Binary trees, Data Structure & Algorithms

Assignment Help:

A binary tree is a special tree where each non-leaf node can have atmost two child nodes. Most important types of trees which are used to model yes/no, on/off, higher/lower, i.e., binary decisions are binary trees.

Recursive Definition: A binary tree is either empty or a node that has left and right sub-trees that are binary trees. Empty trees are represented as boxes (but we will almost always omit the boxes).

In a formal way, we can described binary tree as a finite set of nodes which is either empty or partitioned in to sets of T0, Tl, Tr , where T0 is the root and Tl and Tr are left and right binary trees, respectively.

Properties of a binary tree are following

  • If a binary tree contains n nodes, then it have exactly n - 1 edges;
  • A Binary tree of height h contains 2h - 1nodes or less.
  • If we have a binary tree having n nodes, then the height of the tree is at most n and at least ceiling log2(n + 1).
  • If a binary tree contain n nodes at a level l then, it has at most 2n nodes at a level l+1
  • The total number of nodes in binary tree with depth d (root has depth zero) is

                       N = 20 + 21 + 22 + .......+ 2d = 2d+1 - 1


Related Discussions:- Binary trees

Graph, For the following graph find the adjacency matrix and adjacency list...

For the following graph find the adjacency matrix and adjacency list representation of the graph.

Explain merge sort, Merge sort: Merge sort is a sorting algorithm that ...

Merge sort: Merge sort is a sorting algorithm that uses the idea of split and conquers. This algorithm splits the array into two halves, sorts them separately and then merges t

Preorder traversal of a binary tree, Preorder traversal of a binary tree ...

Preorder traversal of a binary tree struct NODE { struct NODE *left; int value;     /* can take any data type */ struct NODE *right; };   preorder(struct N

Visual Basic Assignment, When writing a code for a program that basically a...

When writing a code for a program that basically answers Relative Velocity questions how do you go at it? How many conditions should you go through?

Techniques of representing polynomials using arrays, Q. Explain any three m...

Q. Explain any three methods or techniques of representing polynomials using arrays. Write which method is most efficient or effective for representing the following polynomials.

Queue, what''s queue ?

what''s queue ?

Explain the different types of traversal on binary tree, Question 1 What i...

Question 1 What is a data structure? Discuss briefly on types of data structures Question 2 Explain the insertion and deletion operation of linked list in detail Qu

Binary search, An unsorted array is searched through linear search that sca...

An unsorted array is searched through linear search that scans the array elements one by one until the wanted element is found. The cause for sorting an array is that we search

Compute the shortest paths to all network nodes, (i)  Consider a system usi...

(i)  Consider a system using flooding with hop counter. Suppose that the hop counter is originally set to the "diameter" (number of hops in the longest path without traversing any

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd