Merge K Sorted Lists Using Min Heap in DSA C++ - Execution Trace

Concept Flow - Merge K Sorted Lists Using Min Heap

Create min heap

↓

Insert first node of each list

↓

While heap not empty

↓

Extract min node from heap

↓

Add min node to merged list

↓

If min node has next, insert next into heap

↓

Repeat until heap empty

↓

Return merged list head

We build a min heap with the first nodes of all lists, then repeatedly extract the smallest node, add it to the merged list, and insert the next node from that list into the heap until all nodes are merged.

Execution Sample

DSA C++

1. Create min heap
2. Insert first nodes of lists
3. While heap not empty:
4.   Extract min node
5.   Add to merged list
6.   Insert next node if exists

This code merges k sorted linked lists by always picking the smallest current node using a min heap.

Execution Table

Step	Operation	Heap Content (values)	Extracted Node	Merged List State	Heap After Insertion
1	Insert first nodes	[1, 2, 3]	None	Empty	[1, 2, 3]
2	Extract min	[1, 2, 3]	1	1 -> null	[2, 3]
3	Insert next of extracted (1->4)	[2, 3]	None	1 -> null	[2, 3, 4]
4	Extract min	[2, 3, 4]	2	1 -> 2 -> null	[3, 4]
5	Insert next of extracted (2->6)	[3, 4]	None	1 -> 2 -> null	[3, 4, 6]
6	Extract min	[3, 4, 6]	3	1 -> 2 -> 3 -> null	[4, 6]
7	Insert next of extracted (3->5)	[4, 6]	None	1 -> 2 -> 3 -> null	[4, 5, 6]
8	Extract min	[4, 5, 6]	4	1 -> 2 -> 3 -> 4 -> null	[5, 6]
9	Insert next of extracted (4->null)	[5, 6]	None	1 -> 2 -> 3 -> 4 -> null	[5, 6]
10	Extract min	[5, 6]	5	1 -> 2 -> 3 -> 4 -> 5 -> null	[6]
11	Insert next of extracted (5->null)	[6]	None	1 -> 2 -> 3 -> 4 -> 5 -> null	[6]
12	Extract min	[6]	6	1 -> 2 -> 3 -> 4 -> 5 -> 6 -> null	[]
13	Heap empty, done	[]	None	1 -> 2 -> 3 -> 4 -> 5 -> 6 -> null	[]

💡 Heap is empty, all nodes merged

Variable Tracker

Variable	Start	After Step 2	After Step 4	After Step 6	After Step 8	After Step 10	Final
Heap	[]	[2, 3]	[3, 4]	[4, 6]	[5, 6]	[6]	[]
Merged List	null	1 -> null	1 -> 2 -> null	1 -> 2 -> 3 -> null	1 -> 2 -> 3 -> 4 -> null	1 -> 2 -> 3 -> 4 -> 5 -> null	1 -> 2 -> 3 -> 4 -> 5 -> 6 -> null

Key Moments - 3 Insights

Why do we insert only the next node of the extracted node into the heap?

Because each list is sorted, after extracting the smallest node, the next node in that list is the next smallest candidate. This keeps the heap size manageable and ensures correct order, as shown in steps 3, 5, 7, 9, and 11 in the execution_table.

What happens if one of the lists is empty at the start?

If a list is empty, we simply don't insert any node from it into the heap initially. The heap only contains nodes from non-empty lists, so the algorithm still works correctly without that list, as implied in step 1.

How does the heap help in merging k sorted lists efficiently?

The heap always gives the smallest current node among all lists in O(log k) time. This avoids scanning all lists repeatedly. The execution_table shows how the heap content changes and always extracts the smallest node.

Visual Quiz - 3 Questions

Look at the execution_table at Step 4. What is the merged list state after extracting the min node?

A 1 -> 2 -> null

B 2 -> null

C 1 -> null

D Empty

💡 Hint

Check the 'Merged List State' column at Step 4 in the execution_table.

At which step does the heap become empty, ending the merge process?

A Step 12

B Step 13

C Step 10

D Step 8

💡 Hint

Look at the 'Heap Content' column and the exit_note in the execution_table.

If the next node of extracted node 3 was null, what would happen to the heap after Step 6?

A Heap would become [4, 6, 5]

B Heap would become [6]

C Heap would remain [4, 6]

D Heap would be empty

💡 Hint

Refer to Step 7 where the next node of 3 is inserted; if null, no insertion happens.

Concept Snapshot

Merge K Sorted Lists Using Min Heap:
- Insert first node of each list into a min heap
- Extract min node from heap and add to merged list
- Insert next node of extracted node into heap if exists
- Repeat until heap is empty
- Result is a fully merged sorted list

Full Transcript

To merge k sorted linked lists, we use a min heap to always pick the smallest current node. We start by inserting the first node of each list into the heap. Then, we repeatedly extract the smallest node from the heap, add it to our merged list, and if that node has a next node, we insert it into the heap. This process continues until the heap is empty, meaning all nodes are merged. The heap helps efficiently find the smallest node among all lists at each step, keeping the merged list sorted. This method handles empty lists by simply not inserting nodes from them initially. The key is that each insertion into the heap is the next node from the list of the extracted node, ensuring order and efficiency.