Construct A Binary Tree From Inorder And Postorder Traversals

May 27, 2021

Construct A Binary Tree From Inorder And Postorder Traversal

Suppose we have a inorder and postorder sequence of a binary tree . We have to generate tree from these sequences. In this article we will see if the inorder and postorder sequence is [10 30 40 50 60 70 90 ] and [10 40 30 60 90 70 50] , then the tree will be – 

Binary Tree

Example to construct a Binary Tree from Inorder And Postorder Traversal

Example of Binary Tree from inorder and postorder traversal

Let us see the process of constructing tree :-

 inorder =  [ 10 30 40 50 60 70 90]

 postorder= [ 10 40 30 60 90 70 50 ]

  1. We first find the last node in postorder []. The last node is 50 , we know this value is root as root always appear in the end of postorder traversal.
  2. we search 50 in inorder [] to find left and right subtrees of root. Everything on left of 50 in inorder [] is in left subtree and everything on right is in right subtree. 
  3.  Recur the above process for following two.                                                                                                                                                                                             a) Recur for inorder[]=[ 10 30 40 ] and postorder = [ 10 40 30 ] . And make the created tree as left child of root.                                                                       b) Recur for inorder = [ 60 70 90 ] and postorder [ 60 90 70]. And make the created tree as right child of root. 
Process for constructing a binary tree using inorder and postorder

CODE FOR CONSTRUCTING A BINARY TREE IN JAVA 

import java.util.*;
/*Representing Node of the Binary Tree */
class Node
{
    int value;
    Node left,right;
    //constructor 
    Node(int value)
    {
        this.value=value;
        left=right=null;
    }
}
class BinaryTree
{
    Node root;
    BinaryTree()
    {
        root=null;
    }
    /*inorder traversal of binary tree */
    public void inorder(Node ptr)
    {
        if(ptr==null)
            return ;
        /*first traverse left child */
        inorder(ptr.left);
        /*then print the value of node */
        System.out.print(ptr.value+" ");
        /* now traverse the right child */
        inorder(ptr.right);
    }
    /*preorder traversal of binary tree */  
    public  void preorder(Node ptr)
    {
        if(ptr==null)
            return ;
        /*first print the value of node*/  
        System.out.print(ptr.value+" ");
        /*then traverse the left child */
        preorder(ptr.left);
        /*now traverse the right child*/
        preorder(ptr.right);
    }
    /*postorder traversal of binary tree */
    public  void postorder(Node ptr)
    {
        if(ptr==null)
        return ;
        /*first traverse left child*/   
        postorder(ptr.left);
        /*then traverse the right child*/
        postorder(ptr.right);
        /*now print the value of node*/
        System.out.print(ptr.value+" ");
    }
    //function to find index of values in inArr[start....end]
    int search(int arr[],int start,int end,int value)
    {
        int i;
        for( i=start;i<=end;i++)
           if(arr[i]==value)
             break;
    return i;
    } 
    Node createTree(int inArr[],int postArr[],int inStart,int inEnd,int postStart,int postEnd)
    {
        if(inEnd<inStart)
            return null;
        //Take the last node of postorder
        Node ptr=new Node(postArr[postEnd]);
        //if it has no child then simply returns
        if(inEnd==inStart)
            return ptr;
        int index=search(inArr,inStart,inEnd,ptr.value);
        /*create left and right subtree*/
        ptr.left=createTree(inArr,postArr,inStart,index-1,postStart,postStart-inStart+index-1);
        ptr.right=createTree(inArr,postArr,index+1,inEnd,postEnd-inEnd+index,postEnd-1);
        return ptr;
    }
    public static void main(String[] args)
    {
        BinaryTree tree=new BinaryTree();
        int inorder[]={10,30,40,50,60,70,90};  //given inorder of a binary tree
        int postorder[]={10,40,30,60,90,70,50}; //given postorder of a binarytree
        int length=inorder.length;
        tree.root=tree.createTree(inorder,postorder,0,length-1,0,length-1);
        System.out.println("Inorder of the tree:");
        tree.inorder(tree.root);
        System.out.println();
        System.out.println("Preorder of the tree");
        tree.preorder(tree.root);
        System.out.println();
        System.out.println("Postorder of the tree");
        tree.postorder(tree.root);
    }
}

 

Output:

Inorder of the tree:
10 30 40 50 60 70 90
Preorder of the tree
50 30 10 40 70 60 90
Postorder of the tree
10 40 30 60 90 70 50

Time Complexity For constructing A Binary Tree

Time Complexity :

O(n²)