Maximum absolute difference between the sibling nodes of given BST

Given a BST (Binary Search Tree) with N Nodes, the task is to find the maximum absolute difference between the sibling nodes.

Two nodes are said to be siblings if they are present at the same level, and their parents are the same.]

Examples:

Input:

Diagram 1 for Ex-1

Output: 70
Explanation:
105 – 50 = 55 (As 105 and 50 nodes are siblings)
75 – 5 = 70 (As 75 and 5 nodes are siblings)
106 – 101 = 5 (As 106 and 5 nodes are siblings)
Other than these, there is no other pair of nodes that are siblings.
So among them the max difference is 70. (75 – 5 = 70)

Input: 

Diagram 2 for Ex-2

Output: 60
Explanation:
120 – 60 = 60
90 – 45 =  45
160 – 110 = 50 
Other than these, there is no other pair of nodes that are siblings.
So among them the max difference is 60. (120 – 60 = 60)

Approach:

The basic Idea is to check whether the nodes are siblings or not if sibling then find out the maximum difference.

Follow the steps mentioned below to implement the idea:

• Iterate the BST in the preorder fashion. Root Left Right.
• At every point,
  • Check if the left and right children are available.
  • If both are available, then calculate the difference between the right and left values. (By default BST right val > left val)
  • Maximize the absolute maximum difference.
  • Else just continue the traversal.
• After the traversal ends, return the maximum difference between the sibling nodes.

Below is the Implementation of the above approach:

C++

// C++ code to implement the approach

#include <bits/stdc++.h>
using namespace std;

// Structure of a BST node
struct TreeNode {
    int val;
    struct TreeNode *left, *right;
};

// Function to form a new node
TreeNode* newNode(int data)
{
    TreeNode* temp = new TreeNode;

    temp->val = data;

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

    return temp;
}

// Function to insert a new node to the BST
TreeNode* insert(TreeNode* root, int val)
{
    TreeNode* newnode = newNode(val);
    TreeNode* x = root;
    TreeNode* y = NULL;

    while (x != NULL) {
        y = x;
        if (val < x->val)
            x = x->left;
        else
            x = x->right;
    }

    if (y == NULL)
        y = newnode;

    else if (val < y->val)
        y->left = newnode;

    else
        y->right = newnode;

    return y;
}

// Function to find the maximum absolute difference
void findMaxDiff(TreeNode* root, int& max_diff)
{
    if (root == NULL) {
        return;
    }

    int lval, rval;

    // Only when both siblings are there
    if (root->left != NULL && root->right != NULL) {
        lval = root->left->val;
        rval = root->right->val;
        max_diff = max(max_diff, rval - lval);
    }

    findMaxDiff(root->left, max_diff);
    findMaxDiff(root->right, max_diff);
}

// Driver code
int main()
{
    TreeNode* root = NULL;
    TreeNode* root2 = NULL;

    // Structure of first tree
    root = insert(root, 100);
    insert(root, 50);
    insert(root, 105);
    insert(root, 75);
    insert(root, 5);
    insert(root, 101);
    insert(root, 106);

    // Structure of second tree
    root2 = insert(root2, 100);
    insert(root2, 60);
    insert(root2, 120);
    insert(root2, 45);
    insert(root2, 90);
    insert(root2, 110);
    insert(root2, 160);

    int max_diff = INT_MIN;
    int max_diff2 = INT_MIN;

    findMaxDiff(root, max_diff);
    cout << max_diff << "\n";

    findMaxDiff(root2, max_diff2);
    cout << max_diff2 << "\n";

    return 0;
}

Java

// java code implementation
import java.util.Scanner;

class TreeNode {
    int val;
    TreeNode left, right;

    TreeNode(int val)
    {
        this.val = val;
        this.left = null;
        this.right = null;
    }
}

class GFG {
    // Function to form a new node
    public static TreeNode newNode(int data)
    {
        TreeNode temp = new TreeNode(data);

        return temp;
    }

    // Function to insert a new node to the BST
    public static TreeNode insert(TreeNode root, int val)
    {
        TreeNode newnode = newNode(val);
        TreeNode x = root;
        TreeNode y = null;

        while (x != null) {
            y = x;
            if (val < x.val)
                x = x.left;
            else
                x = x.right;
        }

        if (y == null)
            y = newnode;

        else if (val < y.val)
            y.left = newnode;

        else
            y.right = newnode;

        return y;
    }

    // Function to find the maximum absolute difference
    public static void findMaxDiff(TreeNode root,
                                   int[] max_diff)
    {
        if (root == null) {
            return;
        }

        int lval, rval;

        // Only when both siblings are there
        if (root.left != null && root.right != null) {
            lval = root.left.val;
            rval = root.right.val;
            max_diff[0]
                = Math.max(max_diff[0], rval - lval);
        }

        findMaxDiff(root.left, max_diff);
        findMaxDiff(root.right, max_diff);
    }

    // Driver code
    public static void main(String[] args)
    {
        TreeNode root = null;
        TreeNode root2 = null;

        // Structure of first tree
        root = insert(root, 100);
        insert(root, 50);
        insert(root, 105);
        insert(root, 75);
        insert(root, 5);
        insert(root, 101);
        insert(root, 106);

        // Structure of second tree
        root2 = insert(root2, 100);
        insert(root2, 60);
        insert(root2, 120);
        insert(root2, 45);
        insert(root2, 90);
        insert(root2, 110);
        insert(root2, 160);

        int[] max_diff = { Integer.MIN_VALUE };
        int[] max_diff2 = { Integer.MIN_VALUE };

        findMaxDiff(root, max_diff);
        System.out.println(max_diff[0]);

        findMaxDiff(root2, max_diff2);
        System.out.println(max_diff2[0]);
    }
}

// This code is contributed by ksam24000

Python3

# Python code implementation
class TreeNode:
    def __init__(self, val):
        self.val = val
        self.left = None
        self.right = None

# Function to form a new node
def newNode(data):
    temp = TreeNode(data)
    return temp

# Function to insert a new node to the BST
def insert(root, val):
    newnode = newNode(val)
    x = root
    y = None
    while x is not None:
        y = x
        if val < x.val:
            x = x.left
        else:
            x = x.right
    if y is None:
        y = newnode
    elif val < y.val:
        y.left = newnode
    else:
        y.right = newnode
    return y

# Function to find the maximum absolute difference
def findMaxDiff(root, max_diff):
    if root is None:
        return
    lval, rval = None, None

    # Only when both siblings are there
    if root.left is not None and root.right is not None:
        lval = root.left.val
        rval = root.right.val
        max_diff[0] = max(max_diff[0], rval - lval)
    findMaxDiff(root.left, max_diff)
    findMaxDiff(root.right, max_diff)


root = None
root2 = None

# Structure of first tree
root = insert(root, 100)
insert(root, 50)
insert(root, 105)
insert(root, 75)
insert(root, 5)
insert(root, 101)
insert(root, 106)

# Structure of second tree
root2 = insert(root2, 100)
insert(root2, 60)
insert(root2, 120)
insert(root2, 45)
insert(root2, 90)
insert(root2, 110)
insert(root2, 160)

max_diff = [float("-inf")]
max_diff2 = [float("-inf")]

findMaxDiff(root, max_diff)
print(max_diff[0])

findMaxDiff(root2, max_diff2)
print(max_diff2[0])

# This code is contributed by lokesh.

C#

// C# code implementation

using System;

class TreeNode {
  public int val;
  public TreeNode left, right;

  public TreeNode(int val)
  {
    this.val = val;
    this.left = null;
    this.right = null;
  }
}

public class GFG {

  // Function to form a new node
  static TreeNode newNode(int data)
  {
    TreeNode temp = new TreeNode(data);

    return temp;
  }

  // Function to insert a new node to the BST
  static TreeNode insert(TreeNode root, int val)
  {
    TreeNode newnode = newNode(val);
    TreeNode x = root;
    TreeNode y = null;

    while (x != null) {
      y = x;
      if (val < x.val)
        x = x.left;
      else
        x = x.right;
    }

    if (y == null)
      y = newnode;

    else if (val < y.val)
      y.left = newnode;

    else
      y.right = newnode;

    return y;
  }

  // Function to find the maximum absolute difference
  static void findMaxDiff(TreeNode root, int[] max_diff)
  {
    if (root == null) {
      return;
    }

    int lval, rval;

    // Only when both siblings are there
    if (root.left != null && root.right != null) {
      lval = root.left.val;
      rval = root.right.val;
      max_diff[0]
        = Math.Max(max_diff[0], rval - lval);
    }

    findMaxDiff(root.left, max_diff);
    findMaxDiff(root.right, max_diff);
  }

  static public void Main()
  {

    // Code
    TreeNode root = null;
    TreeNode root2 = null;

    // Structure of first tree
    root = insert(root, 100);
    insert(root, 50);
    insert(root, 105);
    insert(root, 75);
    insert(root, 5);
    insert(root, 101);
    insert(root, 106);

    // Structure of second tree
    root2 = insert(root2, 100);
    insert(root2, 60);
    insert(root2, 120);
    insert(root2, 45);
    insert(root2, 90);
    insert(root2, 110);
    insert(root2, 160);

    int[] max_diff = { Int32.MinValue };
    int[] max_diff2 = { Int32.MinValue };

    findMaxDiff(root, max_diff);
    Console.WriteLine(max_diff[0]);

    findMaxDiff(root2, max_diff2);
    Console.WriteLine(max_diff2[0]);
  }
}

// This code is contributed by lokeshmvs21.

Javascript

// JavaScript Code to implement the approach
// Structure of a BST node
class TreeNode{
    constructor(data){
        this.val = data;
        this.left = null;
        this.right = null;
    }
}

// Function to insert a new node to the BST
function insert(root, val){
    let newnode = new TreeNode(val);
    let x = root;
    let y = null;

    while(x != null){
        y = x;
        if(val < x.val)
            x = x.left;
        else
            x = x.right;
    }

    if(y == null){
        y = newnode;
    }
    else if(val < y.val){
        y.left = newnode;
    }
    else{
        y.right = newnode;
    }
    return y;
}

// Function to find the maximum absolute difference
function findMaxDiff(root, max_diff){
    if(root == null) return;

    let lval, rval;

    // Only when both siblings are there
    if(root.left != null && root.right != null){
        lval = root.left.val;
        rval = root.right.val;
        max_diff[0] = Math.max(max_diff[0], rval-lval);
    }

    findMaxDiff(root.left, max_diff);
    findMaxDiff(root.right, max_diff);
}

// Driver Code
let root = null;
let root2 = null;

// structure of first tree
root = insert(root, 100);
insert(root, 50);
insert(root, 105);
insert(root, 75);
insert(root, 5);
insert(root, 101);
insert(root, 106);

// Structure of second tree
root2 = insert(root2, 100);
insert(root2, 60);
insert(root2, 120);
insert(root2, 45);
insert(root2, 90);
insert(root2, 110);
insert(root2, 160);

let max_diff = [Number.MIN_VALUE];
let max_diff2 = [Number.MIN_VALUE];

findMaxDiff(root, max_diff);
document.write(max_diff[0]);

document.write("<br>");

findMaxDiff(root2, max_diff2);
document.write(max_diff2[0]);

// This code is contributed by Yash Agarwal

Output

70
60

Time Complexity: O(N)
Auxiliary Space: O(h)