Construct Tree from given Postorder and Preorder traversal in C

March 9, 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

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.

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

Code in C to Construct Tree from given Postorder and Preorder Traversals

Run

#include <stdio.h>
#include<stdlib.h>
struct node
{
  int data;
  struct node *left;
  struct node *right;
};

struct node *newNode (int data)
{
  struct node *temp = (struct node *) malloc (sizeof (struct node));

  temp->data = data;
  temp->left = temp->right = NULL;

  return temp;
}

struct node *
constructTreeUtil (int pre[], int post[], int *preIndex, int l, int h,
		   int size)
{
  if (*preIndex >= size || l > h)
    return NULL;

  struct node *root = newNode (pre[*preIndex]);
  ++*preIndex;

  if (l == h)
    return root;
  int i;
  for (i = l; i <= h; ++i)
    if (pre[*preIndex] == post[i])
      break;

  if (i <= h)
    {
      root->left = constructTreeUtil (pre, post, preIndex, l, i, size);
      root->right =
	constructTreeUtil (pre, post, preIndex, i + 1, h - 1, size);
    }

  return root;
}

struct node *constructTree (int pre[], int post[], int size)
{
  int preIndex = 0;
  return constructTreeUtil (pre, post, &preIndex, 0, size - 1, size);
}

void printInorder (struct node *node)
{
  if (node == NULL)
    return;
  printInorder (node->left);
  printf ("%d ", node->data);
  printInorder (node->right);
}

int main ()
{
  int pre[] = { 10, 20, 40, 80, 90, 50, 30, 60, 70 };
  int post[] = { 80, 90, 40, 50, 20, 60, 70, 30, 10 };
  int size = sizeof (pre) / sizeof (pre[0]);

  struct node *root = constructTree (pre, post, size);

  printf ("Inorder traversal of the constructed tree: \n");
  printInorder (root);

  return 0;
}

Output:

Inorder traversal of the constructed tree:
80 40 90 20 50 10 60 30 70

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