Unit 11.3A · Term 3

1D & 2D Arrays

Arrays are the most fundamental data structure in programming. They store fixed-size collections of elements of the same type in contiguous memory. Understanding arrays is critical for efficient data processing, forming the basis for sorting, searching, and more complex structures like matrices.

Learning Objectives

11.5.2.1 Use the terms upper and lower bounds of an array
11.5.2.3 Write code using one-dimensional and two-dimensional arrays

Lesson Presentation

11.3A-arrays.pdf · Slides for classroom use

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Conceptual Anchor

The Locker Row Analogy

Imagine a row of numbered lockers in a school hallway. Each locker has a fixed number (its index), can hold exactly one item (a value), and all lockers are the same size (same data type). You can go directly to locker #5 — you don't need to open lockers #1 through #4 first. This is random access, and it's what makes arrays fast.

A one-dimensional (1D) array is a single row of lockers. A two-dimensional (2D) array is a grid of lockers — like a wall of mailboxes with rows and columns. To find your mailbox, you need two numbers: the row and the column.

Rules & Theory

Key Terminology

Term	Definition	Example
Array	An ordered, fixed-size collection of elements of the same data type stored in contiguous memory locations.	`int marks[5];`
Index	The position number used to access a specific element. In C++ and pseudocode, indexing starts at 0.	`marks[0]` = first element
Lower Bound	The smallest valid index of the array.	For `marks[5]` → lower bound = 0
Upper Bound	The largest valid index of the array.	For `marks[5]` → upper bound = 4
Size / Length	The total number of elements. `size = upper bound − lower bound + 1`	For `marks[5]` → size = 5
Element	A single value stored at a specific index.	`marks[2] = 87;`

1D Array — Declaration & Initialization

Pseudocode:

DECLARE marks : ARRAY[0:4] OF INTEGER
marks[0] ← 90
marks[1] ← 78
marks[2] ← 85
marks[3] ← 92
marks[4] ← 88

C++:

// Declaration and initialization
int marks[5] = {90, 78, 85, 92, 88};

// Or declare first, then assign
int marks[5];
marks[0] = 90;
marks[1] = 78;
marks[2] = 85;
marks[3] = 92;
marks[4] = 88;

Memory Layout

Arrays are stored in contiguous memory. If marks[0] is at memory address 1000 and each int is 4 bytes, then marks[1] is at 1004, marks[2] at 1008, etc. The formula is: address = base + index × sizeof(type).

2D Array — Declaration & Initialization

A 2D array is essentially an array of arrays — a table with rows and columns.

Pseudocode:

DECLARE grid : ARRAY[0:2, 0:3] OF INTEGER

// 3 rows × 4 columns
// Access: grid[row, col]
grid[0, 0] ← 1
grid[0, 1] ← 2
grid[1, 0] ← 5
grid[2, 3] ← 12

C++:

// 3 rows, 4 columns
int grid[3][4] = {
    {1,  2,  3,  4},
    {5,  6,  7,  8},
    {9, 10, 11, 12}
};

// Access element at row 1, column 2
cout << grid[1][2];  // Output: 7

Aspect	1D Array	2D Array
Indices needed	1 (position)	2 (row, column)
Real-world analogy	A single row of seats	A cinema seating plan
C++ declaration	`int a[5];`	`int a[3][4];`
Pseudocode	`ARRAY[0:4] OF INT`	`ARRAY[0:2, 0:3] OF INT`
Total elements	size	rows × columns

Worked Examples

1 Traversing a 1D Array — Linear Search

Find whether a value exists in an array.

Pseudocode:

DECLARE names : ARRAY[0:4] OF STRING
names ← ["Alice", "Bob", "Clara", "David", "Eve"]

DECLARE target : STRING
OUTPUT "Enter name to find: "
INPUT target

DECLARE found : BOOLEAN ← FALSE
FOR i ← 0 TO 4
    IF names[i] = target THEN
        OUTPUT target, " found at index ", i
        found ← TRUE
    ENDIF
NEXT i

IF found = FALSE THEN
    OUTPUT target, " not found"
ENDIF

C++:

#include <iostream>
#include <string>
using namespace std;

int main() {
    string names[5] = {"Alice", "Bob", "Clara", "David", "Eve"};
    string target;

    cout << "Enter name to find: ";
    cin >> target;

    bool found = false;
    for (int i = 0; i < 5; i++) {
        if (names[i] == target) {
            cout << target << " found at index " << i << endl;
            found = true;
        }
    }

    if (!found) {
        cout << target << " not found" << endl;
    }
    return 0;
}

2 Sum & Average of Array Elements

Calculate the total and average of numeric values stored in a 1D array.

Pseudocode:

DECLARE scores : ARRAY[0:4] OF INTEGER ← [90, 78, 85, 92, 88]
DECLARE total : INTEGER ← 0

FOR i ← 0 TO 4
    total ← total + scores[i]
NEXT i

DECLARE average : REAL ← total / 5
OUTPUT "Total: ", total
OUTPUT "Average: ", average

C++:

#include <iostream>
using namespace std;

int main() {
    int scores[5] = {90, 78, 85, 92, 88};
    int total = 0;

    for (int i = 0; i < 5; i++) {
        total += scores[i];
    }

    double average = (double)total / 5;
    cout << "Total: " << total << endl;
    cout << "Average: " << average << endl;

    return 0;
}

3 Finding Maximum in a 1D Array

Pseudocode:

DECLARE temps : ARRAY[0:6] OF REAL ← [23.1, 19.5, 28.3, 22.0, 31.7, 25.4, 20.8]
DECLARE maxVal : REAL ← temps[0]
DECLARE maxIdx : INTEGER ← 0

FOR i ← 1 TO 6
    IF temps[i] > maxVal THEN
        maxVal ← temps[i]
        maxIdx ← i
    ENDIF
NEXT i

OUTPUT "Maximum temperature: ", maxVal, " at day ", maxIdx + 1

C++:

#include <iostream>
using namespace std;

int main() {
    double temps[7] = {23.1, 19.5, 28.3, 22.0, 31.7, 25.4, 20.8};
    double maxVal = temps[0];
    int maxIdx = 0;

    for (int i = 1; i < 7; i++) {
        if (temps[i] > maxVal) {
            maxVal = temps[i];
            maxIdx = i;
        }
    }

    cout << "Maximum temperature: " << maxVal
         << " at day " << maxIdx + 1 << endl;
    return 0;
}

4 Working with a 2D Array — Classroom Grades

Store grades for 3 students across 4 subjects and find each student's average.

Pseudocode:

// grades[student][subject]
DECLARE grades : ARRAY[0:2, 0:3] OF INTEGER
grades ← [[85, 90, 78, 92],
           [70, 88, 95, 80],
           [92, 76, 84, 91]]

DECLARE studentNames : ARRAY[0:2] OF STRING ← ["Alice", "Bob", "Clara"]

FOR s ← 0 TO 2
    DECLARE total : INTEGER ← 0
    FOR subj ← 0 TO 3
        total ← total + grades[s, subj]
    NEXT subj
    DECLARE avg : REAL ← total / 4
    OUTPUT studentNames[s], " average: ", avg
NEXT s

C++:

#include <iostream>
#include <string>
using namespace std;

int main() {
    int grades[3][4] = {
        {85, 90, 78, 92},
        {70, 88, 95, 80},
        {92, 76, 84, 91}
    };
    string names[3] = {"Alice", "Bob", "Clara"};

    for (int s = 0; s < 3; s++) {
        int total = 0;
        for (int subj = 0; subj < 4; subj++) {
            total += grades[s][subj];
        }
        double avg = (double)total / 4;
        cout << names[s] << " average: " << avg << endl;
    }

    return 0;
}

Pitfalls & Common Errors

Off-by-One Error (Fence Post Error)

The most common array mistake. An array of size 5 has indices 0–4, not 1–5. Accessing arr[5] on a 5-element array causes undefined behaviour in C++ (buffer overflow).

Wrong: for (int i = 0; i <= 5; i++) — iterates 6 times!
Correct: for (int i = 0; i < 5; i++) — iterates 5 times ✓

Uninitialized Arrays

In C++, local arrays are not automatically initialized to zero. They contain garbage values. Always initialize explicitly:

int arr[5] = {0};  // All elements set to 0
int arr[5] = {};   // Same effect in C++

Fixed Size

Arrays in C++ have a fixed size determined at compile time. You cannot resize them after declaration. If you declare int arr[10];, you always have exactly 10 slots — no more, no less. Plan your size carefully.

2D Array Row/Column Confusion

In grid[row][col], the first index is the row and the second is the column. Swapping them gives wrong data. Think: Row comes before Column, just like R comes before C in the alphabet.

Pro-Tips for Exams

Exam Strategy — Bounds Questions

When asked about bounds, always state: Lower bound = 0, Upper bound = size − 1. For a 2D array ARRAY[0:R-1, 0:C-1] the total elements = R × C. Examiners love asking "how many elements?" — multiply rows by columns.

Exam Strategy — Writing Pseudocode Loops

For 1D arrays: FOR i ← 0 TO n-1
For 2D arrays: Use nested loops. Outer loop = rows, inner loop = columns.
Always declare the array with its type: DECLARE arr : ARRAY[0:N-1] OF INTEGER
Use meaningful variable names: row, col instead of i, j to avoid confusion.

Exam Strategy — Trace Table Tips

When tracing array operations in an exam, draw the array as a row of boxes with indices above them. Update values in the boxes as the loop iterates. This visual approach prevents mistakes and earns method marks even if the final answer is wrong.

Graded Tasks

Remember

Define the terms: array, index, lower bound, upper bound. Give the lower and upper bounds of ARRAY[0:99] OF REAL.

Understand

Explain, using a diagram, how elements of a 1D array of 6 integers are stored in memory starting at address 2000. What is the address of the element at index 4 if each integer occupies 4 bytes?

Apply

Write a C++ program that reads 10 integers from the user into an array, then outputs them in reverse order.

Apply

Write pseudocode that takes a 2D array ARRAY[0:4, 0:2] OF INTEGER representing 5 students' marks in 3 subjects, and finds the student with the highest total.

Analyze

A programmer writes for (int i = 1; i <= 10; i++) to traverse an array declared as int data[10];. Identify the two bugs in this loop and explain the consequences of each.

Create

Design a C++ program that uses a 2D array to store a 5×5 multiplication table. The program should fill the table automatically and display it in a formatted grid.

Self-Check Quiz

1. What is the upper bound of ARRAY[0:7] OF STRING?

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2. How many elements does int grid[4][6]; contain?

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3. In C++, what happens if you access arr[10] on an array declared as int arr[10];?

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4. Write the pseudocode to declare a 2D array of 3 rows and 5 columns of type REAL.

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5. What is the formula to calculate the memory address of element arr[i]?

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