What is a binary tree and what are the common traversal orders?

Question

IT Interview Practice · Accepted Answer

A **binary tree** is a hierarchical structure where each **node** has at most **two children**, called `left` and `right`. It has a single **root**; nodes with no children are **leaves**. It is the basis for BSTs, heaps, and expression trees.

## Structure

```text
        1            depth 0 (root)
       / \
      2   3          depth 1
     / \
    4   5            depth 2 (leaves: 4,5,3)
```

## Traversals

```python
class Node:
    def __init__(self, val, left=None, right=None):
        self.val, self.left, self.right = val, left, right

def inorder(n):     # left, node, right -> 4 2 5 1 3
    if n:
        inorder(n.left); print(n.val); inorder(n.right)

def preorder(n):    # node, left, right -> 1 2 4 5 3
    if n:
        print(n.val); preorder(n.left); preorder(n.right)

def postorder(n):   # left, right, node -> 4 5 2 3 1
    if n:
        postorder(n.left); postorder(n.right); print(n.val)
```

A **level-order** (BFS) traversal uses a queue and visits depth by depth.

| Traversal | Order | Common use |
|---|---|---|
| Inorder | L, N, R | sorted output of a BST |
| Preorder | N, L, R | copy/serialize a tree |
| Postorder | L, R, N | delete a tree, evaluate expr |
| Level-order | by depth | BFS, shortest path on tree |

Each traversal visits every node once → **O(n)** time, **O(h)** stack space where `h` is the height.

## Why it matters

Binary trees model naturally hierarchical data (file systems, parse trees, decision trees) and underpin efficient search and sorting structures.

Mastering the four traversals is essential — most tree interview problems are a variation of one of them.

Traversal	Order	Common use
Inorder	L, N, R	sorted output of a BST
Preorder	N, L, R	copy/serialize a tree
Postorder	L, R, N	delete a tree, evaluate expr
Level-order	by depth	BFS, shortest path on tree

Structure

Traversals

Why it matters

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