# Binary tree

In computer science, a binary tree is a type of tree (data structure) where each item within the tree has at most two children.

## Types of binary trees

• In a balanced binary tree the left and right branches of every item differ in height by no more than 1.
• In a complete binary tree every level, except possibly the last, is completely filled, and all items in the last level are as far left as possible.
• In a full binary tree every item has either 0 or 2 children.
• In a perfect binary tree all interior items have two children and all leaves have the same depth or same level. A perfect binary tree is also a full and complete binary tree.

## Representations

### Array

A binary tree can be implemented using an array by storing its level-order traversal.[1] In a zero-indexed array, the root is often stored at index 1.

For the nth item of the array its:

• left child is stored at the 2n index.
• right child is stored at the 2n+1 index.
• parent is stored at the n/2 index.

### References

In a programming language with references, binary trees are typically constructed by having a tree structure which contains references to its left child and its right child.

## Traversals

### Pre-order

The current item is visited, then the left branch is visited, and then the right branch is visited.

```void preOrder(Item item) {
if (item == null) return;
visit(item);
preOrder(item.left);
preOrder(item.right);
}
```

### In-order

The left branch is visited, then the current item is visited, and then the right branch is visited.

```void inOrder(Item item) {
if (item == null) return;
inOrder(item.left);
visit(item);
inOrder(item.right);
}
```

### Post-order

The left branch is visited, the right branch is visited, and then the current item is visited.

```void postOrder(Item item) {
if (item == null) return;
postOrder(item.left);
postOrder(item.right);
visit(item);
}
```

## References

1. Adamchik, Victor. "Binary Heap". Computer Science - 121 Fall 2009. CMU. Archived from the original on 25 April 2020. Retrieved 11 October 2020.