Data Structures and Algorithms (Some Questions for You - Answer to Question 2) - Tirthankar Pal - MBA from IIT Kharagpur, GATE, GMAT, IIT Written Test, Interview were a part of MBA Entrance, B.S. in Computer Science from NIELIT

With the help of an example, explain how a binary tree can be represented using an array.

Given an array that represents a tree in such a way that array indexes are values in tree nodes and array values give the parent node of that particular index (or node). The value of the root node index would always be -1 as there is no parent for root. Construct the standard linked representation of given Binary Tree from this given representation. 

Ways to represent: 

Trees can be represented in two ways as listed below:

1. Dynamic Node Representation (Linked Representation).
2. Array Representation (Sequential Representation).

Now, we are going to talk about the sequential representation of the trees.  In order to represent a tree using an array, the numbering of nodes can start either from 0–(n-1) or 1– n, consider the below illustration as follows:

Illustration:

       A(0)    
     /   \
    B(1)  C(2)  
  /   \      \
 D(3)  E(4)   F(6) 
OR,
      A(1)    
     /   \
    B(2)  C(3)  
  /   \      \
 D(4)  E(5)   F(7)  

Procedure:

Note: father, left_son and right_son are the values of indices of the array.

 Case 1: (0—n-1) 

if (say)father=p; 
then left_son=(2*p)+1; 
and right_son=(2*p)+2;

Case 2: 1—n

if (say)father=p; 
then left_son=(2*p); 
and right_son=(2*p)+1; 

Implementation:

• C++
• Java
• C#
• Python3

// C++ implementation of tree using array // numbering starting from 0 to n-1. #include<bits/stdc++.h> using namespace std; char tree[10]; int root(char key) {   if (tree[0] != '\0')     cout << "Tree already had root";   else     tree[0] = key;   return 0; }   int set_left(char key, int parent) {   if (tree[parent] == '\0')     cout << "\nCan't set child at "     << (parent * 2) + 1     << " , no parent found";   else     tree[(parent * 2) + 1] = key;   return 0; }   int set_right(char key, int parent) {   if (tree[parent] == '\0')     cout << "\nCan't set child at "     << (parent * 2) + 2     << " , no parent found";   else     tree[(parent * 2) + 2] = key;   return 0; }   int print_tree() {   cout << "\n";   for (int i = 0; i < 10; i++) {     if (tree[i] != '\0')       cout << tree[i];     else       cout << "-";   }   return 0; }   // Driver Code int main() {   root('A');   set_left('B',0);   set_right('C', 0);   set_left('D', 1);   set_right('E', 1);   set_right('F', 2);   print_tree();   return 0; }

Output

Can't set child at 3 , no parent found
Can't set child at 4 , no parent found
A-C---F---

Time complexity: O(log n) since using heap to create a binary tree
Space complexity: O(n) for array

Tirthankar Pal

MBA from IIT Kharagpur with GATE, GMAT, IIT Kharagpur Written Test, and Interview
2 year PGDM (E-Business) from Welingkar, Mumbai
4 years of Bachelor of Science (Hons) in Computer Science from the National Institute of Electronics and Information Technology
Google and Hubspot Certification
Brain Bench Certification in C++, VC++, Data Structure and Project Management
10 years of Experience in Software Development out of that 6 years 8 months in Wipro
Selected in Six World Class UK Universities:-
King's College London, Durham University, University of Exeter, University of Sheffield, University of Newcastle, University of Leeds