Difference between complete binary tree

Difference between Complete binary tree, Balanced binary tree, Ordered binary tree, Full binary tree, Perfect Binary tree Binary Tree: A Tree in which each node has a degree of atmost 2. i.e. it can have either 0,1 or 2 children.

Here, leaves are H, I, J. Except these, remaining internal nodes has atmost 2 nodes as their child.

Full Binary tree:

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Every node should have exactly 2 nodes except the leaves. It is also called as Strict Binary Tree or 2- Binary Tree or Proper Binary Tree.

Complete Binary Tree: It is a binary tree in which every level (except possibly the last) is completely filled, and all nodes are as far left as possible.

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The above 3 fig’s are Complete Binary Trees.

Fig1

fig2

fig 4

fig3

fig 5

These are not complete trees as in fig1 at level 1, the 0 node has no children. In fig 2, nodes 2, 5, 9 doesn’t have left child. For a tree to be complete tree, right child is not necessary but left child is must if right child is present incase of last level. For fig 3, the node 0 doesn’t have a left child.same as for fig 4 and fig 5.

Ordered Binary Tree : It is a Binary Tree in which all the elements are arranged in an order i.e. For a node, All elements of left sub-tree should be smaller than the node and all elements of right sub-tree should be larger than the node.

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In the above fig, Every node has smaller element as left child and larger element as right child.  An Ordered Tree may or may not be balanced. It may have time complexity of O(n) or O(logn).

In the above Tree, we see that even though it is an Ordered Tree, it is not balanced. For adding,deleting and Searching operations, it has time complexity of O(n) same as linked list.

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Balanced Binary Tree: It is a Binary tree in which the elements are ordered and no leaf is at “much greater” depth than any other leaf. It will have time complxity of O(logn).

Perfectly balanced binary tree: It is a Balanced binary tree in which the difference in the left and right tree nodes’ count of any node is at most one.

In the given fig, the left binary tree is ordered whereas right binary tree is ordered and balanced.

To avoid imbalance in the tree to search, apply operations that rearrange some elements of the tree when adding or removing an item from it. These operations are called Rotations.

The type of rotation should be further specified and depends on the implementation of the specific data structure. As examples for structures like these we can give Red-Black tree, AVLtree, AA-tree, Splay-tree and others.

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Non-binary balanced trees: Non-binary

balanced

search

trees also

have

multiple

implementations with different special properties. Examples are B- Trees, B+ Trees and Interval Trees. All of them are ordered, balanced, but not binary. Their nodes can typically hold more than one key and can have more than two child nodes.

These trees also perform operations like insert / search / delete very fast.

Perfect binary tree: In this tree, Every node has exactly two nodes and all levels are completely filled. ( or ) A perfect binary tree is a binary tree in which all leaves have the same depth or same level.  In general A perfect binary tree satisfies all the properties of complete and full binary trees.

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 For an Orderded perfect binary tree, time complexity for search, insert and remove operations has O(logn).

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For Graph Terminology : Click here Why analysis of Algorithms : Click here 4 pillars of OOPS concept : Click here

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