How many children can a node have in a binary tree?

Question

BlackTom AI · Accepted Answer

A node in a binary tree can have 0, 1 or 2 children because by definition each node has at most two child links: left and right.

1. Relevant knowledge points and concepts
- Binary tree: a tree data structure where each node has no more than two children, commonly referred to as the left and right child.
- Child and leaf: a child is a direct descendant connected by an edge; a leaf (terminal node) has 0 children.
- Degree of a node: the number of children a node has.

2. Step-by-step reasoning
- Start from the binary tree definition: "at most two children" per node. This constraint directly limits possibilities to 0, 1, or 2 children.
- Enumerate the possible cases:
  - 0 children: the node has no left or right child pointers — this is a leaf node.
  - 1 child: exactly one of the left or right child pointers is present; the other is null. This is often called a unary node.
  - 2 children: both left and right child pointers are present; the node is an internal node with two descendants.
- There is no other allowed number because "at most two" excludes three or more.

3. Intermediate steps / demonstration
- Represent a node by two child pointers (L, R). Each pointer can be null (0) or non-null (1). The number of children is the count of non-null pointers: possibilities are 0 (null,null), 1 (non-null,null) or (null,non-null), and 2 (non-null,non-null). No other combinations exist.

4. Why the correct answer is correct
- The binary tree definition enforces the maximum of two children, and the pointer model shows exactly three possible child-count outcomes: 0, 1, or 2.

5. Why other choices would be incorrect
- "More than 2 children" is incorrect because it violates the binary (two-child) constraint.
- "Only 0 or 2 children" (strict/full binary) is incorrect for general binary trees because nodes can legally have exactly one child.
- "Exactly 2 children" is incorrect because leaves (0 children) and unary nodes (1 child) are allowed.

6. Conclusion
Therefore, the correct answer is: A node can have 0, 1 or 2 children, which matches the provided answer.

How many children can a node have in a binary tree?单项选择题

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