equals n - 1).
4. 4Reset accumulators to 0 at the start of each row or column.
5. 5Check every index stays within 0 to length - 1.

Double Dimensional Arrays: Row, Column and Diagonal Sums in real life

The idea, met in an everyday situation. Answer the question in your own words, then compare with the model answer. The one-line hook is what to remember.

Tricks to remember Double Dimensional Arrays: Row, Column and Diagonal Sums

Short memory aids. Say each one aloud once, then use it on a question the same day.

• Row then column

  m[row][column]: read it like a street address, street first, house number second.

  Use it when: Indexing.

• i equals j is the main road

  The left diagonal has equal indices; the right diagonal indices add up to n - 1.

  Use it when: Diagonal elements.

• Reset the bucket

  Empty the sum variable before each new row or column.

  Use it when: Avoiding running totals.

Double Dimensional Arrays: Row, Column and Diagonal Sums: solved examples

Ordered from board level to HOTS. Try each one before you open the solution.

int[][] m = {{1, 2, 3}, {4, 5, 6}, {7, 8, 9}};
for (int i = 0; i < 3; i++) {
    int s = 0;
    for (int j = 0; j < 3; j++)
        s += m[i][j];
    System.out.print(s + " ");
}
System.out.println();
for (int j = 0; j < 3; j++) {
    int s = 0;
    for (int i = 0; i < 3; i++)
        s += m[i][j];
    System.out.print(s + " ");
}

int[][] m = {{2, 4, 6}, {1, 3, 5}, {9, 7, 8}};
int left = 0, right = 0;
for (int i = 0; i < 3; i++) {
    left += m[i][i];
    right += m[i][2 - i];
}
System.out.println(left + " " + right);

for (int j = 0; j < 3; j++) {
    for (int i = 0; i < 2; i++)
        System.out.print(a[i][j] + " ");
    System.out.println();
}

Where students lose marks in Double Dimensional Arrays: Row, Column and Diagonal Sums

The slips examiners see most often, and what to write instead.

• ✗Mistake: Not resetting the sum

  If s is declared outside the outer loop, each row adds to the previous total.

  Wrong working

  int s = 0; before the loops: row sums 6, 21, 45

  Right working

  int s = 0; inside the outer loop: 6, 15, 24

  ✓Do this: Reset for each row or column.

  Usually costs: 1 to 2 marks

• ✗Mistake: Writing m[j][i] for a row traversal

  The first index is the row; swapping them gives the transpose.

  Wrong working

  row sum: s += m[j][i]

  Right working

  row sum: s += m[i][j]

  ✓Do this: Row index first.

  Usually costs: 1 mark

• ✗Mistake: Using 3 as the last index of a 3 by 3 array

  Valid indices are 0 to 2.

  Wrong working

  m[3][3]

  Right working

  m[2][2]

  ✓Do this: Last index = length - 1.

  Usually costs: 1 mark

Practice questions on Double Dimensional Arrays: Row, Column and Diagonal Sums

Write each answer on paper first. Open the hint only if you are stuck, and the answer only when you have finished.

1. Q1 · 1 mark · MCQBoard level

   For int[][] x = new int[4][5]; the value of x.length is:
   (a) 5 (b) 4 (c) 20 (d) 9

   Hint

   Number of rows.

   Answer

   (b) 4

2. Q2 · 1 mark · Very short answerBoard level

   What is the index of the last element of a 3 by 3 array?

   Hint

   Both indices start at 0.

   Answer

   [2][2]

3. Q3 · 2 marks · Short answerHarder board level

   Write the output:

   int[][] b = {{1, 2}, {3, 4}};
   System.out.println(b[0][1] + b[1][0] + " " + b[0][0] * b[1][1]);

   Hint

   Multiply before the string joining; evaluate left to right.

   Answer

   5 4 (2 + 3 = 5 first, then a space, then 1 x 4 = 4)

4. Q4 · 4 marks · Short answerHarder board level

   Write loops to display the array {{1, 2, 3}, {4, 5, 6}, {7, 8, 9}} in matrix format and to find the sum of the elements of its second column (index 1).

   Hint

   Column sum: one loop over i with j fixed at 1.

   Answer

   for (int i = 0; i < 3; i++) {
   for (int j = 0; j < 3; j++)
   System.out.print(m[i][j] + " ");
   System.out.println();
   }
   int s = 0;
   for (int i = 0; i < 3; i++)
   s += m[i][1];
   The sum is 2 + 5 + 8 = 15.

5. Q5 · 1 mark · Assertion-reasonHOTS / competency

   Assertion (A): In a square matrix the elements of the left diagonal have equal row and column indices.
   Reason (R): The left diagonal elements are m[0][0], m[1][1], m[2][2] and so on, that is m[i][i].
   (a) Both A and R are true and R is the correct explanation of A. (b) Both A and R are true but R is not the correct explanation of A. (c) A is true but R is false. (d) A is false but R is true.

   Hint

   Does R restate A with an example?

   Answer

   (a) Both are true and R explains A.

Test your recall

Answer in your head or on paper first, then open the card. Pulling an answer out of memory makes it stick far better than re-reading.

1. 1.What does m.length give for a 2D array?Show answer

   The number of rows.

2. 2.What does m[0].length give?Show answer

   The number of columns.

3. 3.Which elements form the left diagonal?Show answer

   m[i][i].

4. 4.Which elements form the right diagonal of an n by n matrix?Show answer

   m[i][n - 1 - i].

5. 5.What is the value of an unassigned int element?Show answer

   0

6. 6.Which loop is outside for a column sum?Show answer

   The loop over the columns.

Double Dimensional Arrays: Row, Column and Diagonal Sums: frequently asked questions