Think together · Start with a little story
The girl asks each task to split into at most two subtasks: a left one and a right one. Why is this structure called a binary tree?
Lay out the process
- Root nodeA starting point
- Left childMay be present or absent
- Right childMay be present or absent
Each node in a binary tree has at most two children, called left and right.
“At most two” allows zero or one; a node does not need to branch twice.
01What is a binary tree?
A binary tree is a tree in which each node has at most two child nodes.
02What are the two children called?
Left child
left child
Right child
right child
Even if a node has only one child, that child is still identified as either its left child or its right child.
03Does “binary” mean every node has two children?
No.
0 children
Allowed; the node is a leaf.
1 child
Allowed.
2 children
Also allowed.
A node simply cannot have more than two children.
04Is a binary tree the same as a binary search tree?
No.
A binary search tree (BST) is a special kind of binary tree with an additional ordering rule for its keys.
05Why do binary trees work well with recursion?
Below a node in a binary tree, there are two smaller binary trees:
This matches the idea you learned earlier: break a problem into smaller problems of the same kind.
06How do you traverse a binary tree?
Common traversal orders include:
Preorder
Root → Left → Right
Inorder
Left → Root → Right
Postorder
Left → Right → Root
There is also level-order traversal, which visits nodes one level at a time and usually uses a queue.
What have you learned?
- Each node in a binary tree has at most two children.
- The children are called left and right.
- A node does not need to have exactly two children.
- A binary tree and a binary search tree are different concepts.
- Binary trees have a natural recursive structure.
Next: What is a graph?
Your turn to try
Can a tree with only one node be a binary tree?
Ready? Open to see the explanation
Yes. It has zero children, which is no more than two, and it does not break the left-right position rule.