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

Explain about the structured types - built-in types, Explain about the Stru...

Explain about the Structured types - Built-In Types Values of the carrier set are not atomic, consisting rather than several atomic values arranged in some way. Common illu

Depth first search and breadth first search, Q. Illustrate the result of ru...

Q. Illustrate the result of running BFS and DFS on the directed graph given below using vertex 3 as source.  Show the status of the data structure used at each and every stage.

Matrix stored in memory, Method to measure address of any element of a matr...

Method to measure address of any element of a matrix stored in memory. Let us consider 2 dimensional array a of size m*n further consider that the lower bound for the row index

Explain memory allocation strategies, Memory Allocation Strategies If i...

Memory Allocation Strategies If it is not desirable to move blocks of due storage from one area of memory to another, it must be possible to relocate memory blocks that have be

Explain the prim''s minimum spanning tree algorithm, Question 1. Explai...

Question 1. Explain the different types of traversal on binary tree 2. Explain the Prim's minimum spanning tree algorithm 3. Differentiate fixed and variable storage allo

Enumerate the types in ruby, Enumerate the Types in Ruby Ruby is a pure...

Enumerate the Types in Ruby Ruby is a pure object-oriented language, meaning that all types in Ruby are classes, and each value in a Ruby program is an instance of a class. Thi

#titlestrings, given the string "Data Structures & , Algorithms", write a p...

given the string "Data Structures & , Algorithms", write a program that uses sequential search to return index of ''&''

Full binary trees, Full Binary Trees: A binary tree of height h that had 2...

Full Binary Trees: A binary tree of height h that had 2h -1 elements is called a Full Binary Tree. Complete Binary Trees: A binary tree whereby if the height is d, and all of

Define binary tree, Define Binary Tree  A binary tree T is explained as...

Define Binary Tree  A binary tree T is explained as a finite set of nodes that is either empty or having of root and two disjoint binary trees TL, and TR known as, respectively

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