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Find the median array for Binary tree
  • Last Updated : 04 Jan, 2021

Prerequisite: Tree Traversals (Inorder, Preorder and Postorder), Median
Given a Binary tree having integral nodes, the task is to find the median for each position in the preorder, postorder and inorder traversal of the tree.
 

The median array is given as the array formed with the help of PreOrder, PostOrder, and Inorder traversal of a tree, such that 
med[i] = median(preorder[i], inorder[i], postorder[i])

Examples: 
 

Input: Tree =
               1
             /   \
            2     3
          /  \
         4    5 
Output: {4, 2, 4, 3, 3}
Explanation:
Preorder traversal = {1 2 4 5 3}
Inorder traversal =  {4 2 5 1 3}
Postorder traversal = {4 5 2 3 1}
median[0] = median(1, 4, 4) = 4
median[1] = median(2, 2, 5) = 2
median[2] = median(4, 5, 2) = 4
median[3] = median(5, 1, 3) = 3
median[4] = median(3, 3, 1) = 3
Hence, Median array = {4 2 4 3 3}

Input: Tree = 
               25
             /    \
           20      30
         /    \   /   \
       18     22 24   32 
Output: 18 20 20 24 30 30 32

 

Approach: 
 



  • First, find the preorder, postorder and inorder traversal of the given binary tree and store them each in a vector.
  • Now, for each position from 0 to N, insert the values at that position in each of the traversal arrays into a vector. The vector will be of 3N size.
  • Finally, sort this vector and the median for this position is given by the 2nd element. In this vector, it has 3N elements. Therefore after sorting, the median will be given by the middle element, the 2nd element, in every 3 elements.

Below is the implementation of the above approach:
 

CPP

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// C++ program to Obtain the median
// array for the preorder, postorder
// and inorder traversal of a binary tree
   
#include <bits/stdc++.h>
using namespace std;
   
// A binary tree node has data,
// a pointer to the left child
// and a pointer to the right child
struct Node {
    int data;
    struct Node *left, *right;
    Node(int data)
    {
        this->data = data;
        left = right = NULL;
    }
};
   
// Postorder traversal
void Postorder(
    struct Node* node,
    vector<int>& postorder)
{
    if (node == NULL)
        return;
   
    // First recur on left subtree
    Postorder(node->left, postorder);
   
    // then recur on right subtree
    Postorder(node->right, postorder);
   
    // now deal with the node
    postorder.push_back(node->data);
}
   
// Inorder traversal
void Inorder(
    struct Node* node,
    vector<int>& inorder)
{
    if (node == NULL)
        return;
   
    // First recur on left child
    Inorder(node->left, inorder);
   
    // then print the data of node
    inorder.push_back(node->data);
   
    // now recur on right child
    Inorder(node->right, inorder);
}
   
// Preorder traversal
void Preorder(
    struct Node* node,
    vector<int>& preorder)
{
    if (node == NULL)
        return;
   
    // First print data of node
    preorder.push_back(node->data);
   
    // then recur on left subtree
    Preorder(node->left, preorder);
   
    // now recur on right subtree
    Preorder(node->right, preorder);
}
   
// Function to print the any array
void PrintArray(vector<int> median)
{
    for (int i = 0;
         i < median.size(); i++)
        cout << median[i] << " ";
   
    return;
}
   
// Function to create and print
// the Median array
void MedianArray(struct Node* node)
{
    // Vector to store
    // the median values
    vector<int> median;
   
    if (node == NULL)
        return;
   
    vector<int> preorder,
        postorder,
        inorder;
   
    // Traverse the tree
    Postorder(node, postorder);
    Inorder(node, inorder);
    Preorder(node, preorder);
   
    int n = preorder.size();
    for (int i = 0; i < n; i++) {
   
        // Temporary vector to sort
        // the three values
        vector<int> temp;
   
        // Insert the values at ith index
        // for each traversal into temp
        temp.push_back(postorder[i]);
        temp.push_back(inorder[i]);
        temp.push_back(preorder[i]);
   
        // Sort the temp vector to
        // find the median
        sort(temp.begin(), temp.end());
   
        // Insert the middle value in
        // temp into the median vector
        median.push_back(temp[1]);
    }
   
    PrintArray(median);
    return;
}
   
// Driver Code
int main()
{
    struct Node* root = new Node(1);
    root->left = new Node(2);
    root->right = new Node(3);
    root->left->left = new Node(4);
    root->left->right = new Node(5);
   
    MedianArray(root);
   
    return 0;
}

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Java

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// Java program to Obtain the median
// array for the preorder, postorder
// and inorder traversal of a binary tree
import java.io.*;
import java.util.*;
 
// A binary tree node has data,
// a pointer to the left child
// and a pointer to the right child
class Node
{
  int data;
  Node left,right;
  Node(int item)
  {
    data = item;
    left = right = null;
  }
}
class Tree {
  public static Vector<Integer> postorder = new Vector<Integer>();
  public static Vector<Integer> inorder = new Vector<Integer>();
  public static Vector<Integer> preorder = new Vector<Integer>();
  public static Node root;
 
  // Postorder traversal
  public static void Postorder(Node node)
  {
    if(node == null)
    {
      return;
    }
 
    // First recur on left subtree
    Postorder(node.left);
 
    // then recur on right subtree
    Postorder(node.right);
 
    // now deal with the node
    postorder.add(node.data);
  }
  // Inorder traversal
  public static void Inorder(Node node)
  {
    if(node == null)
    {
      return;
    }
 
    // First recur on left child
    Inorder(node.left);
 
    // then print the data of node
    inorder.add(node.data);
 
    // now recur on right child
    Inorder(node.right);      
  }
 
  // Preorder traversal
  public static void Preorder(Node node)
  {
    if(node == null)
    {
      return;
    }
 
    // First print data of node
    preorder.add(node.data);
 
    // then recur on left subtree
    Preorder(node.left);
 
    // now recur on right subtree
    Preorder(node.right);
  }
 
  // Function to print the any array    
  public static void PrintArray(Vector<Integer> median)
  {
    for(int i = 0; i < median.size(); i++)
    {
      System.out.print(median.get(i) + " ");
    }
  }
 
  // Function to create and print
  // the Median array
  public static void MedianArray(Node node)
  {
 
    // Vector to store
    // the median values
    Vector<Integer> median = new Vector<Integer>();
    if(node == null)
    {
      return;
    }
 
    // Traverse the tree
    Postorder(node);
    Inorder(node);
    Preorder(node);
    int n = preorder.size();
    for(int i = 0; i < n; i++)
    {
 
      // Temporary vector to sort
      // the three values
      Vector<Integer> temp = new Vector<Integer>();
 
      // Insert the values at ith index
      // for each traversal into temp
      temp.add(postorder.get(i));
      temp.add(inorder.get(i));
      temp.add(preorder.get(i));
 
      // Sort the temp vector to
      // find the median
      Collections.sort(temp);
 
      // Insert the middle value in
      // temp into the median vector
      median.add(temp.get(1));
    }
    PrintArray(median);
  }
 
  // Driver Code
  public static void main (String[] args)
  {
    Tree.root = new Node(1);
    Tree.root.left = new Node(2);
    Tree.root.right = new Node(3);
    Tree.root.left.left = new Node(4);
    Tree.root.left.right = new Node(5);
    MedianArray(root);
  }
}
 
// This code is contributed by avanitrachhadiya2155

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Python3

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# Python3 program to Obtain the median
# array for the preorder, postorder
# and inorder traversal of a binary tree
 
 
# A binary tree node has data,
# a pointer to the left child
# and a pointer to the right child
class Node:
    def __init__(self, x):
        self.data = x
        self.left = None
        self.right = None
 
# Postorder traversal
def Postorder(node):
    global preorder
    if (node == None):
        return
    # First recur on left subtree
    Postorder(node.left)
 
    # then recur on right subtree
    Postorder(node.right)
 
    # now deal with the node
    postorder.append(node.data)
 
# Inorder traversal
def Inorder(node):
    global inorder
    if (node == None):
        return
 
    # First recur on left child
    Inorder(node.left)
 
    # then print the data of node
    inorder.append(node.data)
 
    # now recur on right child
    Inorder(node.right)
 
# Preorder traversal
def Preorder(node):
    global preorder
 
    if (node == None):
        return
 
    # First print data of node
    preorder.append(node.data)
 
    # then recur on left subtree
    Preorder(node.left)
 
    # now recur on right subtree
    Preorder(node.right)
 
# Function to print the any array
def PrintArray(median):
    for i in range(len(median)):
        print(median[i], end = " ")
 
    return
 
# Function to create and print
# the Median array
def MedianArray(node):
    global inorder, postorder, preorder
 
    # Vector to store
    # the median values
    median = []
 
    if (node == None):
        return
 
    # Traverse the tree
    Postorder(node)
    Inorder(node)
    Preorder(node)
 
    n = len(preorder)
 
    for i in range(n):
 
        # Temporary vector to sort
        # the three values
        temp = []
 
        # Insert the values at ith index
        # for each traversal into temp
        temp.append(postorder[i])
        temp.append(inorder[i])
        temp.append(preorder[i])
 
        # Sort the temp vector to
        # find the median
        temp = sorted(temp)
 
        # Insert the middle value in
        # temp into the median vector
        median.append(temp[1])
 
    PrintArray(median)
 
# Driver Code
if __name__ == '__main__':
    preorder, inorder, postorder = [], [], []
    root = Node(1)
    root.left = Node(2)
    root.right = Node(3)
    root.left.left = Node(4)
    root.left.right = Node(5)
 
    MedianArray(root)
 
# This code is contributed by mohit kumar 29

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Output: 

4 2 4 3 3

 

Time Complexity: O(N)
 

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