Linked List vs Array When to Choose Which in DSA C - Complexity Comparison

Time Complexity: Linked List vs Array When to Choose Which

O(1)

Understanding Time Complexity

We want to understand how the time to do tasks changes when using linked lists or arrays.

Which data structure is faster for different operations?

Scenario Under Consideration

Analyze the time complexity of these two simple operations: accessing an element and inserting at the start.

// Access element at index i in array
int getArrayElement(int arr[], int i) {
    return arr[i];
}

// Insert element at start of linked list
void insertAtStart(struct Node** head, int val) {
    struct Node* newNode = malloc(sizeof(struct Node));
    newNode->data = val;
    newNode->next = *head;
    *head = newNode;
}
    

The first gets an element by index in an array. The second adds a new node at the start of a linked list.

Identify Repeating Operations

Look at what repeats or how many steps each operation takes.

• Primary operation: Accessing array element is direct; inserting in linked list changes pointers.
• How many times: Array access is one step; linked list insertion is also one step.

How Execution Grows With Input

Accessing an array element stays quick no matter how big the array is.

Input Size (n)	Approx. Operations for Access
10	1
100	1
1000	1

Inserting at the start of a linked list also takes the same small number of steps regardless of size.

Input Size (n)	Approx. Operations for Insert
10	1
100	1
1000	1

Both operations take constant time, not growing with input size.

Final Time Complexity

Time Complexity: O(1) for both operations

This means the time to do these tasks stays the same no matter how big the data is.

Common Mistake

[X] Wrong: "Accessing any element in a linked list is as fast as in an array."

[OK] Correct: Linked lists need to follow nodes one by one to reach an element, so access time grows with size.

Interview Connect

Knowing when to use arrays or linked lists shows you understand how data structure choices affect speed.

Self-Check

"What if we tried to insert an element in the middle of the linked list? How would the time complexity change?"

Practice

1. Which data structure is better when you need fast random access to elements by index?

easy

A. Array

B. Linked List

C. Stack

D. Queue

Solution

1. Step 1: Understand random access in arrays

   Arrays store elements in contiguous memory, so accessing any element by index is fast and direct.

2. Step 2: Compare with linked list access

   Linked lists require traversal from the head to reach an element, making random access slower.

3. Final Answer:

   Array -> Option A

4. Quick Check:

   Random access = Array [OK]

Hint: For fast index access, choose arrays [OK]

Common Mistakes:

• Thinking linked lists provide fast random access
• Confusing stack or queue with random access
• Ignoring memory layout differences

2. Which of the following is the correct way to declare an array of 5 integers in C?

easy

A. int arr{};

B. int arr();

C. int arr[5];

D. int arr = new int[5];

Solution

1. Step 1: Recall C array declaration syntax

   In C, arrays are declared with type, name, and size in square brackets, like int arr[5];

2. Step 2: Check other options for errors

   int arr(); uses parentheses which is a function declaration, C uses braces which is invalid, D uses 'new' which is C++ syntax.

3. Final Answer:

   int arr[5]; -> Option C

4. Quick Check:

   C array declaration = int arr[5]; [OK]

Hint: Use square brackets for arrays in C [OK]

Common Mistakes:

• Using parentheses instead of brackets
• Using C++ 'new' keyword in C
• Using braces for array declaration

3. Consider the following C code snippet:

typedef struct Node {
  int data;
  struct Node* next;
} Node;

Node* head = NULL;

// Insert 3 nodes at the beginning
for (int i = 1; i <= 3; i++) {
  Node* newNode = (Node*)malloc(sizeof(Node));
  newNode->data = i;
  newNode->next = head;
  head = newNode;
}

// Print list
Node* temp = head;
while (temp != NULL) {
  printf("%d -> ", temp->data);
  temp = temp->next;
}
printf("NULL\n");

What is the printed output?

medium

A. 1 -> 2 -> 3 -> NULL

B. 3 -> 2 -> 1 -> NULL

C. NULL

D. 3 -> 1 -> 2 -> NULL

Solution

1. Step 1: Understand insertion at beginning in linked list

   Each new node is added at the head, so the last inserted node becomes the first in the list.

2. Step 2: Trace the loop values and list order

   Insert 1: list is 1 -> NULL Insert 2: list is 2 -> 1 -> NULL Insert 3: list is 3 -> 2 -> 1 -> NULL

3. Final Answer:

   3 -> 2 -> 1 -> NULL -> Option B

4. Quick Check:

   Insertion at head reverses order [OK]

Hint: Insertion at head reverses order [OK]

Common Mistakes:

• Assuming insertion appends at end
• Confusing order of nodes after insertion
• Ignoring pointer updates

4. The following code tries to insert a node at the end of a singly linked list but causes a runtime error. What is the error?

void insertEnd(Node** head, int val) {
  Node* newNode = (Node*)malloc(sizeof(Node));
  newNode->data = val;
  newNode->next = NULL;

  Node* temp = *head;
  while (temp->next != NULL) {
    temp = temp->next;
  }
  temp->next = newNode;
}

medium

A. Dereferencing NULL pointer when list is empty

B. Memory leak due to missing free()

C. Incorrect data assignment to newNode

D. Missing return statement in void function

Solution

1. Step 1: Analyze behavior when list is empty

   If *head is NULL, then temp = NULL. Accessing temp->next causes a runtime error (segmentation fault).

2. Step 2: Identify fix for empty list case

   Need to check if *head is NULL before loop and assign newNode as head if true.

3. Final Answer:

   Dereferencing NULL pointer when list is empty -> Option A

4. Quick Check:

   Empty list causes NULL pointer error [OK]

Hint: Check for empty list before traversal [OK]

Common Mistakes:

• Ignoring empty list case
• Confusing memory leak with pointer error
• Thinking missing return causes runtime error

5. You need to store a large number of elements where insertions and deletions happen frequently at random positions. Which data structure is more suitable and why? A) Array because it uses less memory B) Linked List because it allows efficient insertions and deletions C) Array because it provides faster random access D) Linked List because it uses contiguous memory

hard

A. Array because it uses less memory

B. Linked List because it uses contiguous memory

C. Array because it provides faster random access

D. Linked List because it allows efficient insertions and deletions

Solution

1. Step 1: Understand insertion and deletion costs

   Arrays require shifting elements for insertions/deletions at random positions, which is costly.

2. Step 2: Compare with linked list behavior

   Linked lists allow insertions and deletions by changing pointers without shifting elements, making them efficient for frequent changes.

3. Final Answer:

   Linked List because it allows efficient insertions and deletions -> Option D

4. Quick Check:

   Frequent insert/delete = Linked List [OK]

Hint: Frequent insert/delete? Choose linked list [OK]

Common Mistakes:

• Choosing array for frequent insertions
• Thinking linked list uses contiguous memory
• Ignoring cost of shifting in arrays