Checking if a Binary Tree is Full: A Hint

In summary, a full binary tree is a type of binary tree where each node has either 0 or 2 children, except possibly the last level. To check if a binary tree is full, a recursive approach can be used with a time complexity of O(n), where n is the number of nodes in the tree. A binary tree can be both full and complete, but a perfect binary tree is a type of full binary tree where every level is completely filled with nodes and all nodes are as far left as possible.
  • #1
evinda
Gold Member
MHB
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Hello! (Smile)

I want to write an algorithm, that checks if a binary tree is full or not.

Could you give me a hint how I could do this? (Thinking)
 
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  • #2
evinda said:
Hello! (Smile)

I want to write an algorithm, that checks if a binary tree is full or not.

Could you give me a hint how I could do this? (Thinking)

If every node is either a leaf, or has two children, then it's a full tree. So traverse the tree recursively, and for each node, compute the logical expression (IsLeaf OR HasTwoChildren), then AND all the results together.
 

FAQ: Checking if a Binary Tree is Full: A Hint

What is a full binary tree?

A full binary tree is a type of binary tree in which every node has either 0 or 2 children. This means that every level of the tree, except possibly the last, is completely filled with nodes.

How can I check if a binary tree is full?

To check if a binary tree is full, you can use a recursive approach. Start by checking if the tree is empty, if so, it is considered full. Then, check if the current node has both left and right children. If it does, recursively check if both children are also full binary trees. If any of the children are not full, the entire tree is not full. If the current node has only one child or no children, the tree is not full.

What is the time complexity of checking if a binary tree is full?

The time complexity of checking if a binary tree is full is O(n), where n is the number of nodes in the tree. This is because the algorithm needs to visit each node in the tree to determine if it is full or not.

Can a binary tree be both full and complete?

Yes, a binary tree can be both full and complete. A complete binary tree is a type of binary tree in which every level, except possibly the last, is completely filled with nodes and all nodes are as far left as possible. So, a full binary tree can also be complete if all nodes are as far left as possible.

What is the difference between a full binary tree and a perfect binary tree?

A full binary tree is a type of binary tree in which every node has either 0 or 2 children. On the other hand, a perfect binary tree is a type of binary tree in which every level is completely filled with nodes and all nodes are as far left as possible. This means that in a perfect binary tree, all nodes have 2 children. So, a perfect binary tree is also a full binary tree, but a full binary tree may not necessarily be perfect.

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