Intersection Point of Two Linked Lists in DSA C - Time & Space Complexity

Time Complexity: Intersection Point of Two Linked Lists

O(m + n)

Understanding Time Complexity

We want to find where two linked lists meet, if at all. Understanding how long this takes helps us write efficient code.

How does the time needed grow as the lists get longer?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

// Find intersection node of two singly linked lists
struct Node* getIntersectionNode(struct Node* headA, struct Node* headB) {
    struct Node *a = headA, *b = headB;
    while (a != b) {
        a = (a == NULL) ? headB : a->next;
        b = (b == NULL) ? headA : b->next;
    }
    return a;
}
    

This code tries to find the node where two linked lists intersect by traversing both lists with two pointers.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Traversing nodes of both linked lists using two pointers.
• How many times: Each pointer moves through its list and then switches to the other list once, repeating until they meet or both reach the end.

How Execution Grows With Input

As the lists get longer, the pointers travel through each node at most twice before meeting or ending.

Input Size (n)	Approx. Operations
10	About 20 steps (each pointer traverses both lists)
100	About 200 steps
1000	About 2000 steps

Pattern observation: The total steps grow roughly linearly with the sum of the lengths of both lists.

Final Time Complexity

Time Complexity: O(m + n)

This means the time grows linearly with the total number of nodes in both lists combined.

Common Mistake

[X] Wrong: "The pointers only traverse one list each, so time is O(max(m, n))"

[OK] Correct: Each pointer may traverse both lists once, so total steps depend on the sum of lengths, not just the longer list.

Interview Connect

Understanding this approach shows you can handle linked list problems efficiently by clever pointer use, a skill valued in many coding challenges.

Self-Check

"What if we used a hash set to store visited nodes from one list? How would the time complexity change?"

Practice

1. What does the term intersection point of two linked lists mean?

easy

A. The node where both linked lists have the same value but different references

B. The node where both linked lists share the same reference

C. The first node of the longer linked list

D. The last node of the shorter linked list

Solution

1. Step 1: Understand linked list nodes and references

   Each node in a linked list has a reference (address) to the next node. Two lists intersect if they share the same node reference, not just the same value.

2. Step 2: Define intersection point

   The intersection point is the first node where both lists point to the exact same node object in memory.

3. Final Answer:

   The node where both linked lists share the same reference -> Option B

4. Quick Check:

   Intersection means shared node reference [OK]

Hint: Intersection means same node object, not just same value [OK]

Common Mistakes:

• Confusing same value with same node reference
• Thinking intersection is based on node values
• Assuming intersection is at list ends

2. Which of the following C code snippets correctly declares a node structure for a singly linked list used to find intersection?

easy

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

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

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

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

Solution

1. Step 1: Understand correct struct declaration

   In C, to declare a linked list node, you define a struct with data and a pointer to the same struct type.

2. Step 2: Check each option

   typedef struct Node { int data; struct Node* next; } Node; correctly uses typedef and struct Node with a pointer to struct Node. struct Node { int data; Node* next; }; misses typedef and uses Node* without struct keyword. typedef struct { int data; struct Node* next; } Node; misses struct name. struct Node { int data; struct Node next; }; incorrectly uses struct Node next (not a pointer).

3. Final Answer:

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

4. Quick Check:

   Correct struct with pointer to same struct [OK]

Hint: Use 'struct Node* next;' inside struct for pointer to next node [OK]

Common Mistakes:

• Forgetting 'struct' keyword before pointer type
• Using struct variable instead of pointer for next
• Missing typedef or struct name

3. Given the following code snippet to find the intersection point of two linked lists, what will be the output?

Node* getIntersectionNode(Node* headA, Node* headB) {
    Node *a = headA, *b = headB;
    while (a != b) {
        a = (a == NULL) ? headB : a->next;
        b = (b == NULL) ? headA : b->next;
    }
    return a;
}

// Lists:
// List A: 1 -> 2 -> 3 \
//                      6 -> 7 -> NULL
// List B:       4 -> 5 /

// Intersection at node with value 6
Node* result = getIntersectionNode(headA, headB);
printf("%d", result->data);

medium

A. 3

B. 5

C. 6

D. NULL

Solution

1. Step 1: Understand the two-pointer approach

   Two pointers traverse each list; when reaching end, switch to other list head. They meet at intersection or NULL if none.

2. Step 2: Trace pointers on given lists

   Lists intersect at node with value 6. Pointers will meet there after switching lists.

3. Final Answer:

   6 -> Option C

4. Quick Check:

   Two-pointer meet at intersection node value 6 [OK]

Hint: Two pointers switch lists to align lengths and meet at intersection [OK]

Common Mistakes:

• Assuming pointers meet at first node
• Not switching pointers to other list head
• Confusing node value with pointer address

4. Identify the bug in the following code snippet intended to find the intersection point of two linked lists:

Node* getIntersectionNode(Node* headA, Node* headB) {
    Node *a = headA, *b = headB;
    while (a != b) {
        if (a == NULL || b == NULL) {
            a = headB;
            b = headA;
        } else {
            a = a->next;
            b = b->next;
        }
    }
    return a;
}

medium

A. The loop may run infinitely if no intersection exists

B. Pointers should not switch lists when NULL

C. The function does not handle empty lists

D. The comparison should be 'a->data == b->data' instead of 'a != b'

Solution

1. Step 1: Analyze loop termination condition

   The loop ends when pointers a and b are equal (same node or NULL).

2. Step 2: Check pointer switching logic

   When a or b is NULL, they switch to other list head. But if no intersection, pointers cycle indefinitely without becoming equal.

3. Final Answer:

   The loop may run infinitely if no intersection exists -> Option A

4. Quick Check:

   Loop lacks proper NULL check, causing infinite loop [OK]

Hint: Add explicit NULL check to break loop if no intersection [OK]

Common Mistakes:

• Assuming pointers always meet
• Comparing node data instead of node pointers
• Not handling empty list inputs

5. You have two singly linked lists that may or may not intersect. Write a function to find the intersection point efficiently. Which approach below is best and why? A) Use two pointers starting at heads, switch to other list when reaching end, until they meet. B) Use nested loops to compare every node of list A with every node of list B. C) Store all nodes of list A in a hash set, then check nodes of list B for presence. D) Reverse both lists and compare nodes from the start until they differ.

hard

A. Two-pointer switching approach; O(n) time, O(1) space

B. Nested loops; O(n*m) time, O(1) space

C. Hash set approach; O(n+m) time, O(n) space

D. Reverse lists; modifies input and O(n) time

Solution

1. Step 1: Evaluate time and space complexity of each approach

   Two-pointer switching approach; O(n) time, O(1) space uses two pointers switching lists, runs in linear time and constant space. Nested loops; O(n*m) time, O(1) space is nested loops, very slow. Hash set approach; O(n+m) time, O(n) space uses extra space for hash set. Reverse lists; modifies input and O(n) time modifies lists, which is not ideal.

2. Step 2: Choose best approach for efficiency and safety

   Two-pointer switching approach; O(n) time, O(1) space is best because it is efficient (O(n)) and does not use extra space or modify lists.

3. Final Answer:

   Two-pointer switching approach; O(n) time, O(1) space -> Option A

4. Quick Check:

   Two-pointer method is optimal for intersection detection [OK]

Hint: Two-pointer switch method is fastest and uses no extra space [OK]

Common Mistakes:

• Choosing nested loops causing slow performance
• Using extra memory unnecessarily
• Modifying input lists causing side effects