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Maximum difference between node and its ancestor in Binary Tree

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  • Difficulty Level : Medium
  • Last Updated : 13 Oct, 2022
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Given a Binary tree, The task is to find the maximum value by subtracting the value of node B from the value of node A, where A and B are two nodes of the binary tree and A is an ancestor of B.

Examples:

Input:

tree

Output: 7
Explanation: We can have various ancestor-node difference, some of which are given below : 
8 – 3 = 5 , 3 – 7 = -4, 8 – 1 = 7, 10 – 13 = -3
Among all those differences maximum value is 7 obtained by subtracting 1 from 8, which we need to return as result. 

Input:
            9
          /  \
        6    3
            /  \
          1    4
Output: 8

Approach:

Traverse whole binary tree to get max difference and we can obtain the result in one traversal only by following below steps : 

  • If current node is a leaf node then just return its value because it can’t be ancestor of any node. 
  • Then at each internal node try to get minimum value from left subtree and right subtree and calculate the difference between node value and this minimum value and according to that update the result. 

Follow the below steps to Implement the idea:

  • Recursively traverse every node (say t) of the tree:
    • If t = NULL return INT_MAX
    • If the current node is the leaf node then just return the node’s value.
    • Recursively calling for left and right subtree for minimum value
      • Update res if node value – minimum value from subtree is bigger than res i.e res = max(*res, t->key – val).
    • Return minimum value got so far i.e. return min(val, t->key);.

Below is the implementation of the above idea.

C++




// C++ program to find maximum difference between node
// and its ancestor
#include <bits/stdc++.h>
using namespace std;
 
/* A binary tree node has key, pointer to left
   child and a pointer to right child */
struct Node {
    int key;
    struct Node *left, *right;
};
 
/* To create a newNode of tree and return pointer */
struct Node* newNode(int key)
{
    Node* temp = new Node;
    temp->key = key;
    temp->left = temp->right = NULL;
    return (temp);
}
 
/* Recursive function to calculate maximum ancestor-node
   difference in  binary tree. It updates value at 'res'
   to store the result.  The returned value of this function
   is minimum value in subtree rooted with 't' */
int maxDiffUtil(Node* t, int* res)
{
    /* Returning Maximum int value if node is not
       there (one child case)  */
    if (t == NULL)
        return INT_MAX;
 
    /* If leaf node then just return node's value  */
    if (t->left == NULL && t->right == NULL)
        return t->key;
 
    /* Recursively calling left and right subtree
       for minimum value  */
    int val = min(maxDiffUtil(t->left, res),
                  maxDiffUtil(t->right, res));
 
    /* Updating res if (node value - minimum value
       from subtree) is bigger than res  */
    *res = max(*res, t->key - val);
 
    /* Returning minimum value got so far */
    return min(val, t->key);
}
 
/* This function mainly calls maxDiffUtil() */
int maxDiff(Node* root)
{
    // Initialising result with minimum int value
    int res = INT_MIN;
 
    maxDiffUtil(root, &res);
 
    return res;
}
 
/* Helper function to print inorder traversal of
  binary tree   */
void inorder(Node* root)
{
    if (root) {
        inorder(root->left);
        cout << root->key << " ";
        inorder(root->right);
    }
}
 
// Driver program to test above functions
int main()
{
    // Making above given diagram's binary tree
    Node* root;
    root = newNode(8);
    root->left = newNode(3);
 
    root->left->left = newNode(1);
    root->left->right = newNode(6);
    root->left->right->left = newNode(4);
    root->left->right->right = newNode(7);
 
    root->right = newNode(10);
    root->right->right = newNode(14);
    root->right->right->left = newNode(13);
 
    cout << maxDiff(root);
}

Java




/* Java program to find maximum difference between node
   and its ancestor */
 
// A binary tree node has key, pointer to left
// and right child
class Node {
    int key;
    Node left, right;
 
    public Node(int key)
    {
        this.key = key;
        left = right = null;
    }
}
 
/* Class Res created to implement pass by reference
   of 'res' variable */
class Res {
    int r = Integer.MIN_VALUE;
}
 
public class BinaryTree {
    Node root;
 
    /* Recursive function to calculate maximum ancestor-node
       difference in  binary tree. It updates value at 'res'
       to store the result.  The returned value of this
       function
       is minimum value in subtree rooted with 't' */
    int maxDiffUtil(Node t, Res res)
    {
        /* Returning Maximum int value if node is not
           there (one child case)  */
        if (t == null)
            return Integer.MAX_VALUE;
 
        /* If leaf node then just return node's value  */
        if (t.left == null && t.right == null)
            return t.key;
 
        /* Recursively calling left and right subtree
           for minimum value  */
        int val = Math.min(maxDiffUtil(t.left, res),
                           maxDiffUtil(t.right, res));
 
        /* Updating res if (node value - minimum value
           from subtree) is bigger than res  */
        res.r = Math.max(res.r, t.key - val);
 
        /* Returning minimum value got so far */
        return Math.min(val, t.key);
    }
 
    /* This function mainly calls maxDiffUtil() */
    int maxDiff(Node root)
    {
        // Initialising result with minimum int value
        Res res = new Res();
        maxDiffUtil(root, res);
 
        return res.r;
    }
 
    /* Helper function to print inorder traversal of
       binary tree   */
    void inorder(Node root)
    {
        if (root != null) {
            inorder(root.left);
            System.out.print(root.key + "");
            inorder(root.right);
        }
    }
 
    // Driver program to test the above functions
    public static void main(String[] args)
    {
        BinaryTree tree = new BinaryTree();
 
        // Making above given diagram's binary tree
        tree.root = new Node(8);
        tree.root.left = new Node(3);
        tree.root.left.left = new Node(1);
        tree.root.left.right = new Node(6);
        tree.root.left.right.left = new Node(4);
        tree.root.left.right.right = new Node(7);
 
        tree.root.right = new Node(10);
        tree.root.right.right = new Node(14);
        tree.root.right.right.left = new Node(13);
 
        System.out.println(tree.maxDiff(tree.root));
    }
}
 
// This code has been contributed by Mayank
// Jaiswal(mayank_24)

Python3




# Python3 program to find maximum difference
# between node and its ancestor
 
_MIN = -2147483648
_MAX = 2147483648
 
# Helper function that allocates a new
# node with the given data and None left
# and right pointers.
 
 
class newNode:
 
    # Constructor to create a new node
    def __init__(self, key):
        self.key = key
        self.left = None
        self.right = None
 
 
"""
Recursive function to calculate maximum
ancestor-node difference in binary tree.
It updates value at 'res' to store the
result. The returned value of this function
is minimum value in subtree rooted with 't' """
 
 
def maxDiffUtil(t, res):
    """ Returning Maximum value if node
    is not there (one child case) """
    if (t == None):
        return _MAX, res
 
    """ If leaf node then just return
        node's value """
    if (t.left == None and t.right == None):
        return t.key, res
 
    """ Recursively calling left and right
    subtree for minimum value """
    a, res = maxDiffUtil(t.left, res)
    b, res = maxDiffUtil(t.right, res)
    val = min(a, b)
 
    """ Updating res if (node value - minimum
    value from subtree) is bigger than res """
    res = max(res, t.key - val)
 
    """ Returning minimum value got so far """
    return min(val, t.key), res
 
 
""" This function mainly calls maxDiffUtil() """
 
 
def maxDiff(root):
 
    # Initialising result with minimum value
    res = _MIN
    x, res = maxDiffUtil(root, res)
    return res
 
 
""" Helper function to print inorder
traversal of binary tree """
 
 
def inorder(root):
 
    if (root):
 
        inorder(root.left)
        prf("%d ", root.key)
        inorder(root.right)
 
 
# Driver Code
if __name__ == '__main__':
 
    """
    Let us create Binary Tree shown
    in above example """
    root = newNode(8)
    root.left = newNode(3)
 
    root.left.left = newNode(1)
    root.left.right = newNode(6)
    root.left.right.left = newNode(4)
    root.left.right.right = newNode(7)
 
    root.right = newNode(10)
    root.right.right = newNode(14)
    root.right.right.left = newNode(13)
    print(maxDiff(root))
 
# This code is contributed by
# Shubham Singh(SHUBHAMSINGH10)

C#




using System;
 
/* C# program to find maximum difference between node
   and its ancestor */
 
// A binary tree node has key, pointer to left
// and right child
public class Node {
    public int key;
    public Node left, right;
 
    public Node(int key)
    {
        this.key = key;
        left = right = null;
    }
}
 
/* Class Res created to implement pass by reference
   of 'res' variable */
public class Res {
    public int r = int.MinValue;
}
 
public class BinaryTree {
    public Node root;
 
    /* Recursive function to calculate maximum ancestor-node
       difference in  binary tree. It updates value at 'res'
       to store the result.  The returned value of this
       function
       is minimum value in subtree rooted with 't' */
    public virtual int maxDiffUtil(Node t, Res res)
    {
        /* Returning Maximum int value if node is not
           there (one child case)  */
        if (t == null) {
            return int.MaxValue;
        }
 
        /* If leaf node then just return node's value  */
        if (t.left == null && t.right == null) {
            return t.key;
        }
 
        /* Recursively calling left and right subtree
           for minimum value  */
        int val = Math.Min(maxDiffUtil(t.left, res),
                           maxDiffUtil(t.right, res));
 
        /* Updating res if (node value - minimum value
           from subtree) is bigger than res  */
        res.r = Math.Max(res.r, t.key - val);
 
        /* Returning minimum value got so far */
        return Math.Min(val, t.key);
    }
 
    /* This function mainly calls maxDiffUtil() */
    public virtual int maxDiff(Node root)
    {
        // Initialising result with minimum int value
        Res res = new Res();
        maxDiffUtil(root, res);
 
        return res.r;
    }
 
    /* Helper function to print inorder traversal of
       binary tree   */
    public virtual void inorder(Node root)
    {
        if (root != null) {
            inorder(root.left);
            Console.Write(root.key + "");
            inorder(root.right);
        }
    }
 
    // Driver program to test the above functions
    public static void Main(string[] args)
    {
        BinaryTree tree = new BinaryTree();
 
        // Making above given diagram's binary tree
        tree.root = new Node(8);
        tree.root.left = new Node(3);
        tree.root.left.left = new Node(1);
        tree.root.left.right = new Node(6);
        tree.root.left.right.left = new Node(4);
        tree.root.left.right.right = new Node(7);
 
        tree.root.right = new Node(10);
        tree.root.right.right = new Node(14);
        tree.root.right.right.left = new Node(13);
 
        Console.WriteLine(tree.maxDiff(tree.root));
    }
}
 
// This code is contributed by Shrikant13

Javascript




<script>
/* javascript program to find maximum difference between node
   and its ancestor */
 
// A binary tree node has key, pointer to left
// and right child
class Node {
    constructor(key) {
        this.key = key;
        this.left = this.right = null;
    }
}
 
/*
 * Class Res created to implement pass by reference of 'res' variable
 */
class Res {
constructor(){
    this.r = Number.MIN_VALUE;
    }
}
 
var root;
 
    /*
     * Recursive function to calculate maximum ancestor-node difference in binary
     * tree. It updates value at 'res' to store the result. The returned value of
     * this function is minimum value in subtree rooted with 't'
     */
    function maxDiffUtil( t,  res) {
        /*
         * Returning Maximum var value if node is not there (one child case)
         */
        if (t == null)
            return Number.MAX_VALUE;
 
        /* If leaf node then just return node's value */
        if (t.left == null && t.right == null)
            return t.key;
 
        /*
         * Recursively calling left and right subtree for minimum value
         */
        var val = Math.min(maxDiffUtil(t.left, res), maxDiffUtil(t.right, res));
 
        /*
         * Updating res if (node value - minimum value from subtree) is bigger than res
         */
        res.r = Math.max(res.r, t.key - val);
 
        /* Returning minimum value got so far */
        return Math.min(val, t.key);
    }
 
    /* This function mainly calls maxDiffUtil() */
    function maxDiff( root) {
        // Initialising result with minimum var value
         res = new Res();
        maxDiffUtil(root, res);
 
        return res.r;
    }
 
    /*
     * Helper function to print inorder traversal of binary tree
     */
    function inorder( root) {
        if (root !=null) {
            inorder(root.left);
            document.write(root.key + "");
            inorder(root.right);
        }
    }
 
    // Driver program to test the above functions
     
 
 
        // Making above given diagram's binary tree
        root = new Node(8);
        root.left = new Node(3);
        root.left.left = new Node(1);
        root.left.right = new Node(6);
        root.left.right.left = new Node(4);
        root.left.right.right = new Node(7);
 
        root.right = new Node(10);
        root.right.right = new Node(14);
        root.right.right.left = new Node(13);
 
        document.write(maxDiff(root));
 
// This code contributed by umadevi9616
</script>

Output

7

Time Complexity: O(N), for visiting every node of the tree.
Auxiliary Space: O(N) for recursion call stack.

This article is contributed by Utkarsh Trivedi. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.


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