What is a degenerate tree?

What is a degenerate tree?

A degenerate (or pathological) tree A Tree where every internal node has one child. Such trees are performance-wise same as linked list.

What is the difference between balanced and complete trees?

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 is an unbalanced 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 .

Is a degenerate tree balanced?

A balanced binary tree is binary tree where the depth of all leaves is the same or 1 plus the least. A degenerate binary tree is a binary tree in which each node has 1 child.

What is the cause of a degenerate tree?

A degenerate tree is one that contains n nodes and has a height of n − 1. The reason why this shape is so bad is because a lookup would essentially be a linear-time search, because you might have to visit every node.

What is difference between full binary tree and 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.

Is B tree balanced search tree?

B-trees: a form of balanced search tree that uses flexibility in its node degrees to efficiently keep the tree balanced.

What is the depth of a balanced binary tree?

A binary tree of depth 0 or 1 is always balanced.

What is a balanced tree?

Balanced tree is a tree whose height is of order of log (number of elements in the tree). height = O (log (n)) O, as in asymptotic notation i.e. height should have same or lower asymptotic growth rate than log (n) n: number of elements in the tree

What is the difference between degenerate and densely filled in trees?

Think of the degenerate case where the tree is just a long line. Every node we visit just removes that node from consideration. Whereas in a densely filled in tree, each node we visit excludes all the nodes along the other branch that we could have visited, which will be almost half the remaining nodes.

How do you find the efficiency of a balanced tree?

Balanced Trees We have seen that the efficiency of many important operations on trees is related to the Height of the tree – for example searching, inserting, and deleting in a BST are all O(Height). In general, the relation between Height (H) and the number of nodes (N) in a tree can vary from H = N (degenerate tree) to H = log(N).

How do you force a tree to be height balanced?

One way to do this is to force our trees to be height-balanced. A tree is perfectly height-balanced if the left and right subtrees of any node are the same height. e.g. It is clear that at every level there are twice as many nodes as at the previous level, so we do indeed get H = O(logN).