What is the difference between a perfectly balanced binary tree and a complete binary tree?

What is the difference between a perfectly balanced binary tree and a complete binary tree?

A balanced binary tree is the binary tree where the depth of the two subtrees of every node never differ by more than 1. A complete binary tree is a binary tree whose all levels except the last level are completely filled and all the leaves in the last level are all to the left side.

What are the differences between fully complete binary tree and partially complete binary tree?

Full v.s. Complete Binary Trees. A full binary tree (sometimes proper binary tree or 2-tree) is a tree in which every node other than the leaves has two children. A complete binary tree is a binary tree in which every level, except possibly the last, is completely filled, and all nodes are as far left as possible.

What does it mean when a binary tree is balanced?

A balanced binary tree is a binary tree structure in which the left and right subtrees of every node differ in height by no more than 1. One may also consider binary trees where no leaf is much farther away from the root than any other leaf. (Different balancing schemes allow different definitions of “much farther”.)

Can we say that all perfect binary trees are complete binary tree?

Hence this tree is a complete binary tree. Thus, we can conclude that a perfect binary tree IS A complete binary tree, as in a perfect binary tree all the leaf nodes are present in the same level and in a complete binary tree the nodes in the last level needs to be present as left as possible.

Which binary tree is not always balanced?

An unbalanced binary tree is one that is not balanced. A complete binary tree has all levels completely filled, except possibly the last. If a complete tree has maximum depth n, then it has at least 2n and at most 2n+1−1 nodes. A complete tree with exactly 2n+1−1 nodes is called perfect .

How can you tell a binary tree is complete or not?

If the current node under examination is NULL, then the tree is a complete binary tree. Return true. If index (i) of the current node is greater than or equal to the number of nodes in the binary tree (count) i.e. (i>= count), then the tree is not a complete binary.

How will you say a tree is balanced tree?

To check if a tree is height-balanced, get the height of left and right subtrees. Return true if difference between heights is not more than 1 and left and right subtrees are balanced, otherwise return false.

Is BST a complete binary tree?

A Binary Search Tree (BST) is a binary tree with the following properties: The left subtree of a particular node will always contain nodes whose keys are less than that node’s key. The right subtree of a particular node will always contain nodes with keys greater than that node’s key.

How do you check if a binary tree is balanced?

To check if a Binary tree is balanced we need to check three conditions : 1 The absolute difference between heights of left and right subtrees at any node should be less than 1. 2 For each node, its left subtree should be a balanced binary tree. 3 For each node, its right subtree should be a balanced binary tree.

What is the difference between an empty and non-empty binary tree?

An empty tree is height-balanced. A non-empty binary tree T is balanced if: 3) The difference between heights of left subtree and right subtree is not more than 1. The above height-balancing scheme is used in AVL trees.

Why is the second tree not height balanced?

The diagram below shows two trees, one of them is height-balanced and other is not. The second tree is not height-balanced because height of left subtree is 2 more than height of right subtree. Recommended: Please solve it on “ PRACTICE ” first, before moving on to the solution.

What is the time complexity of a binary search tree?

In general, time complexity is O (h). AVL tree is binary search tree with additional property that difference between height of left sub-tree and right sub-tree of any node can’t be more than 1. For example, BST shown in Figure 2 is not AVL as difference between left sub-tree and right sub-tree of node 3 is 2.