Construct Tree From Given Postorder And Preorder Traversal In C++

March 17, 2023

Construct Tree From Given Postorder And Preorder Traversal in C++

There are three types of traversals in a tree: Inorder, Preorder and Postorder Traversal. In this article, a tree is constructed using postorder and preorder traversal. In this article , we will learn about how to construct tree from given postorder and preorder traversal in C++.

Algorithm For PreOrder Traversal:

Print the node.
Traverse the left subtree.
Traverse the right subtree.

Algorithm For PostOrder Traversal:

Traverse the left subtree.
Traverse the right subtree.
Print the node.

Algorithm:

Take the first element of preorder traversal and increase the count.
Find the index of the next element in the postorder traversal.
All the elements to the left including this element will be in the left subtree and other elements in the right subtree.
Recursively call for the right subtree too.
Repeat until array is traversed.

Depth First Traversals

Level Order Traversal

Construct Tree from given Inorder and Preorder traversals

Construct Tree from given Postorder and Inorder traversals

Find size of the Binary tree

Code Implementation for constructing tree from postorder and preorder traversals in C++

Run

#include<bits/stdc++.h> 
using namespace std;
class Tree
{
public:
  int data;
  Tree *left = NULL, *right = NULL;
    Tree (int x)
  {
    data = x;
    left = NULL;
    right = NULL;
  }
};
int search (int postorder[], int start, int end, int element)
{
  int i;
  for (i = start; i <= end; i++)
    {
      if (postorder[i] == element)
	{
	  return i;
	}
    }
  return i;
}

void print_postorder (Tree * root)
{
  if (root == NULL)
    return;
  print_postorder (root->left);
  print_postorder (root->right);
  cout << root->data << " ";
}

Tree *build_tree (int preorder[], int postorder[], int presi, int preei, int postsi,int postei)
{
  if (presi > preei)
    {
      return NULL;
    }
  Tree *curr_node = new Tree (preorder[presi]);
  int x = curr_node->data;
  if (presi == preei)
    return curr_node;
  int search_index = search (postorder, postsi, postei, preorder[presi + 1]);
  int elements = search_index - postsi + 1;
  curr_node->left =
    build_tree (preorder, postorder, presi + 1, presi + elements, postsi,
		search_index);
  curr_node->right =
    build_tree (preorder, postorder, presi + elements + 1, preei,
		search_index + 1, postei - 1);

  return curr_node;
}

int main ()
{
  int preorder[] = { 10, 20, 40, 60, 70, 50, 30 };
  int postorder[] = { 60, 70, 40, 50, 20, 30, 10 };
  Tree *root = build_tree (preorder, postorder, 0, 6, 0, 6);
  cout << "Postorder traversal\n";
  print_postorder (root);
  return 0;
}

Output:

Postorder traversal
60 70 40 50 20 30 10

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Introduction to Trees

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Inorder Postorder PreOrder Traversals Examples
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- Preorder Tree Traversal in Binary Tree : C | C++ | Java
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Construct Tree from given Inorder and Preorder traversals – C | C++ | Java
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