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

Time Complexity: Linked List vs Array When to Choose Which

O(n) for array insert at start, O(1) for linked list insert at start

Understanding Time Complexity

Choosing between a linked list and an array affects how fast your program runs for different tasks.

We want to know how their time costs grow as we add more items.

Scenario Under Consideration

Analyze the time complexity of inserting an element at the start for both array and linked list.

// Insert at start in array
void insertAtStartArray(int arr[], int &size, int value) {
  for (int i = size; i > 0; i--) {
    arr[i] = arr[i - 1];
  }
  arr[0] = value;
  size++;
}

// Insert at start in linked list
struct Node {
  int data;
  Node* next;
  Node(int val) : data(val), next(nullptr) {}
};

void insertAtStartList(Node* &head, int value) {
  Node* newNode = new Node(value);
  newNode->next = head;
  head = newNode;
}
    

This code shows how adding an item at the start works differently in arrays and linked lists.

Identify Repeating Operations

Look at what repeats when inserting at the start.

• Primary operation in array: Shifting all existing elements one step right.
• How many times: Once for each existing element (n times).
• Primary operation in linked list: Creating a new node and changing two pointers.
• How many times: Always once, no matter how many elements.

How Execution Grows With Input

As the list or array grows, see how the work changes.

Input Size (n)	Array Insert Steps	Linked List Insert Steps
10	10 shifts	1 pointer change
100	100 shifts	1 pointer change
1000	1000 shifts	1 pointer change

Pattern observation: Array insert grows linearly with size; linked list insert stays constant.

Final Time Complexity

Time Complexity: O(n) for array insert at start, O(1) for linked list insert at start

This means adding at the start gets slower with bigger arrays but stays fast with linked lists.

Common Mistake

[X] Wrong: "Arrays and linked lists have the same speed for all operations."

[OK] Correct: Arrays need to move many items to insert at start, but linked lists just change pointers, so their speeds differ a lot depending on the task.

Interview Connect

Understanding these differences helps you pick the right tool for the job and explain your choices clearly in interviews.

Self-Check

"What if we changed the insertion to the end of the array and 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. Queue

B. Array

C. Stack

D. Linked List

Solution

1. Step 1: Understand random access requirement

   Random access means accessing any element directly by its position quickly.

2. Step 2: Compare array and linked list access times

   Arrays allow direct access by index in constant time, while linked lists require traversal.

3. Final Answer:

   Array -> Option B

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 traversal cost in linked lists

2. Which of the following is the correct way to declare a dynamic array in C++?

easy

A. int arr[] = new int(10);

B. int arr[10];

C. int arr = new int[10];

D. int* arr = new int[10];

Solution

1. Step 1: Identify dynamic array syntax in C++

   Dynamic arrays use pointers with 'new' keyword and size in brackets.

2. Step 2: Check each option

   int* arr = new int[10]; correctly uses 'int* arr = new int[10];'. Others are either static arrays or incorrect syntax.

3. Final Answer:

   int* arr = new int[10]; -> Option D

4. Quick Check:

   Dynamic array = new int[size] [OK]

Hint: Use 'new' with pointer for dynamic arrays in C++ [OK]

Common Mistakes:

• Using static array syntax for dynamic arrays
• Missing pointer (*) in declaration
• Incorrect use of parentheses instead of brackets

3. What will be the output of the following C++ code snippet?

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

Node* head = new Node{1, nullptr};
head->next = new Node{2, nullptr};
head->next->next = new Node{3, nullptr};

Node* temp = head;
while(temp != nullptr) {
  std::cout << temp->data << " ";
  temp = temp->next;
}

medium

A. 1 2 3

B. 3 2 1

C. 1 3 2

D. Compilation error

Solution

1. Step 1: Understand linked list creation

   Nodes are created with values 1, 2, 3 linked in order: head -> 1 -> 2 -> 3 -> nullptr.

2. Step 2: Trace the while loop output

   Loop prints data of each node from head to end: 1, then 2, then 3, each followed by space.

3. Final Answer:

   1 2 3 -> Option A

4. Quick Check:

   Traverse linked list prints 1 2 3 [OK]

Hint: Traverse linked list from head to print data [OK]

Common Mistakes:

• Confusing order of nodes
• Forgetting to update temp pointer
• Assuming array-like indexing

4. Identify the error in the following code that tries to insert a new node at the beginning of a linked list:

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

void insertAtHead(Node* head, int val) {
  Node* newNode = new Node{val, nullptr};
  newNode->next = head;
  head = newNode;
}

medium

A. head pointer is passed by value, so original list is not updated

B. Missing return type in function

C. newNode->next should be nullptr

D. Memory leak due to not deleting old head

Solution

1. Step 1: Analyze function parameter passing

   head is passed by value, so changes inside function do not affect original head pointer.

2. Step 2: Understand effect on linked list

   Assigning head = newNode only changes local copy; original list head remains unchanged.

3. Final Answer:

   head pointer is passed by value, so original list is not updated -> Option A

4. Quick Check:

   Pass pointer by reference to update list head [OK]

Hint: Pass head by reference to modify original list [OK]

Common Mistakes:

• Assuming pointer changes affect caller without reference
• Incorrect next pointer assignment
• Ignoring memory management

5. You need to store a large collection of elements where insertions and deletions happen frequently at random positions. Which data structure is more suitable and why?

hard

A. Array, because it provides fast random access

B. Array, because it uses less memory than linked list

C. Linked List, because it allows efficient insertions and deletions without shifting elements

D. Linked List, because it supports binary search efficiently

Solution

1. Step 1: Understand operation requirements

   Frequent insertions and deletions at random positions require efficient element rearrangement.

2. Step 2: Compare array and linked list for these operations

   Arrays require shifting elements on insert/delete, which is costly. Linked lists adjust pointers, making these operations efficient.

3. Final Answer:

   Linked List, because it allows efficient insertions and deletions without shifting elements -> Option C

4. Quick Check:

   Frequent insert/delete = Linked List [OK]

Hint: Use linked list for frequent insertions/deletions [OK]

Common Mistakes:

• Choosing array for frequent insert/delete ignoring shift cost
• Thinking linked list supports fast random access
• Confusing binary search applicability