What a heap with a linked list is, and why you might build one
A heap is a way to organize data so that you can always find the smallest (or largest) item quickly. A linked list is a chain of containers, where each container holds one piece of data and points to the next container. When you combine them, you build a heap using linked list nodes instead of an array — this trades some speed for flexibility, since a linked list can grow or shrink without needing to reserve space in advance.
In practice, most heaps use arrays because arrays are faster. But a linked-list heap is useful when you do not know how many items you will store, or when you need to insert and remove items constantly without wasting memory. It is also a good way to understand how heaps actually work, since you have to build the structure yourself instead of relying on a built-in array.
This guide assumes you already know what a linked list is and how to create nodes. If you need to refresh that first, go back to the file organization guide and look for the linked list section.
Key Takeaways
- A linked-list heap stores data in nodes connected by pointers, where each parent node has up to two children, and every level is filled from left to right.
- To insert a new item, add it as the next node in left-to-right order, then swap it upward with its parent until it is in the correct position.
- To remove the smallest (or largest) item, take the root, replace it with the last node, then swap that node downward until the heap is valid again.
- A linked-list heap is slower than an array heap for lookups, but uses less memory when the number of items changes often.
- You must track the parent of every node so you can move items upward; this is harder in a linked list than in an array.
Building the node structure for a linked-list heap
Start by creating a node class that holds a value and pointers to two children. Unlike a binary search tree, a heap does not care about left-child-smaller or right-child-larger rules — it only cares that the parent is smaller (or larger) than both children.
Each node needs: a data field to hold the value, a left child pointer, and a right child pointer. You do not need a parent pointer in the node itself, but you will need to track parents separately when you insert or remove items, because a linked list does not let you jump backward the way an array does.
Here is a minimal node structure in pseudocode:
class HeapNode { int value HeapNode left HeapNode right }
The heap class itself needs to store the root node (the top of the tree) and the count of how many nodes are in the heap. You will also need a reference to the last node, because when you remove the root, you always replace it with the last node in left-to-right order.
Inserting a new item into the heap
To insert a new value, you add it as a new node in the next left-to-right position, then move it upward until it satisfies the heap rule. In a min-heap, the rule is that every parent must be smaller than its children. In a max-heap, every parent must be larger.
The tricky part is finding the next left-to-right position. In an array, you just append to the end. In a linked list, you have to walk the tree level by level, left to right, until you find the spot where the new node belongs. One way to do this is to use a queue: add the root to the queue, then process nodes one at a time, adding their children to the queue. When you find a node that does not have both children, that is where the new node goes.
Once you have added the new node, swap it upward with its parent as long as it violates the heap rule. This is called bubbling up. To do this, you need to know the parent of the node you are moving. Keep a reference to the parent as you walk the tree to find the insertion point.
Here is the insertion process in steps:
- Use a queue to find the next left-to-right position and its parent.
- Create a new node with the value and attach it as the left or right child of the parent.
- While the new node is smaller than its parent (in a min-heap), swap their values and move up to the parent's parent.
- Stop when the new node is in the correct position or reaches the root.
Removing the root (smallest or largest item)
To remove the root, you cannot just delete it — you have to replace it with another node so the tree stays connected. The rule is: always replace the root with the last node in left-to-right order, then move that node downward until the heap is valid again.
Finding the last node is the same process as finding the insertion point: walk the tree level by level, left to right, and remember the last node you visit. Once you have it, copy its value into the root, delete the last node, and then bubble the root downward.
Bubbling down means: if the root is larger than either of its children (in a min-heap), swap it with the smaller child, then repeat at the child's position. Stop when the node is smaller than both children or has no children.
Here is the removal process in steps:
- Save the root's value (this is what you are returning).
- Find the last node in left-to-right order and its parent.
- Copy the last node's value into the root.
- Delete the last node and update its parent's pointer.
- While the root is larger than either child, swap it with the smaller child and move down.
- Return the saved value.
Tracking parent pointers in a linked-list heap
The biggest difference between a linked-list heap and an array heap is that you cannot calculate a parent's position. In an array, if a node is at index i, its parent is at index (i-1)/2. In a linked list, you have to remember the parent as you walk the tree.
When you use a queue to find the insertion point or the last node, store both the node and its parent in the queue. This way, when you find the right spot, you already know the parent without having to walk back up.
If you find yourself walking the tree many times (once to find the insertion point, once to find the last node, once to bubble up), you can optimize by doing multiple things in a single walk. For example, you can find the insertion point and the last node in the same queue traversal, storing both results.
Common mistakes and how to avoid them
The most common mistake is forgetting to update parent pointers when you delete the last node. If the last node is a left child, set the parent's left pointer to null. If it is a right child, set the right pointer to null. If you forget this, you will have a dangling pointer and the heap will be corrupted.
Another mistake is not bubbling far enough. When you insert a node, keep swapping until it is in the correct position, not just one level up. The same applies to removal: keep bubbling down until the heap rule is satisfied at every level.
A third mistake is confusing the heap rule with the binary search tree rule. In a heap, you only care that parents are smaller (or larger) than children. You do not care whether the left child is smaller than the right child. This means you have a choice when bubbling down: swap with whichever child is smaller (in a min-heap), not always the left child.
When a linked-list heap makes sense
Use a linked-list heap when the number of items changes constantly and you want to avoid wasting memory. An array heap requires you to guess the maximum size in advance, or to copy the entire array when it gets full. A linked list grows one node at a time.
Use a linked-list heap when you are learning how heaps work, because building it yourself forces you to understand every step. Once you understand the concept, you can switch to an array heap for better performance.
Do not use a linked-list heap for a priority queue in production code unless you have measured and found that the memory savings outweigh the speed cost. Array heaps are much faster because they use cache-friendly memory and do not require pointer chasing.
Frequently Asked Questions
Can I use a linked-list heap for a priority queue?
Yes, but an array heap is usually faster. A priority queue needs to insert and remove items constantly, and an array heap does both in O(log n) time with less overhead. A linked-list heap does the same operations in O(log n) time but with more pointer chasing, so it is slower in practice.
What is the difference between a min-heap and a max-heap?
In a min-heap, every parent is smaller than its children, so the root is the smallest item. In a max-heap, every parent is larger than its children, so the root is the largest item. The insertion and removal algorithms are identical; you just swap the comparison operators.
Do I need a parent pointer in the node class?
No. You can track parents separately as you walk the tree, which saves memory. If you add a parent pointer to every node, insertion and removal are slightly faster, but you use more memory and have to update parent pointers whenever you move a node.
How do I find the last node without walking the entire tree?
You cannot, in a linked list. You have to traverse level by level, left to right, until you reach the last node. This is why array heaps are faster: you can calculate the last node's position directly. If finding the last node is a bottleneck, consider switching to an array heap or storing a pointer to the last node and updating it after each insertion and removal.
What happens if I insert or remove items while walking the tree?
The tree structure will change, and your queue will have stale pointers. Always finish one operation (insert or remove) before starting another. If you need to insert and remove in parallel, use a lock or a thread-safe queue to protect the heap.