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Find the closest element in Binary Search Tree

Given a binary search tree and a target node K. The task is to find the node with minimum absolute difference with given target value K.

Examples:

// For above binary search tree
Input  :  k = 4
Output :  4

Input  :  k = 18
Output :  17

Input  :  k = 12
Output :  9



A simple solution for this problem is to store Inorder traversal of given binary search tree in an auxiliary array and then by taking absolute difference of each element find the node having minimum absolute difference with given target value K in linear time.

An efficient solution for this problem is to take advantage of characteristics of BST. Here is the algorithm to solve this problem :

  • If target value K is present in given BST, then it’s the node having minimum absolute difference.
  • If target value K is less than the value of current node then move to the left child.
  • If target value K is greater than the value of current node then move to the right child.
  • C++

    // Recursive C++ program to find key closest to k
    // in given Binary Search Tree.
    #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;
    };
      
    /* Utility that allocates a new node with the
      given key and NULL left and right pointers. */
    struct Node* newnode(int key)
    {
        struct Node* node = new (struct Node);
        node->key = key;
        node->left = node->right  = NULL;
        return (node);
    }
      
    // Function to find node with minimum absolute
    // difference with given K
    // min_diff   --> minimum difference till now
    // min_diff_key  --> node having minimum absolute
    //                   difference with K
    void maxDiffUtil(struct Node *ptr, int k, int &min_diff,
                                          int &min_diff_key)
    {
        if (ptr == NULL)
            return ;
      
        // If k itself is present
        if (ptr->key == k)
        {
            min_diff_key = k;
            return;
        }
      
        // update min_diff and min_diff_key by checking
        // current node value
        if (min_diff > abs(ptr->key - k))
        {
            min_diff = abs(ptr->key - k);
            min_diff_key = ptr->key;
        }
      
        // if k is less than ptr->key then move in
        // left subtree else in right subtree
        if (k < ptr->key)
            maxDiffUtil(ptr->left, k, min_diff, min_diff_key);
        else
            maxDiffUtil(ptr->right, k, min_diff, min_diff_key);
    }
      
    // Wrapper over maxDiffUtil()
    int maxDiff(Node *root, int k)
    {
        // Initialize minimum difference
        int min_diff = INT_MAX, min_diff_key = -1;
      
        // Find value of min_diff_key (Closest key
        // in tree with k)
        maxDiffUtil(root, k, min_diff, min_diff_key);
      
        return min_diff_key;
    }
      
    // Driver program to run the case
    int main()
    {
        struct Node *root = newnode(9);
        root->left    = newnode(4);
        root->right   = newnode(17);
        root->left->left = newnode(3);
        root->left->right = newnode(6);
        root->left->right->left = newnode(5);
        root->left->right->right = newnode(7);
        root->right->right = newnode(22);
        root->right->right->left = newnode(20);
        int k = 18;
        cout << maxDiff(root, k);
        return 0;
    }

    Java

    // Recursive Java program to find key closest to k
    // in given Binary Search Tree.
      
     class solution
     {
           
         static int min_diff, min_diff_key;
            
    /*  A binary tree node has key, pointer to left child
    and a pointer to right child */
    static class Node
    {
        int key;
          
         Node  left,  right;
    };
       
    /*  Utility that allocates a new node with the
      given key and null left and right pointers.  */
      
     static Node  newnode(int key)
    {
          
         Node  node = new Node();
        node.key = key;
        node.left = node.right  = null;
        return (node);
    }
       
    // Function to find node with minimum absolute
    // difference with given K
    // min_diff   -. minimum difference till now
    // min_diff_key  -. node having minimum absolute
    //                   difference with K
    static void maxDiffUtil(Node  ptr, int k)
    {
        if (ptr == null)
            return ;
       
        // If k itself is present
        if (ptr.key == k)
        {
            min_diff_key = k;
            return;
        }
       
        // update min_diff and min_diff_key by checking
        // current node value
        if (min_diff > Math.abs(ptr.key - k))
        {
            min_diff = Math.abs(ptr.key - k);
            min_diff_key = ptr.key;
        }
       
        // if k is less than ptr.key then move in
        // left subtree else in right subtree
        if (k < ptr.key)
            maxDiffUtil(ptr.left, k);
        else
            maxDiffUtil(ptr.right, k);
    }
       
    // Wrapper over maxDiffUtil()
    static int maxDiff(Node  root, int k)
    {
        // Initialize minimum difference
        min_diff = 999999999; min_diff_key = -1;
       
        // Find value of min_diff_key (Closest key
        // in tree with k)
        maxDiffUtil(root, k);
       
        return min_diff_key;
    }
       
    // Driver program to run the case
    public static void main(String args[])
    {
          
         Node  root = newnode(9);
        root.left    = newnode(4);
        root.right   = newnode(17);
        root.left.left = newnode(3);
        root.left.right = newnode(6);
        root.left.right.left = newnode(5);
        root.left.right.right = newnode(7);
        root.right.right = newnode(22);
        root.right.right.left = newnode(20);
        int k = 18;
        System.out.println( maxDiff(root, k));
          
    }
    }
    //contributed by Arnab Kundu

    Python3

    # Recursive Python program to find key 
    # closest to k in given Binary Search Tree. 
      
    # Utility that allocates a new node with the 
    # given key and NULL left and right pointers. 
    class newnode: 
      
        # Constructor to create a new node 
        def __init__(self, data): 
            self.key = data 
            self.left = None
            self.right = None
      
    # Function to find node with minimum 
    # absolute difference with given K 
    # min_diff --> minimum difference till now 
    # min_diff_key --> node having minimum absolute 
    #                  difference with K 
    def maxDiffUtil(ptr, k, min_diff, min_diff_key):
        if ptr == None
            return
              
        # If k itself is present 
        if ptr.key == k:
            min_diff_key[0] =
            return
      
        # update min_diff and min_diff_key by  
        # checking current node value 
        if min_diff > abs(ptr.key - k):
            min_diff = abs(ptr.key - k) 
            min_diff_key[0] = ptr.key
      
        # if k is less than ptr->key then move 
        # in left subtree else in right subtree 
        if k < ptr.key:
            maxDiffUtil(ptr.left, k, min_diff, 
                                     min_diff_key)
        else:
            maxDiffUtil(ptr.right, k, min_diff, 
                                      min_diff_key)
      
    # Wrapper over maxDiffUtil() 
    def maxDiff(root, k):
          
        # Initialize minimum difference 
        min_diff, min_diff_key = 999999999999, [-1]
      
        # Find value of min_diff_key (Closest 
        # key in tree with k) 
        maxDiffUtil(root, k, min_diff, min_diff_key)
      
        return min_diff_key[0]
      
    # Driver Code
    if __name__ == '__main__':
        root = newnode(9
        root.left = newnode(4
        root.right = newnode(17)
        root.left.left = newnode(3
        root.left.right = newnode(6)
        root.left.right.left = newnode(5
        root.left.right.right = newnode(7
        root.right.right = newnode(22)
        root.right.right.left = newnode(20
        k = 18
        print(maxDiff(root, k))
      
    # This code is contributed by PranchalK

    C#

    using System;
      
    // Recursive C# program to find key closest to k 
    // in given Binary Search Tree. 
      
     public class solution
     {
      
         public static int min_diff, min_diff_key;
      
    /*  A binary tree node has key, pointer to left child 
    and a pointer to right child */
    public class Node
    {
        public int key;
      
         public Node left, right;
    }
      
    /*  Utility that allocates a new node with the 
      given key and null left and right pointers.  */
      
    public static Node newnode(int key)
     {
      
         Node node = new Node();
        node.key = key;
        node.left = node.right = null;
        return (node);
     }
      
    // Function to find node with minimum absolute 
    // difference with given K 
    // min_diff   -. minimum difference till now 
    // min_diff_key  -. node having minimum absolute 
    //                   difference with K 
    public static void maxDiffUtil(Node ptr, int k)
    {
        if (ptr == null)
        {
            return;
        }
      
        // If k itself is present 
        if (ptr.key == k)
        {
            min_diff_key = k;
            return;
        }
      
        // update min_diff and min_diff_key by checking 
        // current node value 
        if (min_diff > Math.Abs(ptr.key - k))
        {
            min_diff = Math.Abs(ptr.key - k);
            min_diff_key = ptr.key;
        }
      
        // if k is less than ptr.key then move in 
        // left subtree else in right subtree 
        if (k < ptr.key)
        {
            maxDiffUtil(ptr.left, k);
        }
        else
        {
            maxDiffUtil(ptr.right, k);
        }
    }
      
    // Wrapper over maxDiffUtil() 
    public static int maxDiff(Node root, int k)
    {
        // Initialize minimum difference 
        min_diff = 999999999;
        min_diff_key = -1;
      
        // Find value of min_diff_key (Closest key 
        // in tree with k) 
        maxDiffUtil(root, k);
      
        return min_diff_key;
    }
      
    // Driver program to run the case 
    public static void Main(string[] args)
    {
      
         Node root = newnode(9);
        root.left = newnode(4);
        root.right = newnode(17);
        root.left.left = newnode(3);
        root.left.right = newnode(6);
        root.left.right.left = newnode(5);
        root.left.right.right = newnode(7);
        root.right.right = newnode(22);
        root.right.right.left = newnode(20);
        int k = 18;
        Console.WriteLine(maxDiff(root, k));
      
    }
     }
      
      // This code is contributed by Shrikant13


    Output:

    17
    

    Time complexity : O(h) where h is height of given Binary Search Tree.

    Reference :
    http://stackoverflow.com/questions/6209325/how-to-find-the-closest-element-to-a-given-key-value-in-a-binary-search-tree

    Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.



This article is attributed to GeeksforGeeks.org

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