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Maximum height of the binary search tree created from the given array

  • Last Updated : 30 Jun, 2021

Given an array arr[] of N integers, the task is to make two binary search trees. One while traversing from the left side of the array and another while traversing from the right and find which tree has a greater height.
Examples: 
 

Input: arr[] = {2, 1, 3, 4}
Output: 0
BST starting from first index           BST starting from last index 
    2                                             4
   / \                                           /
  1   3                                         3
       \                                       /
        4                                     1
                                               \
                                                2

Input: arr[] = {1, 2, 6, 3, 5}
Output: 1

 

Prerequisites: Inserting a node in a Binary Search tree and Finding the height of a binary tree.
Approach: 
 

  • Create a binary search tree while inserting the nodes starting from the first element of the array till the last and find the height of this created tree say leftHeight.
  • Create another binary search tree while inserting the nodes starting from the last element of the array till the first and find the height of this created tree say rightHeight.
  • Print the maximum of these calculated heights i.e. max(leftHeight, rightHeight)

Below is the implementation of the above approach: 
 

C++




// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;
 
struct node {
    int key;
    struct node *left, *right;
};
 
// A utility function to create a new BST node
struct node* newNode(int item)
{
    struct node* temp = (struct node*)malloc(sizeof(struct node));
    temp->key = item;
    temp->left = temp->right = NULL;
    return temp;
}
 
/* A utility function to insert a new node with given key in BST */
struct node* insert(struct node* node, int key)
{
    /* If the tree is empty, return a new node */
    if (node == NULL)
        return newNode(key);
 
    /* Otherwise, recur down the tree */
    if (key < node->key)
        node->left = insert(node->left, key);
    else if (key > node->key)
        node->right = insert(node->right, key);
 
    /* return the (unchanged) node pointer */
    return node;
}
 
/* Compute the "maxDepth" of a tree -- the number of
    nodes along the longest path from the root node
    down to the farthest leaf node.*/
int maxDepth(node* node)
{
    if (node == NULL)
        return 0;
    else {
        /* compute the depth of each subtree */
        int lDepth = maxDepth(node->left);
        int rDepth = maxDepth(node->right);
 
        /* use the larger one */
        if (lDepth > rDepth)
            return (lDepth + 1);
        else
            return (rDepth + 1);
    }
}
 
// Function to return the maximum
// heights among the BSTs
int maxHeight(int a[], int n)
{
    // Create a BST starting from
    // the first element
    struct node* rootA = NULL;
    rootA = insert(rootA, a[0]);
    for (int i = 1; i < n; i++)
        insert(rootA, a[i]);
 
    // Create another BST starting
    // from the last element
    struct node* rootB = NULL;
    rootB = insert(rootB, a[n - 1]);
    for (int i = n - 2; i >= 0; i--)
        insert(rootB, a[i]);
 
    // Find the heights of both the trees
    int A = maxDepth(rootA) - 1;
    int B = maxDepth(rootB) - 1;
 
    return max(A, B);
}
 
// Driver code
int main()
{
    int a[] = { 2, 1, 3, 4 };
    int n = sizeof(a) / sizeof(a[0]);
 
    cout << maxHeight(a, n);
 
    return 0;
}

Java




// Java implementation of the approach
class GFG
{
 
static class node
{
    int key;
    node left, right;
};
 
// A utility function to create a new BST node
static node newNode(int item)
{
    node temp = new node();
    temp.key = item;
    temp.left = temp.right = null;
    return temp;
}
 
/* A utility function to insert
a new node with given key in BST */
static node insert(node node, int key)
{
    /* If the tree is empty,
    return a new node */
    if (node == null)
        return newNode(key);
 
    /* Otherwise, recur down the tree */
    if (key < node.key)
        node.left = insert(node.left, key);
    else if (key > node.key)
        node.right = insert(node.right, key);
 
    /* return the (unchanged) node pointer */
    return node;
}
 
/* Compute the "maxDepth" of a tree --
the number of nodes along the longest path
from the root node down to the farthest leaf node.*/
static int maxDepth(node node)
{
    if (node == null)
        return 0;
    else
    {
         
        /* compute the depth of each subtree */
        int lDepth = maxDepth(node.left);
        int rDepth = maxDepth(node.right);
 
        /* use the larger one */
        if (lDepth > rDepth)
            return (lDepth + 1);
        else
            return (rDepth + 1);
    }
}
 
// Function to return the maximum
// heights among the BSTs
static int maxHeight(int a[], int n)
{
    // Create a BST starting from
    // the first element
    node rootA = null;
    rootA = insert(rootA, a[0]);
    for (int i = 1; i < n; i++)
        rootA = insert(rootA, a[i]);
 
    // Create another BST starting
    // from the last element
    node rootB = null;
    rootB = insert(rootB, a[n - 1]);
    for (int i = n - 2; i >= 0; i--)
        rootB =insert(rootB, a[i]);
 
    // Find the heights of both the trees
    int A = maxDepth(rootA) - 1;
    int B = maxDepth(rootB) - 1;
 
    return Math.max(A, B);
}
 
// Driver code
public static void main(String args[])
{
    int a[] = { 2, 1, 3, 4 };
    int n = a.length;
 
    System.out.println(maxHeight(a, n));
}
}
 
// This code is contributed by Arnab Kundu

Python3




# Python implementation of the approach
 
class Node:
    def __init__(self, key):
        self.key = key
        self.left = None
        self.right = None
 
# A utility function to insert
# a new node with given key in BST */
def insert(node: Node, key: int) -> Node:
 
    # If the tree is empty,
    # return a new node */
    if node is None:
        return Node(key)
    # Otherwise, recur down the tree
    if key < node.key:
        node.left = insert(node.left, key)
    elif key > node.key:
        node.right = insert(node.right, key)
 
    # return the (unchanged) node pointer
    return node
 
# Compute the "maxDepth" of a tree --
# the number of nodes along the longest path
# from the root node down to the farthest leaf node.*/
def maxDepth(node: Node) -> int:
    if node is None:
        return 0
    else:
 
        # compute the depth of each subtree
        lDepth = maxDepth(node.left)
        rDepth = maxDepth(node.right)
 
        # use the larger one
        if lDepth > rDepth:
            return lDepth + 1
        else:
            return rDepth + 1
 
# Function to return the maximum
# heights among the BSTs
def maxHeight(a: list, n: int) -> int:
 
    # Create a BST starting from
    # the first element
    rootA = Node(a[0])
    for i in range(1, n):
        rootA = insert(rootA, a[i])
 
    # Create another BST starting
    # from the last element
    rootB = Node(a[n - 1])
    for i in range(n - 2, -1, -1):
        rootB = insert(rootB, a[i])
 
    # Find the heights of both the trees
    A = maxDepth(rootA) - 1
    B = maxDepth(rootB) - 1
 
    return max(A, B)
 
# Driver Code
if __name__ == "__main__":
    a = [2, 1, 3, 4]
    n = len(a)
 
    print(maxHeight(a, n))
 
# This code is contributed by
# sanjeev2552

C#




// C# implementation of the approach
using System;
 
class GFG
{
    public class node
    {
        public int key;
        public node left, right;
    };
     
    // A utility function to create a new BST node
    static node newNode(int item)
    {
        node temp = new node();
        temp.key = item;
        temp.left = temp.right = null;
        return temp;
    }
     
    /* A utility function to insert
    a new node with given key in BST */
    static node insert(node node, int key)
    {
        /* If the tree is empty,
        return a new node */
        if (node == null)
            return newNode(key);
     
        /* Otherwise, recur down the tree */
        if (key < node.key)
            node.left = insert(node.left, key);
        else if (key > node.key)
            node.right = insert(node.right, key);
     
        /* return the (unchanged) node pointer */
        return node;
    }
     
    /* Compute the "maxDepth" of a tree --
    the number of nodes along the longest path
    from the root node down to the farthest leaf node.*/
    static int maxDepth(node node)
    {
        if (node == null)
            return 0;
        else
        {
             
            /* compute the depth of each subtree */
            int lDepth = maxDepth(node.left);
            int rDepth = maxDepth(node.right);
     
            /* use the larger one */
            if (lDepth > rDepth)
                return (lDepth + 1);
            else
                return (rDepth + 1);
        }
    }
     
    // Function to return the maximum
    // heights among the BSTs
    static int maxHeight(int []a, int n)
    {
        // Create a BST starting from
        // the first element
        node rootA = null;
        rootA = insert(rootA, a[0]);
        for (int i = 1; i < n; i++)
            rootA = insert(rootA, a[i]);
     
        // Create another BST starting
        // from the last element
        node rootB = null;
        rootB = insert(rootB, a[n - 1]);
        for (int i = n - 2; i >= 0; i--)
            rootB =insert(rootB, a[i]);
     
        // Find the heights of both the trees
        int A = maxDepth(rootA) - 1;
        int B = maxDepth(rootB) - 1;
     
        return Math.Max(A, B);
    }
     
    // Driver code
    public static void Main()
    {
        int []a = { 2, 1, 3, 4 };
        int n = a.Length;
     
        Console.WriteLine(maxHeight(a, n));
    }
}
 
// This code is contributed by AnkitRai01

Javascript




<script>
 
 
// Javascript implementation of the approach
class node
{
    constructor()
    {
        this.key = 0;
        this.left = null;
        this.right = null;
    }
};
 
// A utility function to create a new BST node
function newNode(item)
{
    var temp = new node();
    temp.key = item;
    temp.left = temp.right = null;
    return temp;
}
 
/* A utility function to insert
a new node with given key in BST */
function insert(node, key)
{
    /* If the tree is empty,
    return a new node */
    if (node == null)
        return newNode(key);
 
    /* Otherwise, recur down the tree */
    if (key < node.key)
        node.left = insert(node.left, key);
    else if (key > node.key)
        node.right = insert(node.right, key);
 
    /* return the (unchanged) node pointer */
    return node;
}
 
/* Compute the "maxDepth" of a tree --
the number of nodes along the longest path
from the root node down to the farthest leaf node.*/
function maxDepth(node)
{
    if (node == null)
        return 0;
    else
    {
         
        /* compute the depth of each subtree */
        var lDepth = maxDepth(node.left);
        var rDepth = maxDepth(node.right);
 
        /* use the larger one */
        if (lDepth > rDepth)
            return (lDepth + 1);
        else
            return (rDepth + 1);
    }
}
 
// Function to return the maximum
// heights among the BSTs
function maxHeight(a, n)
{
    // Create a BST starting from
    // the first element
    var rootA = null;
    rootA = insert(rootA, a[0]);
    for (var i = 1; i < n; i++)
        rootA = insert(rootA, a[i]);
 
    // Create another BST starting
    // from the last element
    var rootB = null;
    rootB = insert(rootB, a[n - 1]);
    for (var i = n - 2; i >= 0; i--)
        rootB =insert(rootB, a[i]);
 
    // Find the heights of both the trees
    var A = maxDepth(rootA) - 1;
    var B = maxDepth(rootB) - 1;
 
    return Math.max(A, B);
}
 
// Driver code
var a = [2, 1, 3, 4];
var n = a.length;
document.write(maxHeight(a, n));
 
// This code is contributed by rrrtnx.
</script>
Output: 
3

 


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