Merge Two Sorted Linked Lists in DSA C# - Time & Space Complexity

Time Complexity: Merge Two Sorted Linked Lists

O(n + m)

Understanding Time Complexity

We want to understand how the time needed to merge two sorted linked lists changes as the lists get bigger.

Specifically, how does the work grow when the input lists grow?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

public ListNode MergeTwoLists(ListNode l1, ListNode l2) {
    if (l1 == null) return l2;
    if (l2 == null) return l1;
    if (l1.val < l2.val) {
        l1.next = MergeTwoLists(l1.next, l2);
        return l1;
    } else {
        l2.next = MergeTwoLists(l1, l2.next);
        return l2;
    }
}
    

This code merges two sorted linked lists by comparing their nodes one by one and linking them in order.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Comparing nodes and moving to the next node in either list.
• How many times: Each node from both lists is visited exactly once during the merge.

How Execution Grows With Input

As the total number of nodes in both lists grows, the number of comparisons and linkings grows roughly the same.

Input Size (n = total nodes)	Approx. Operations
10	About 10 comparisons and linkings
100	About 100 comparisons and linkings
1000	About 1000 comparisons and linkings

Pattern observation: The work grows linearly with the total number of nodes.

Final Time Complexity

Time Complexity: O(n + m)

This means the time to merge grows directly with the total number of nodes in both lists combined.

Common Mistake

[X] Wrong: "The merge takes quadratic time because of the recursion."

[OK] Correct: Each node is visited only once, so the recursion depth matches the total nodes, not their square.

Interview Connect

Understanding this merge process and its time cost helps you handle linked list problems confidently in interviews.

Self-Check

"What if the input lists were arrays instead of linked lists? How would the time complexity change?"

Practice

1. What is the main goal when merging two sorted linked lists?

easy

A. Remove duplicates from both lists

B. Create a new sorted linked list containing all elements from both lists

C. Reverse both linked lists

D. Sort each list individually without merging

Solution

1. Step 1: Understand the problem goal

   The goal is to combine two sorted linked lists into one sorted linked list.

2. Step 2: Clarify the expected output

   The output should be a single linked list that maintains sorted order and contains all nodes from both input lists.

3. Final Answer:

   Create a new sorted linked list containing all elements from both lists -> Option B

4. Quick Check:

   Merge means combine sorted lists into one sorted list [OK]

Hint: Merging means combining sorted lists into one sorted list [OK]

Common Mistakes:

• Thinking merge means reversing lists
• Trying to sort lists separately without merging
• Removing duplicates instead of merging

2. Which of the following is the correct C# syntax to declare a node class for a singly linked list used in merging?

easy

A. class Node { int val; Node next; Node(int x) { val = x; next = null; } }

B. public struct Node { int val; Node next; }

C. public class Node { public int val; public Node next; public Node(int x) { val = x; next = null; } }

D. public class Node { int val; int next; public Node(int x) { val = x; next = 0; } }

Solution

1. Step 1: Check class declaration and access modifiers

   public class Node { public int val; public Node next; public Node(int x) { val = x; next = null; } } correctly declares a public class with public fields and a constructor initializing values.

2. Step 2: Verify field types and initialization

   public class Node { public int val; public Node next; public Node(int x) { val = x; next = null; } } uses 'int val' and 'Node next' with proper initialization; others miss public or use wrong types.

3. Final Answer:

   public class Node { public int val; public Node next; public Node(int x) { val = x; next = null; } } -> Option C

4. Quick Check:

   Correct class with public fields and constructor [OK]

Hint: Node class needs public fields and constructor for linked list [OK]

Common Mistakes:

• Missing public keyword causing access errors
• Using struct instead of class for linked list node
• Incorrect type for next pointer

3. What will be the output linked list after merging these two sorted lists?

List1: 1 -> 3 -> 5 -> null
List2: 2 -> 4 -> 6 -> null

Assuming the merge function merges correctly.

medium

A. 1 -> 2 -> 3 -> 4 -> 5 -> 6 -> null

B. 1 -> 3 -> 5 -> 2 -> 4 -> 6 -> null

C. 2 -> 4 -> 6 -> 1 -> 3 -> 5 -> null

D. 1 -> 2 -> 4 -> 3 -> 5 -> 6 -> null

Solution

1. Step 1: Compare first nodes of both lists

   1 (List1) < 2 (List2), so 1 is first in merged list.

2. Step 2: Continue comparing nodes in order

   Next compare 3 and 2, 2 is smaller, then 3 and 4, 3 is smaller, then 5 and 4, 4 is smaller, then 5 and 6, 5 is smaller, finally 6.

3. Final Answer:

   1 -> 2 -> 3 -> 4 -> 5 -> 6 -> null -> Option A

4. Quick Check:

   Merge sorted lists by picking smaller node each step [OK]

Hint: Pick smaller node from heads repeatedly to merge [OK]

Common Mistakes:

• Appending one list entirely before the other
• Not maintaining sorted order
• Mixing node order incorrectly

4. Given the following code snippet for merging two sorted linked lists, what is the error?

public Node Merge(Node l1, Node l2) {
    if (l1 == null) return l2;
    if (l2 == null) return l1;
    if (l1.val < l2.val) {
        l1.next = Merge(l1.next, l2);
        return l1;
    } else {
        l2.next = Merge(l1, l2.next);
        return l2;
    }
}

medium

A. No error; the code correctly merges two sorted linked lists

B. Missing base case for empty lists

C. Incorrect comparison operator used

D. The function does not handle cycles in lists

Solution

1. Step 1: Analyze base cases

   Code returns the other list if one is null, correctly handling empty lists.

2. Step 2: Check recursive merge logic

   Code compares values and recursively merges the rest, correctly linking nodes in sorted order.

3. Final Answer:

   No error; the code correctly merges two sorted linked lists -> Option A

4. Quick Check:

   Recursive merge with base cases and correct comparisons [OK]

Hint: Check base cases and recursive calls carefully [OK]

Common Mistakes:

• Forgetting to return merged list
• Incorrect base case handling
• Wrong comparison operator

5. You have two sorted linked lists:
List1: 1 -> 4 -> 5 -> null
List2: 1 -> 3 -> 4 -> null

After merging, what is the correct merged list?
Also, explain why duplicates appear and how the merge handles them.

hard

A. 1 -> 1 -> 4 -> 3 -> 4 -> 5 -> null

B. 1 -> 3 -> 4 -> 5 -> null

C. 1 -> 4 -> 5 -> 3 -> 4 -> 1 -> null

D. 1 -> 1 -> 3 -> 4 -> 4 -> 5 -> null

Solution

1. Step 1: Merge nodes in sorted order including duplicates

   Both lists have '1' and '4' values; merge keeps all nodes, so duplicates appear in order.

2. Step 2: Explain duplicate handling

   Merge does not remove duplicates; it links nodes as they appear, preserving duplicates in sorted order.

3. Final Answer:

   1 -> 1 -> 3 -> 4 -> 4 -> 5 -> null -> Option D

4. Quick Check:

   Duplicates kept; merge preserves all nodes sorted [OK]

Hint: Merge keeps duplicates; just link nodes in sorted order [OK]

Common Mistakes:

• Removing duplicates mistakenly
• Mixing node order
• Appending lists without sorting