Write pseudocode for 1D and 2D arrays

Topic: 10.2 Arrays

Objective

Write pseudocode for 1‑D and 2‑D arrays.

Key Concepts

• Arrays are contiguous blocks of memory that store elements of the same type.
• Indexing starts at 0 in most programming languages.
• 1‑D arrays are linear; 2‑D arrays can be visualised as a table of rows and columns.
• Accessing an element: array[i] for 1‑D, array[row][col] for 2‑D.
• Iterating over arrays uses loops that run from the first index to the last.

Pseudocode – 1‑D Array

1. Declaration and Initialization

   DECLARE scores[5] AS INTEGER
   FOR i FROM 0 TO 4
   scores[i] ← 0
   END FOR
   

2. Assigning \cdot alues

   scores[0] ← 85
   scores[1] ← 92
   scores[2] ← 78
   scores[3] ← 90
   scores[4] ← 88
   

3. Accessing an Element

   PRINT "Score at index 2: ", scores[2]
   

4. Iterating to Compute Sum

   sum ← 0
   FOR i FROM 0 TO 4
   sum ← sum + scores[i]
   END FOR
   PRINT "Total score: ", sum
   

Pseudocode – 2‑D Array

1. Declaration and Initialization

   DECLARE matrix[3][4] AS INTEGER
   FOR row FROM 0 TO 2
   FOR col FROM 0 TO 3
   matrix[row][col] ← 0
   END FOR
   END FOR
   

2. Assigning \cdot alues

   matrix[0][0] ← 1   matrix[0][1] ← 2   matrix[0][2] ← 3   matrix[0][3] ← 4
   matrix[1][0] ← 5   matrix[1][1] ← 6   matrix[1][2] ← 7   matrix[1][3] ← 8
   matrix[2][0] ← 9   matrix[2][1] ← 10  matrix[2][2] ← 11  matrix[2][3] ← 12
   

3. Accessing an Element

   PRINT "Element at (1,2): ", matrix[1][2]
   

4. Iterating to Compute Row Averages

   FOR row FROM 0 TO 2
   sum ← 0
   FOR col FROM 0 TO 3
   sum ← sum + matrix[row][col]
   END FOR
   average ← sum / 4
   PRINT "Average of row ", row, ": ", average
   END FOR
   

Visualising a 2‑D Array

Mathematical Notation

For a 1‑D array of length \$n\$, the element at index \$i\$ is denoted \$A[i]\$, where \$0 \le i < n\$.

For a 2‑D array with \$r\$ rows and \$c\$ columns, the element at row \$i\$ and column \$j\$ is denoted \$M[i][j]\$, where \$0 \le i < r\$ and \$0 \le j < c\$.

Common Pitfalls

• Off‑by‑one errors: remember that the last valid index is length - 1.
• Assuming 1‑based indexing; always check the language specification.
• Mixing row and column order when accessing 2‑D arrays.

Practice Questions

1. Write pseudocode to find the maximum value in a 1‑D array of size 10.
2. Write pseudocode to transpose a 3×3 matrix.
3. Given a 2‑D array, write pseudocode to calculate the sum of all elements.