Construct Tree from given Postorder and Preorder traversals

March 28, 2023

Construct Tree from given Postorder and Preorder traversal

There are three types of traversals in a tree: Inorder, Preorder and Postorder Traversal. In this article we will discuss how to construct tree from given postorder and preorder traversal .

Preorder Traversal – We first print the node,then move to the left subtree and finally to the right subtree.
Postorder Traversal – Left and right subtree is visited first and then the node is printed
Here, we construct Tree from given Postorder and Preorder traversal

Tree From Given Postorder and Preorder Traversal

Given traversals:
Preorder: 50, 25, 12, 37, 30, 40, 75, 62, 60, 70, 87
Postorder: 12, 30, 40, 37, 25, 60, 70, 62, 87, 75, 50

The first element in the preorder traversal is the root of the tree.
So, here 50 will be the root of the tree.
We will find the index of element next to 50 i.e 25 in the postorder traversal.The index found is 4. Let this index is denoted by ‘pos’.
All the elements to the left of this index and element at this index( i.e from 0 to 4 index) will be in the left subtree of 50.
And all the elements to the right of this index ( from 6 to 10) will be in the right subtree of 50.

Construct Tree from given Inorder and Preorder traversals

Construct Tree from given Postorder and Inorder traversals

Find size of the Binary tree

Find the height of binary tree

Find maximum in binary tree

Now, we will divide preorder and postorder array in two parts.
One is for the left subtree and other is for the right subtree.

Let

presi: starting index for preorder array
preei: ending index for preorder array
postsi: starting index of postorder array
postei: ending index of postorder array
clc: Number of elements in the left subtree

Clearly, clc= pos – postsi + 1;

For left subtree:
Preorder array: from index presi + 1, presi + clc
Postorder array: from index postsi, pos.

For right subtree:
Preorder array: from index presi + clc + 1, preei
Postorder array: from index pos + 1, postei -1

Using the above arrays, all the steps are recursively repeated.

Java Program to Construct Tree from given Postorder and Preorder Traversals

Run

import java.util.*;

public class Main
{

// Binary tree class
  public static class BinaryTree
  {
// Node class
    public class Node
    {

      int data;
      Node left;
      Node right;

      public Node (int data)
      {
	this.data = data;
	this.left = null;
	this.right = null;
      }
    }

    private Node root;
    private int size;

    public BinaryTree (int[]pre, int[]post)
    {
      this.root =
	this.construct (pre, 0, pre.length-1, post, 0, post.length-1);

    }

    private Node construct (int[]pre, int presi, int preei, int[]post,
			    int postsi, int postei)
    {

// this case occurs when a node has only one child
      if (presi > preei)
	{
	  return null;
	}

      Node node = new Node (pre[presi]);
      node.left = null;
      node.right = null;
      this.size++;

      if (presi == preei)
	{
	  return node;
	}

//Searching pre[presi + 1] in postorder array
      int pos = -1;
      for (int i = postsi; i <= postei; i++)
	{
	  if (post[i] == pre[presi + 1])
	    {
	      pos = i;
	      break;
	    }
	}

//Number of elements in left subtree
      int clc = pos-postsi + 1;

//Left subtree
      node.left =
	this.construct (pre, presi + 1, presi + clc, post, postsi, pos);

//Right subtree
      node.right =
	this.construct (pre, presi + clc + 1, preei, post, pos + 1,
			postei-1);

      return node;

    }

// Postorder tree traversal
    public void inOrder ()
    {
      inOrder (this.root);
    }

    private void inOrder (Node node)
    {
      if (node == null)
	{
	  return;
	}

      System.out.print (node.data + " ");
      inOrder (node.left);
      inOrder (node.right);
      
    }
  }

  public static void main (String[]args) throws Exception
  {

// Construct binary tree

    int[] pre = { 50, 25, 12, 37, 30, 40, 75, 62, 60, 70, 87 };
    int[] post = { 12, 30, 40, 37, 25, 60, 70, 62, 87, 75, 50 };

    BinaryTree bt = new BinaryTree (pre, post);
    System.out.println("The new tree constructed is : ");
    bt.inOrder ();

  }
}

Output:

Inorder traversal of the constructed tree: 
50 25 12 37 30 40 75 62 60 70 87

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