Get Length of Linked List in DSA C++ - Time & Space Complexity

Time Complexity: Get Length of Linked List

O(n)

Understanding Time Complexity

We want to understand how the time to find the length of a linked list changes as the list grows.

How does the number of steps increase when the list gets longer?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

int getLength(Node* head) {
    int length = 0;
    Node* current = head;
    while (current != nullptr) {
        length++;
        current = current->next;
    }
    return length;
}
    

This code counts how many nodes are in a linked list by moving from the start to the end.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The while loop that visits each node once.
• How many times: Exactly once per node, so as many times as the list length.

How Execution Grows With Input

As the list gets longer, the number of steps grows directly with the number of nodes.

Input Size (n)	Approx. Operations
10	About 10 steps
100	About 100 steps
1000	About 1000 steps

Pattern observation: The steps increase in a straight line as the list size grows.

Final Time Complexity

Time Complexity: O(n)

This means the time to find the length grows directly with the number of nodes in the list.

Common Mistake

[X] Wrong: "The length can be found instantly without checking each node."

[OK] Correct: Since nodes are linked one by one, you must visit each to count them; there is no shortcut.

Interview Connect

Knowing how to analyze simple linked list operations like this builds a strong base for more complex problems.

Self-Check

"What if the linked list was doubly linked? Would the time complexity to get its length change?"

Practice

1. What does the function getLength do when given the head of a linked list?

easy

A. Deletes the linked list

B. Returns the value of the first node

C. Returns the number of nodes in the linked list

D. Returns the last node of the linked list

Solution

1. Step 1: Understand the function purpose

   The function getLength counts nodes starting from the head until the end.

2. Step 2: Identify the output

   It returns the total count of nodes, which is the length of the linked list.

3. Final Answer:

   Returns the number of nodes in the linked list -> Option C

4. Quick Check:

   Counting nodes = length [OK]

Hint: Count nodes one by one until null [OK]

Common Mistakes:

• Confusing length with node value
• Trying to delete nodes instead of counting
• Returning the last node instead of count

2. Which of the following is the correct syntax to initialize a pointer to the head of a linked list in C++?

easy

A. Node* head = NULL;

B. Node head = NULL;

C. Node* head = 0;

D. Node head = 0;

Solution

1. Step 1: Understand pointer initialization

   In C++, a pointer to a node is declared as Node* and can be initialized to NULL or nullptr.

2. Step 2: Check each option

   Node* head = NULL; uses Node* head = NULL; which is correct pointer initialization syntax.

3. Final Answer:

   Node* head = NULL; -> Option A

4. Quick Check:

   Pointer declaration uses * and NULL [OK]

Hint: Use * for pointers and NULL for empty [OK]

Common Mistakes:

• Declaring pointer without *
• Assigning NULL to non-pointer variable
• Using 0 instead of NULL (less clear)

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

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

int getLength(Node* head) {
  int count = 0;
  while (head != NULL) {
    count++;
    head = head->next;
  }
  return count;
}

int main() {
  Node n3 = {30, NULL};
  Node n2 = {20, &n3};
  Node n1 = {10, &n2};
  int length = getLength(&n1);
  std::cout << length;
  return 0;
}

medium

A. 3

B. 2

C. 1

D. 0

Solution

1. Step 1: Trace the linked list nodes

   The list has nodes n1 -> n2 -> n3 -> NULL, so total 3 nodes.

2. Step 2: Count nodes in getLength

   The function counts each node until NULL, so count becomes 3.

3. Final Answer:

   3 -> Option A

4. Quick Check:

   3 nodes counted = 3 [OK]

Hint: Count nodes by following next pointers until NULL [OK]

Common Mistakes:

• Counting only first node
• Off-by-one error in loop
• Confusing data values with count

4. Identify the error in the following code that tries to get the length of a linked list:

int getLength(Node* head) {
  int count = 0;
  while (head->next != NULL) {
    count++;
    head = head->next;
  }
  return count;
}

medium

A. It causes a segmentation fault

B. It misses counting the last node

C. It counts nodes twice

D. It returns the data of the last node

Solution

1. Step 1: Analyze the loop condition

   The loop runs while head->next != NULL, so it stops before the last node.

2. Step 2: Check counting logic

   Since last node is not counted, the returned count is one less than actual length.

3. Final Answer:

   It misses counting the last node -> Option B

4. Quick Check:

   Loop condition excludes last node [OK]

Hint: Use while(head != NULL) to count all nodes [OK]

Common Mistakes:

• Using head->next in loop condition
• Not counting last node
• Confusing node data with count

5. Given a linked list where each node contains an integer, how would you modify the getLength function to return the length only if all node values are positive? If any node has zero or negative value, return -1.

hard

A. Count nodes normally and ignore values

B. Return -1 if list is empty, else return length

C. Return length only if first node is positive

D. Traverse nodes, if value <= 0 return -1, else count nodes and return count

Solution

1. Step 1: Traverse each node checking value

   While moving through the list, check if node's data is <= 0; if yes, return -1 immediately.

2. Step 2: Count nodes if all values positive

   If all nodes have positive values, count them and return the count as length.

3. Final Answer:

   Traverse nodes, if value <= 0 return -1, else count nodes and return count -> Option D

4. Quick Check:

   Check values during count, return -1 if any non-positive [OK]

Hint: Check values while counting, stop early if non-positive [OK]

Common Mistakes:

• Ignoring node values during count
• Checking only first node value
• Returning length even if negative values exist