Find a pair with given sum in BST

Given a BST and a sum, find if there is a pair with given sum.

Input : sum = 28
        Root of below tree

Output : Pair is found (16, 12)

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

We have discussed different approaches to find a pair with given sum in below post.Find a pair with given sum in a Balanced BST

In this post, hashing based solution is discussed. We traverse binary search tree by inorder way and insert node’s value into a set. Also check for any node, difference between given sum and node’s value in set, if it is found then pair exists otherwise it doesn’t exist.

C++

// CPP program to find a pair with 
// given sum using hashing 
#include <bits/stdc++.h> 
using namespace std; 
  
struct Node { 
    int data; 
    struct Node *left, *right; 
}; 
  
Node* NewNode(int data) 
{ 
    Node* temp = (Node*)malloc(sizeof(Node)); 
    temp->data = data; 
    temp->left = NULL; 
    temp->right = NULL; 
    return temp; 
} 
  
Node* insert(Node* root, int key) 
{ 
    if (root == NULL) 
        return NewNode(key); 
    if (key < root->data) 
        root->left = insert(root->left, key); 
    else
        root->right = insert(root->right, key); 
    return root; 
} 
  
bool findpairUtil(Node* root, int sum,  unordered_set<int> &set) 
{ 
    if (root == NULL) 
        return false; 
  
    if (findpairUtil(root->left, sum, set)) 
        return true; 
  
    if (set.find(sum - root->data) != set.end()) { 
        cout << "Pair is found ("
             << sum - root->data << ", "
             << root->data << ")" << endl; 
        return true; 
    } 
    else
        set.insert(root->data); 
  
    return findpairUtil(root->right, sum, set); 
} 
  
void findPair(Node* root, int sum) 
{ 
    unordered_set<int> set; 
    if (!findpairUtil(root, sum, set)) 
        cout << "Pairs do not exit" << endl; 
} 
  
// Driver code 
int main() 
{ 
    Node* root = NULL; 
    root = insert(root, 15); 
    root = insert(root, 10); 
    root = insert(root, 20); 
    root = insert(root, 8); 
    root = insert(root, 12); 
    root = insert(root, 16); 
    root = insert(root, 25); 
    root = insert(root, 10); 
  
    int sum = 33; 
    findPair(root, sum); 
  
    return 0; 
} 

Python3

# Python3 program to find a pair with  
# given sum using hashing  
import sys 
import math 
  
class Node: 
    def __init__(self,data): 
        self.data = data 
        self.left = None
        self.right = None
  
def insert(root,data): 
    if root is None: 
        return Node(data) 
    if(data < root.data): 
        root.left = insert(root.left, data) 
    if(data > root.data): 
        root.right = insert(root.right, data) 
    return root 
  
def findPairUtil(root, summ, unsorted_set): 
    if root is None: 
        return False
    if findPairUtil(root.left,summ,unsorted_set): 
        return True
    if unsorted_set and (summ-root.data) in unsorted_set: 
        print("Pair is Found ({},{})".format(summ-root.data, root.data)) 
        return True
    else: 
        unsorted_set.add(root.data) 
  
    return findPairUtil(root.right,summ, unsorted_set) 
  
def findPair(root,summ): 
    unsorted_set = set() 
    if(not findPairUtil(root,summ,unsorted_set)): 
        print("Pair do not exist!") 
  
# Driver code 
if __name__=='__main__': 
    root=None
    root = insert(root,15) 
    root = insert(root,10) 
    root = insert(root,20) 
    root = insert(root,8) 
    root = insert(root,12) 
    root = insert(root,16) 
    root = insert(root,25) 
    root = insert(root,10) 
    summ = 33
    findPair(root, summ) 
  
# This code is contributed by Vikash Kumar 37 