Contents

- 1 How do you balance unbalanced BST?
- 2 Why is an unbalanced binary tree bad?
- 3 What is the effect when a binary search tree becomes unbalanced?
- 4 Why do you like red black trees over AVL trees?
- 5 What is unbalanced binary tree?
- 6 Why red black tree is better than AVL tree?
- 7 What is an unbalanced BST?
- 8 What is the efficiency of BST?
- 9 What is the maximum height of an AVL tree with P nodes?
- 10 What will be the height of a balanced full binary tree with 8 leaves?
- 11 What are unbalanced nodes?

## How do you balance unbalanced BST?

**How to keep a tree in balance**

- First, Insert descends recursively down the tree until it finds a node n to append the new value.
- If n is a leaf, adding a new child node increases the height of the subtree n by 1.
- Insert now adds a new child node to node n .
- The height increase is passed back to n 's parent node.

## Why is an unbalanced binary tree bad?

An extremely unbalanced tree, for example a tree where all nodes are linked to the left, means **you still search through every single node before finding the last one**, which is not the point of a tree at all and has no benefit over a linked list.

## What is the effect when a binary search tree becomes unbalanced?

As a binary search tree becomes more and more unbalanced, **the performance of the find, insert and delete algorithms degrades until reaching the worst case of O(n), where n is the number of nodes in the tree**.

## Why do you like red black trees over AVL trees?

Red Black Trees **provide faster insertion and removal operations than AVL trees** as fewer rotations are done due to relatively relaxed balancing. AVL trees store balance factors or heights with each node, thus requires storage for an integer per node whereas Red Black Tree requires only 1 bit of information per node.

## What is unbalanced binary tree?

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 .

## Why red black tree is better than AVL tree?

Red Black Trees **provide faster insertion and removal operations than AVL trees as fewer rotations are done due to relatively relaxed balancing**. AVL trees store balance factors or heights with each node, thus requires storage for an integer per node whereas Red Black Tree requires only 1 bit of information per node.

## What is an unbalanced BST?

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 .

## What is the efficiency of BST?

If BST is balanced, you can expect on average **2^(i-1) nodes at the level i** . This further means, if the tree has k levels ( k is called the height of tree), the expected number of nodes in the tree is 1 + 2 + 4 + ..

## What is the maximum height of an AVL tree with P nodes?

4. What is the maximum height of an AVL tree with p nodes? Explanation: Consider height of tree to be 'he', then number of nodes which totals to p can be written in terms **of height as N(he)=N(he-1)+1+N(he-2)**.

## What will be the height of a balanced full binary tree with 8 leaves?

What will be the height of a balanced full binary tree with 8 leaves? Explanation: A balanced full binary tree with l leaves has height h, where h = log2l + 1. So, the height of a balanced full binary tree with 8 leaves = **log28 + 1 = 3 + 1 = 4**.

## What are unbalanced nodes?

If a tree becomes unbalanced, when **a node is inserted into the right subtree of the right subtree**, then we perform a single left rotation − In our example, node A has become unbalanced as a node is inserted in the right subtree of A's right subtree.