Creating a Singly Linked List from Scratch in DSA C++ - Complexity Walkthrough

Time Complexity: Creating a Singly Linked List from Scratch

O(n^2)

Understanding Time Complexity

When we create a singly linked list by adding nodes one by one, it is important to understand how the time needed grows as we add more nodes.

We want to know how the work changes as the list gets longer.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

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

Node* head = nullptr;

void append(int value) {
  Node* newNode = new Node{value, nullptr};
  if (!head) {
    head = newNode;
    return;
  }
  Node* temp = head;
  while (temp->next) {
    temp = temp->next;
  }
  temp->next = newNode;
}
    

This code creates a singly linked list by adding new nodes at the end one by one.

Identify Repeating Operations

• Primary operation: The while loop that moves through the list to find the last node.
• How many times: For each append, it runs once for each node already in the list, so it grows as the list grows.

How Execution Grows With Input

Each time we add a new node, we walk through the entire list to find the end.

Input Size (n)	Approx. Operations
10	About 1 + 2 + ... + 10 = 55 steps
100	About 5050 steps
1000	About 500,500 steps

Pattern observation: The total work grows roughly like the square of the number of nodes added.

Final Time Complexity

Time Complexity: O(n2)

This means that adding n nodes one by one at the end takes time proportional to n squared, because each new node requires walking through the list so far.

Common Mistake

[X] Wrong: "Appending a node always takes the same constant time, so adding n nodes is O(n)."

[OK] Correct: Because each append walks through the existing list to find the end, the time grows with the list length, making total time grow faster than just n.

Interview Connect

Understanding how linked list operations scale helps you explain trade-offs clearly and shows you know how to write efficient code in real projects.

Self-Check

"What if we kept a pointer to the last node to avoid walking the list each time? How would the time complexity change?"

Practice

1. What is the primary purpose of a Node in a singly linked list?

easy

A. To store data and a reference to the next node

B. To store data and a reference to the previous node

C. To store data only without any references

D. To store the size of the list

Solution

1. Step 1: Understand the Node structure

   A node in a singly linked list holds data and a pointer to the next node.

2. Step 2: Identify the pointer direction

   Since it is singly linked, the node only points forward to the next node, not backward.

3. Final Answer:

   To store data and a reference to the next node -> Option A

4. Quick Check:

   Node = data + next pointer [OK]

Hint: Node always stores data and next pointer in singly linked list [OK]

Common Mistakes:

• Confusing singly linked list with doubly linked list
• Thinking node stores previous node reference
• Assuming node stores list size

2. Which of the following is the correct way to declare a Node struct in C++ for a singly linked list?

easy

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

B. struct Node { int data; Node next; };

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

D. struct Node { int data; Node& next; };

Solution

1. Step 1: Understand pointer syntax in C++

   To link nodes, we use a pointer to the next node: Node* next;.

2. Step 2: Check each option

   struct Node { int data; Node* next; }; correctly uses Node* next;. Options A, B, and C have invalid syntax for pointers or references.

3. Final Answer:

   struct Node { int data; Node* next; }; -> Option C

4. Quick Check:

   Pointer to next node = Node* next [OK]

Hint: Use * for pointer to next node in struct [OK]

Common Mistakes:

• Using object instead of pointer for next
• Using reference incorrectly for next
• Syntax errors in pointer declaration

3. What will be the output of the following code snippet that creates a singly linked list with nodes containing values 10, 20, 30 and prints them?

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

int main() {
  Node* head = new Node{10, nullptr};
  head->next = new Node{20, nullptr};
  head->next->next = new Node{30, nullptr};

  Node* temp = head;
  while (temp != nullptr) {
    std::cout << temp->data << " -> ";
    temp = temp->next;
  }
  std::cout << "null";
  return 0;
}

medium

A. 10 -> 20 -> 30 -> null

B. 10 -> 20 -> null

C. 30 -> 20 -> 10 -> null

D. Compilation error

Solution

1. Step 1: Trace node creation and linking

   Nodes are created with values 10, 20, 30 linked in order: head -> 10 -> 20 -> 30 -> nullptr.

2. Step 2: Trace printing loop

   The loop prints each node's data followed by ' -> ', ending with 'null'. Output is "10 -> 20 -> 30 -> null".

3. Final Answer:

   10 -> 20 -> 30 -> null -> Option A

4. Quick Check:

   Print nodes in order = 10 -> 20 -> 30 -> null [OK]

Hint: Follow next pointers to print nodes in order [OK]

Common Mistakes:

• Printing nodes in reverse order
• Missing last node in output
• Confusing nullptr with null string

4. Identify the error in the following code that attempts to create a singly linked list with two nodes:

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

int main() {
  Node* head = new Node{1, nullptr};
  head->next = new Node{2, nullptr};
  head->next->next = new Node{3, nullptr};
  return 0;
}

medium

A. Incorrect struct definition

B. head->next->next is assigned but head->next is nullptr

C. Missing initialization of head pointer

D. No error, code runs correctly

Solution

1. Step 1: Check node creation and linking

   head is created with data 1, next nullptr. Then head->next is assigned new node with data 2, next nullptr.

2. Step 2: Assign head->next->next

   head->next is not nullptr, so assigning head->next->next to new node with data 3 is valid.

3. Final Answer:

   No error, code runs correctly -> Option D

4. Quick Check:

   Nodes linked properly, no nullptr dereference [OK]

Hint: Check if pointer is nullptr before accessing next [OK]

Common Mistakes:

• Assuming head->next is nullptr before assignment
• Confusing pointer initialization
• Thinking struct definition is wrong

5. You want to create a function appendNode that adds a new node with given data at the end of a singly linked list. Which of the following implementations correctly appends a node?

void appendNode(Node*& head, int value) {
  Node* newNode = new Node{value, nullptr};
  if (head == nullptr) {
    head = newNode;
  } else {
    Node* temp = head;
    while (temp->next != nullptr) {
      temp = temp->next;
    }
    temp->next = newNode;
  }
}

hard

A. Infinite loop due to wrong while condition

B. Correctly appends node at end

C. Fails to update head when list is empty

D. Does not create new node properly

Solution

1. Step 1: Check new node creation

   New node is created with given value and next set to nullptr, which is correct for end node.

2. Step 2: Check list empty and non-empty cases

   If head is nullptr, head is updated to new node. Otherwise, code traverses to last node and sets its next to new node.

3. Final Answer:

   Correctly appends node at end -> Option B

4. Quick Check:

   Traverse to last node and link new node [OK]

Hint: Traverse to last node, then link new node [OK]

Common Mistakes:

• Not updating head when list is empty
• Wrong loop condition causing infinite loop
• Forgetting to set new node's next to nullptr