Representing Lists as Binary Trees

🌱 First, a Quick Reminder

Before we talk about representing lists as binary trees, let’s quickly recall what each structure means:

A list is a linear collection of elements.
Example: [A, B, C, D]
You move through it one element at a time — like walking on a straight road.
A binary tree is a non-linear structure made up of nodes, where each node can have up to two children (a left child and a right child).
You can think of it like a branching family tree.

Now, the question is —

How can we store or represent a list inside a binary tree?

It might sound strange at first because a list is a straight line and a tree branches out. But surprisingly, there’s a clever way to connect them!

When we represent a list as a binary tree, we do it using what’s known as the Left-Child Right-Sibling (LCRS) representation.

This method is often used when you want to convert any list or even general tree into a binary tree form.

Let’s understand the basic rule first:

Each node’s left pointer represents its first child,
and the right pointer represents its next sibling.

Sounds simple, right?
Let’s see how it actually works with an example.

Suppose we have a simple list:

(A, B, C, D)

This is a linear list — A comes first, then B, then C, then D.

If we represent this as a binary tree:

So we end up with something like this:

A
 \
  B
   \
    C
     \
      D

As you can see, the right pointers connect the list elements in order — just like the “next” pointer in a linked list!

This is the simplest way a linear list can be represented as a binary tree.

Now let’s make it a bit more interesting.
What if our list contains sub-lists (like lists inside lists)?

Example:

(A, (B, C, D), E)

Here:

A is the first element.
(B, C, D) is the second element — but it’s not a single item, it’s another list!
E is the third element.

Let’s represent this using the Left-Child Right-Sibling method.

Start with A as the root.
Since the next element is a sub-list (B, C, D), A’s right child will represent that sub-list.
Inside the sub-list:

Finally, E comes after the sub-list, so E becomes the right sibling of the entire sub-list.

Here’s how the tree looks:

In this structure:

The left pointer goes down to represent a sub-list or child.
The right pointer goes sideways to represent the next element in the same list.

List:  (A, (B, C, D), E)

Binary Tree Representation:

        [A]
       /   \
     [B]   [E]
       \
        [C]
          \
           [D]

Here:

A’s left child points to the sub-list (B, C, D).
A’s right child points to E (the next element in the outer list).
B, C, and D are connected through right links because they are part of the same inner list.

You might wonder — why go through all this? Why not just use normal lists?

Good question!

This representation is very useful when:

We need to handle hierarchical or nested lists.
We want to convert general trees (where nodes can have any number of children) into binary trees (where each node has at most two).
It simplifies memory management because every node has only two pointers — left and right — no matter how many children exist logically.

In short, it gives us a unified structure to represent complex data easily in memory.