Working out how many elements a 2D array holds

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Quick Questions

Shade in the A or B circle for each question.

1. How many elements does ARRAY[1:3, 1:3] hold?

A 9

B 6

2. How many elements does ARRAY[1:30, 1:4] hold?

A 120

B 34

3. Which formula gives the total number of elements in a 2D array?

A rows + columns

B rows * columns

4. How many values does one dimension of ARRAY[0:4, 1:3] have for its first index (0:4)?

A 5

B 4

5. How many elements does ARRAY[0:4, 1:3] hold?

A 12

B 15

Match the Pairs

Draw a line connecting each item on the left to its match on the right.

Left column		Right column
1DECLARE Grid : ARRAY[1:3, 1:3] OF INTEGER		AThis 2D array has 30 rows and 4 columns, so it holds 30 * 4 = 120 elements
2DECLARE Marks : ARRAY[1:30, 1:4] OF INTEGER		BThis 2D array has 3 rows and 3 columns, so it holds 3 * 3 = 9 elements
3The total number of elements in a 2D array is the number of rows multiplied by the number of columns		CThe sizes of the dimensions were added instead of multiplied. It should be 3 * 3 = 9 elements.
4The size of each dimension is the upper bound minus the lower bound plus one		DSize ← Upper - Lower + 1
5ARRAY[1:3, 1:3] holds 3 + 3 = 6 elements		ETotal ← Rows * Columns
6ARRAY[1:30, 1:4] has 29 * 3 = 87 elements		FUpper minus lower was used without adding 1. It should be (30 - 1 + 1) * (4 - 1 + 1) = 30 * 4 = 120 elements.

Definitions

rows * columns

Fill in the Blanks

Complete each line of code by filling in the missing parts.

rows ← 3 columns ← 4 total ← rows _ columns

// ARRAY[1:3, 1:3] holds 3 * 3 = _ elements

// 30 rows * 4 columns = 120 elements DECLARE Marks : ARRAY[1:30, 1:_] OF INTEGER

upper ← 30 lower ← 1 rowCount ← upper - lower + _

DECLARE Board : ARRAY[0:2, 0:3] OF CHAR columns ← 3 - _ + 1 OUTPUT 3 * columns

Spot the Error

Shade in the letter of the line that contains an error.

Question 1

A // Grid: ARRAY[1:3, 1:3]

B Rows ← 3

C Cols ← 3

D Total ← Rows + Cols

E OUTPUT Total

Question 2

A // Seats: ARRAY[1:30, 1:4]

B Rows ← 30 - 1

C Cols ← 4 - 1 + 1

D Total ← Rows * Cols

Question 3

A // Marks: ARRAY[1:30, 1:4]

B Rows ← 30

C Cols ← 3

D Total ← Rows * Cols

Question 4

A // Board: ARRAY[1:3, 1:3]

B Rows ← 3 - 1 + 1

C Cols ← 3 - 1 + 1

D Total ← Rows / Cols

E OUTPUT "Total is ", Total

Question 5

A Count ← 0 // ARRAY[1:3, 1:3]

B FOR R ← 1 TO 3

C FOR C ← 1 TO 2

D Count ← Count + 1

E NEXT C

F NEXT R

Answer Key

Working out how many elements a 2D array holds

Section A: Quick Questions

A — 9

A — 120

B — rows * columns

A — 5

B — 15

Section B: Match the Pairs

DECLARE Grid : ARRAY[1:3, 1:3] OF INTEGER → This 2D array has 3 rows and 3 columns, so it holds 3 * 3 = 9 elements

DECLARE Marks : ARRAY[1:30, 1:4] OF INTEGER → This 2D array has 30 rows and 4 columns, so it holds 30 * 4 = 120 elements

The total number of elements in a 2D array is the number of rows multiplied by the number of columns → Total ← Rows * Columns

The size of each dimension is the upper bound minus the lower bound plus one → Size ← Upper - Lower + 1

ARRAY[1:3, 1:3] holds 3 + 3 = 6 elements → The sizes of the dimensions were added instead of multiplied. It should be 3 * 3 = 9 elements.

ARRAY[1:30, 1:4] has 29 * 3 = 87 elements → Upper minus lower was used without adding 1. It should be (30 - 1 + 1) * (4 - 1 + 1) = 30 * 4 = 120 elements.

Section C: Definitions

rows * columns — The total number of elements in a 2D array. Each dimension holds upper - lower + 1 values, so ARRAY[1:3, 1:3] holds 3 * 3 = 9 and ARRAY[1:30, 1:4] holds 30 * 4 = 120.

Section D: Fill in the Blanks

rows ← 3
columns ← 4
total ← rows * columns

// ARRAY[1:3, 1:3] holds 3 * 3 = 9 elements

// 30 rows * 4 columns = 120 elements
DECLARE Marks : ARRAY[1:30, 1:4] OF INTEGER

upper ← 30
lower ← 1
rowCount ← upper - lower + 1

DECLARE Board : ARRAY[0:2, 0:3] OF CHAR
columns ← 3 - 0 + 1
OUTPUT 3 * columns

Section E: Spot the Error

D — The number of elements is rows multiplied by columns, not added. It should be Total ← Rows * Cols, which gives 3 * 3 = 9.

B — Each dimension holds upper - lower + 1 values. The +1 is missing, so Rows would be 29. It should be Rows ← 30 - 1 + 1, which gives 30.

C — The second dimension is 1:4, so it holds 4 - 1 + 1 = 4 columns, not 3. It should be Cols ← 4, giving Total = 30 * 4 = 120.

D — Dividing rows by columns gives 1, not the number of elements. It should be Total ← Rows * Cols, which gives 9.

C — The inner loop must visit all 3 columns. TO 2 skips the last column, so Count would be 6 instead of 9. It should be FOR C ← 1 TO 3.