📊 10. Arrays

10.1 What Is an Array?

An array is a fixed-size collection of elements of the same data type, stored in consecutive memory locations and accessed using one array name plus an index.

Array
  │
  ├── One name
  ├── Same data type
  ├── Multiple elements
  ├── Consecutive memory locations
  └── Index starts at 0

10.2 Why Do We Need Arrays?

Suppose a program must store 100 marks. Creating mark1, mark2, ..., mark100 makes the program difficult to write and maintain. An array gives us one organized collection.

int marks[100];

• One variable name represents many values.
• Loops can process all elements systematically.
• Searching, sorting, counting and aggregation become natural.
• Arrays are the foundation for strings, matrices and many data structures.

10.3 Array Index — The Most Important Rule

C uses zero-based indexing. For an array containing n elements, valid indexes are 0 through n - 1.

int marks[5];

Index:    0     1     2     3     4
          ↓     ↓     ↓     ↓     ↓
Value:   80    75    90    65    88

First index = 0
Last index  = 5 - 1 = 4

10.4 Array Declaration

The basic declaration form is:

data_type array_name[size];

Example:

int marks[5];
float prices[10];
char letters[26];

The size tells the compiler how many elements the array can contain.

10.5 Array Initialization

An array can be initialized when it is declared.

int marks[5] = {80, 75, 90, 65, 88};

10.6 Size Can Be Inferred During Initialization

When an initializer is provided, C can determine the number of elements if the size is omitted.

int numbers[] = {10, 20, 30, 40};

Here the array contains four elements. A useful way to obtain the element count in the same scope is:

size_t n = sizeof numbers / sizeof numbers[0];

10.7 Partial Initialization

If fewer initializers are supplied than the array size, the remaining elements are initialized to zero.

int a[5] = {10, 20};

Index:   0    1    2    3    4
Value:  10   20    0    0    0

10.8 Accessing an Array Element

Use the subscript operator [] to access one element.

int marks[3] = {70, 80, 90};

printf("%d", marks[1]);   // 80

The expression marks[1] refers to the element at index 1.

10.9 Modifying an Array Element

Array elements behave like individual variables and can be assigned new values.

marks[1] = 85;

Only the element at index 1 changes; the other elements remain unchanged.

10.10 Reading Array Elements

Loops are normally used to read many elements.

int a[5];

for (int i = 0; i < 5; i++)
{
    scanf("%d", &a[i]);
}

10.11 Printing Array Elements

for (int i = 0; i < 5; i++)
{
    printf("%d ", a[i]);
}

The same traversal pattern can be used for reading, printing, updating, counting and searching.

10.12 Array Traversal

Traversal means visiting array elements one by one, usually from the first index to the last.

i = 0
  ↓
process a[0]
  ↓
i = 1
  ↓
process a[1]
  ↓
...
  ↓
i = n - 1
  ↓
process a[n - 1]
  ↓
stop

The standard pattern is:

for (int i = 0; i < n; i++)
{
    // process a[i]
}

10.13 Sum of Array Elements

Use an accumulator that starts at zero.

int sum = 0;

for (int i = 0; i < n; i++)
{
    sum += a[i];
}

10.14 Average of Array Elements

First calculate the sum, then divide by the number of elements. Use floating-point division when a fractional result is required.

double average = (double)sum / n;

10.15 Finding the Maximum Element

A safe general approach is to initialize the maximum from the first element rather than assuming zero.

int max = a[0];

for (int i = 1; i < n; i++)
{
    if (a[i] > max)
        max = a[i];
}

10.16 Finding the Minimum Element

int min = a[0];

for (int i = 1; i < n; i++)
{
    if (a[i] < min)
        min = a[i];
}

The same scan pattern works for both maximum and minimum; only the comparison changes.

10.17 Counting Even and Odd Elements

int even = 0, odd = 0;

for (int i = 0; i < n; i++)
{
    if (a[i] % 2 == 0)
        even++;
    else
        odd++;
}

This is a useful example of combining arrays, traversal and decision making.

10.18 Searching an Array

Searching means checking whether a required value occurs in the array.

int key = 30;
int found = 0;

for (int i = 0; i < n; i++)
{
    if (a[i] == key)
    {
        found = 1;
        break;
    }
}

For an unsorted array, a simple scan is called linear search.

10.19 Linear Search

key = 25

a[0] == 25 ? → No
a[1] == 25 ? → No
a[2] == 25 ? → Yes
                   ↓
                Found at index 2

Worst-case time complexity is O(n), because the algorithm may inspect every element.

10.20 Finding the Position of an Element

Because C arrays use indexes, the position can be represented directly by the index.

int position = -1;

for (int i = 0; i < n; i++)
{
    if (a[i] == key)
    {
        position = i;
        break;
    }
}

10.21 Reversing an Array

One simple method is to use two indexes: one from the beginning and one from the end.

int left = 0, right = n - 1;

while (left < right)
{
    int temp = a[left];
    a[left] = a[right];
    a[right] = temp;

    left++;
    right--;
}

Before:  10  20  30  40  50
          ↑               ↑
        left            right

After:   50  40  30  20  10

10.22 Copying One Array to Another

Arrays cannot be copied with a simple assignment such as b = a;. Copy the elements individually.

for (int i = 0; i < n; i++)
{
    b[i] = a[i];
}

10.23 Counting Positive, Negative and Zero

int positive = 0, negative = 0, zero = 0;

for (int i = 0; i < n; i++)
{
    if (a[i] > 0)
        positive++;
    else if (a[i] < 0)
        negative++;
    else
        zero++;
}

10.24 Second Largest Element — Think About the Requirement

“Second largest” can mean second distinct largest or simply the second value after sorting. These are different requirements.

For the distinct version, a robust algorithm must track whether a valid second value has actually been found. Do not blindly initialize the second-largest value to zero.

10.25 Finding Duplicate Elements

A straightforward beginner approach compares each element with later elements.

for (int i = 0; i < n; i++)
{
    for (int j = i + 1; j < n; j++)
    {
        if (a[i] == a[j])
        {
            printf("%d ", a[i]);
        }
    }
}

This nested-loop approach is easy to understand but can take O(n²) time.

10.26 Finding Unique Elements

One common meaning of “unique” is a value that appears exactly once. That requires counting occurrences rather than merely checking whether a value differs from its neighbor.

for (int i = 0; i < n; i++)
{
    int count = 0;

    for (int j = 0; j < n; j++)
    {
        if (a[i] == a[j])
            count++;
    }

    if (count == 1)
        printf("%d ", a[i]);
}

10.27 Frequency of an Element

Frequency means the number of times a particular value occurs.

int key = 5;
int count = 0;

for (int i = 0; i < n; i++)
{
    if (a[i] == key)
        count++;
}

10.28 Finding Largest and Smallest Together

Maximum and minimum can be found in one traversal, so the array does not need to be scanned twice.

int min = a[0];
int max = a[0];

for (int i = 1; i < n; i++)
{
    if (a[i] < min) min = a[i];
    if (a[i] > max) max = a[i];
}

This remains O(n) time and uses constant extra space.

10.29 Swapping Two Array Elements

To exchange two values, use a temporary variable.

int temp = a[i];
a[i] = a[j];
a[j] = temp;

This small pattern appears repeatedly in reversing and sorting algorithms.

10.30 In-Place Array Operations

An in-place operation modifies the original array instead of creating another array of the same size. Reversal using two pointers is an example.

10.31 Introduction to Sorting

Sorting means arranging values in a chosen order, such as ascending or descending order.

Before:  40  10  30  20
After:   10  20  30  40

Sorting is important because many later algorithms become easier after data is ordered.

10.32 Bubble Sort

Bubble sort repeatedly compares adjacent elements and swaps them when they are in the wrong order.

40  10  30  20
│   │
compare → swap
↓
10  40  30  20
    │   │
    compare → swap
↓
10  30  40  20
        │   │
        compare → swap
↓
10  30  20  40

Largest value has moved toward the end.

for (int pass = 0; pass < n - 1; pass++)
{
    for (int j = 0; j < n - 1 - pass; j++)
    {
        if (a[j] > a[j + 1])
        {
            int temp = a[j];
            a[j] = a[j + 1];
            a[j + 1] = temp;
        }
    }
}

10.33 One-Dimensional vs Two-Dimensional Arrays

A one-dimensional array represents a sequence. A two-dimensional array can represent rows and columns, such as a matrix or table.

1D:  [10] [20] [30] [40]

2D:
      col 0  col 1  col 2
row 0   1      2      3
row 1   4      5      6

10.34 Declaring a Two-Dimensional Array

int matrix[2][3];

This declares 2 rows and 3 columns, for a total of 6 int elements.

Access uses two indexes:

matrix[0][1] = 25;

The first index selects the row; the second selects the column.

10.35 Initializing and Reading a Matrix

int matrix[2][3] =
{
    {1, 2, 3},
    {4, 5, 6}
};

To read values, use nested loops:

for (int i = 0; i < 2; i++)
{
    for (int j = 0; j < 3; j++)
    {
        scanf("%d", &matrix[i][j]);
    }
}

10.36 Printing a Matrix

for (int i = 0; i < rows; i++)
{
    for (int j = 0; j < cols; j++)
    {
        printf("%d ", matrix[i][j]);
    }

    printf("\n");
}

10.37 Matrix Addition

Two matrices can be added when they have the same dimensions.

for (int i = 0; i < rows; i++)
{
    for (int j = 0; j < cols; j++)
    {
        C[i][j] = A[i][j] + B[i][j];
    }
}

10.38 Main Diagonal Elements

For a square matrix, the main diagonal contains elements where the row and column indexes are equal.

for (int i = 0; i < n; i++)
{
    printf("%d ", matrix[i][i]);
}

1  2  3
4  5  6
7  8  9

Main diagonal:
1  .  .
.  5  .
.  .  9

Condition: row == column

10.39 Row Sum and Column Sum

For a row sum, keep the row fixed and change the column. For a column sum, keep the column fixed and change the row.

// Row sum
for (int i = 0; i < rows; i++)
{
    int sum = 0;

    for (int j = 0; j < cols; j++)
        sum += matrix[i][j];

    printf("%d\n", sum);
}

10.40 Array Problem-Solving Pattern

Most beginner and placement array problems can be organized around a small number of patterns.

10.41 Common Array Mistakes

• Wrong last index: using a[n] instead of a[n - 1].
• Out-of-bounds access: accessing an index outside the valid range causes undefined behavior.
• Wrong loop condition: using i <= n when the array has n elements.
• Uninitialized local array: local automatic arrays are not automatically filled with zero.
• Wrong maximum initialization: starting with zero can fail for all-negative arrays.
• Integer average: forgetting that integer division discards the fractional part.
• Confusing size with last index: an array of size 5 has indexes 0–4.
• Assuming arrays can be assigned: copy elements explicitly when copying ordinary arrays.
• Forgetting matrix dimensions: row and column limits must both be correct.
• Using an array before knowing its required size: choose a suitable fixed size or later learn dynamic allocation.

10.42 Quick Revision

INTERACTIVE LEARNING

🎬 Arrays — Traversal Visualization

Follow how a loop visits each array element from index 0 to index n - 1.

▶ Open Visualization

—

10.43 Quick MCQs

Select an answer first, then click Check Answer. A correct choice becomes green. If the answer is wrong, your choice becomes red and the correct option becomes green. The explanation appears below.

Run your program to see the output.

#include <stdio.h>

int main()
{
    int n;

    scanf("%d", &n);

    int arr[n];

    for (int i = 0; i < n; i++)
        scanf("%d", &arr[i]);

    for (int i = 0; i < n; i++)
    {
        if (i > 0)
            printf(" ");

        printf("%d", arr[i]);
    }

    return 0;
}

Run your program to see the output.

#include <stdio.h>

int main()
{
    int n;
    long long sum = 0;

    scanf("%d", &n);

    int arr[n];

    for (int i = 0; i < n; i++)
    {
        scanf("%d", &arr[i]);
        sum += arr[i];
    }

    printf("%lld", sum);

    return 0;
}

Run your program to see the output.

#include <stdio.h>

int main()
{
    int n;
    long long sum = 0;

    scanf("%d", &n);

    int arr[n];

    for (int i = 0; i < n; i++)
    {
        scanf("%d", &arr[i]);
        sum += arr[i];
    }

    printf("%.2f", (double)sum / n);

    return 0;
}

Run your program to see the output.

#include <stdio.h>

int main()
{
    int n;

    scanf("%d", &n);

    int arr[n];

    for (int i = 0; i < n; i++)
        scanf("%d", &arr[i]);

    int maximum = arr[0];

    for (int i = 1; i < n; i++)
    {
        if (arr[i] > maximum)
            maximum = arr[i];
    }

    printf("%d", maximum);

    return 0;
}

Run your program to see the output.

#include <stdio.h>

int main()
{
    int n;

    scanf("%d", &n);

    int arr[n];

    for (int i = 0; i < n; i++)
        scanf("%d", &arr[i]);

    int minimum = arr[0];

    for (int i = 1; i < n; i++)
    {
        if (arr[i] < minimum)
            minimum = arr[i];
    }

    printf("%d", minimum);

    return 0;
}

Run your program to see the output.

#include <stdio.h>

int main()
{
    int n;
    int even = 0;
    int odd = 0;

    scanf("%d", &n);

    int arr[n];

    for (int i = 0; i < n; i++)
    {
        scanf("%d", &arr[i]);

        if (arr[i] % 2 == 0)
            even++;
        else
            odd++;
    }

    printf("Even = %d
", even);
    printf("Odd = %d", odd);

    return 0;
}

Run your program to see the output.

#include <stdio.h>

int main()
{
    int n;
    int positive = 0;
    int negative = 0;
    int zero = 0;

    scanf("%d", &n);

    int arr[n];

    for (int i = 0; i < n; i++)
    {
        scanf("%d", &arr[i]);

        if (arr[i] > 0)
            positive++;
        else if (arr[i] < 0)
            negative++;
        else
            zero++;
    }

    printf("Positive = %d
", positive);
    printf("Negative = %d
", negative);
    printf("Zero = %d", zero);

    return 0;
}

Run your program to see the output.

#include <stdio.h>

int main()
{
    int n;
    int target;
    int found = 0;

    scanf("%d", &n);

    int arr[n];

    for (int i = 0; i < n; i++)
        scanf("%d", &arr[i]);

    scanf("%d", &target);

    for (int i = 0; i < n; i++)
    {
        if (arr[i] == target)
        {
            found = 1;
            break;
        }
    }

    printf("%s", found ? "Found" : "Not Found");

    return 0;
}

Run your program to see the output.

#include <stdio.h>

int main()
{
    int n;
    int target;
    int position = -1;

    scanf("%d", &n);

    int arr[n];

    for (int i = 0; i < n; i++)
        scanf("%d", &arr[i]);

    scanf("%d", &target);

    for (int i = 0; i < n; i++)
    {
        if (arr[i] == target)
        {
            position = i + 1;
            break;
        }
    }

    printf("%d", position);

    return 0;
}

Run your program to see the output.

#include <stdio.h>

int main()
{
    int n;

    scanf("%d", &n);

    int arr[n];

    for (int i = 0; i < n; i++)
        scanf("%d", &arr[i]);

    for (int i = n - 1; i >= 0; i--)
    {
        if (i < n - 1)
            printf(" ");

        printf("%d", arr[i]);
    }

    return 0;
}

Run your program to see the output.

#include <stdio.h>

int main()
{
    int n;

    scanf("%d", &n);

    int source[n];
    int destination[n];

    for (int i = 0; i < n; i++)
        scanf("%d", &source[i]);

    for (int i = 0; i < n; i++)
        destination[i] = source[i];

    for (int i = 0; i < n; i++)
    {
        if (i > 0)
            printf(" ");

        printf("%d", destination[i]);
    }

    return 0;
}

Run your program to see the output.

#include <stdio.h>

int main()
{
    int n;
    int printed = 0;

    scanf("%d", &n);

    int arr[n];

    for (int i = 0; i < n; i++)
        scanf("%d", &arr[i]);

    for (int i = 0; i < n; i++)
    {
        int seenEarlier = 0;
        int count = 1;

        for (int k = 0; k < i; k++)
        {
            if (arr[k] == arr[i])
            {
                seenEarlier = 1;
                break;
            }
        }

        if (seenEarlier)
            continue;

        for (int j = i + 1; j < n; j++)
        {
            if (arr[j] == arr[i])
                count++;
        }

        if (count > 1)
        {
            if (printed)
                printf(" ");

            printf("%d", arr[i]);
            printed = 1;
        }
    }

    if (!printed)
        printf("None");

    return 0;
}

Run your program to see the output.

#include <stdio.h>

int main()
{
    int n;
    int printed = 0;

    scanf("%d", &n);

    int arr[n];

    for (int i = 0; i < n; i++)
        scanf("%d", &arr[i]);

    for (int i = 0; i < n; i++)
    {
        int count = 0;

        for (int j = 0; j < n; j++)
        {
            if (arr[j] == arr[i])
                count++;
        }

        if (count == 1)
        {
            if (printed)
                printf(" ");

            printf("%d", arr[i]);
            printed = 1;
        }
    }

    if (!printed)
        printf("None");

    return 0;
}

Run your program to see the output.

#include <stdio.h>

int main()
{
    int n;
    int target;
    int count = 0;

    scanf("%d", &n);

    int arr[n];

    for (int i = 0; i < n; i++)
        scanf("%d", &arr[i]);

    scanf("%d", &target);

    for (int i = 0; i < n; i++)
    {
        if (arr[i] == target)
            count++;
    }

    printf("%d", count);

    return 0;
}

Run your program to see the output.

#include <stdio.h>
#include <limits.h>

int main()
{
    int n;

    scanf("%d", &n);

    int arr[n];

    for (int i = 0; i < n; i++)
        scanf("%d", &arr[i]);

    int largest = INT_MIN;
    int second = INT_MIN;

    for (int i = 0; i < n; i++)
    {
        if (arr[i] > largest)
        {
            second = largest;
            largest = arr[i];
        }
        else if (arr[i] > second && arr[i] != largest)
        {
            second = arr[i];
        }
    }

    if (second == INT_MIN)
        printf("None");
    else
        printf("%d", second);

    return 0;
}

Run your program to see the output.

#include <stdio.h>

int main()
{
    int n;

    scanf("%d", &n);

    int arr[n];

    for (int i = 0; i < n; i++)
        scanf("%d", &arr[i]);

    for (int i = 0; i < n - 1; i++)
    {
        for (int j = 0; j < n - 1 - i; j++)
        {
            if (arr[j] > arr[j + 1])
            {
                int temp = arr[j];
                arr[j] = arr[j + 1];
                arr[j + 1] = temp;
            }
        }
    }

    for (int i = 0; i < n; i++)
    {
        if (i > 0)
            printf(" ");

        printf("%d", arr[i]);
    }

    return 0;
}

Run your program to see the output.

#include <stdio.h>

int main()
{
    int n;

    scanf("%d", &n);

    int arr[n];

    for (int i = 0; i < n; i++)
        scanf("%d", &arr[i]);

    for (int i = 0; i < n - 1; i++)
    {
        for (int j = 0; j < n - 1 - i; j++)
        {
            if (arr[j] < arr[j + 1])
            {
                int temp = arr[j];
                arr[j] = arr[j + 1];
                arr[j + 1] = temp;
            }
        }
    }

    for (int i = 0; i < n; i++)
    {
        if (i > 0)
            printf(" ");

        printf("%d", arr[i]);
    }

    return 0;
}

Run your program to see the output.

#include <stdio.h>

int main()
{
    int r, c;

    scanf("%d %d", &r, &c);

    int a[r][c];

    for (int i = 0; i < r; i++)
    {
        for (int j = 0; j < c; j++)
            scanf("%d", &a[i][j]);
    }

    for (int i = 0; i < r; i++)
    {
        int sum = 0;

        for (int j = 0; j < c; j++)
            sum += a[i][j];

        printf("%d", sum);

        if (i < r - 1)
            printf("
");
    }

    return 0;
}

Run your program to see the output.

#include <stdio.h>

int main()
{
    int r, c;

    scanf("%d %d", &r, &c);

    int a[r][c];

    for (int i = 0; i < r; i++)
    {
        for (int j = 0; j < c; j++)
            scanf("%d", &a[i][j]);
    }

    for (int j = 0; j < c; j++)
    {
        int sum = 0;

        for (int i = 0; i < r; i++)
            sum += a[i][j];

        if (j > 0)
            printf(" ");

        printf("%d", sum);
    }

    return 0;
}

Run your program to see the output.

#include <stdio.h>

int main()
{
    int n;

    scanf("%d", &n);

    int a[n][n];

    for (int i = 0; i < n; i++)
    {
        for (int j = 0; j < n; j++)
            scanf("%d", &a[i][j]);
    }

    for (int i = 0; i < n; i++)
    {
        if (i > 0)
            printf(" ");

        printf("%d", a[i][i]);
    }

    return 0;
}

10.45 Key Takeaway