Count pairs in BST with sum greater than K

Given a binary search tree containing N distinct nodes and a value K. The task is to count pairs in the given binary search tree whose sum is greater than the given value K.

Examples:

Input:  
        5      
       / \      
      3   7      
     / \ / \  
    2  4 6  8   

     k = 11
Output: 6
Explanation:
There are 6 pairs which are (4, 8), (5, 7), (5, 8), (6, 7), (6, 8) and (7, 8).

Input: 
 
         8      
        / \      
       3   9      
       \   / \  
        5 6  18   

       k = 23
Output: 3
Explanation:
There are 3 pairs which are (6, 18), (8, 18) and (9, 18).

Naive Approach:

To solve the problem mentioned above we have to store inorder traversal of BST in an array then run two loops to generate all pairs and one by one check if the current pair’s sum is greater than k or not.

Efficient Approach:
The above method can be optimized if we store the inorder traversal of BST in an array and take the initial and last index of the array in l and r variable to find the total pair in the inorder array. Initially assign l as 0 and r as n-1. Consider a variable and initialize it to zero. This variable result will be our final answer. Now iterate until l < r and if the current left and current right have a sum greater than K, all elements from l+1 to r form a pair with it otherwise it doesn't, therefore, increment current left. Finally, return the result.



Below is the implementation of the above approach:

CPP

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// C++ programm to Count
// pair in BST whose Sum
// is greater than K
  
#include <bits/stdc++.h>
using namespace std;
  
// Structure of each node of BST
struct node {
    int key;
    struct node *left, *right;
};
  
// Function to create a new BST node
node* newNode(int item)
{
    node* temp = new node();
  
    temp->key = item;
    temp->left = temp->right = NULL;
  
    return temp;
}
  
/* Function to insert a new 
node with given key in BST */
struct node* insert(struct node* node, int key)
{
  
    // check if the tree is empty
    if (node == NULL)
        return newNode(key);
  
    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;
}
  
// Function to return the size of the tree
int sizeOfTree(node* root)
{
    if (root == NULL) {
        return 0;
    }
  
    // Calculate left size recursively
    int left = sizeOfTree(root->left);
  
    // Calculate right size recursively
    int right = sizeOfTree(root->right);
  
    // Return total size recursively
    return (left + right + 1);
}
  
// Function to store inorder traversal of BST
void storeInorder(node* root, int inOrder[],
                  int& index)
{
  
    // Base condition
    if (root == NULL) {
        return;
    }
  
    // Left recursive call
    storeInorder(root->left, inOrder, index);
  
    // Store elements in inorder array
    inOrder[index++] = root->key;
  
    // Right recursive call
    storeInorder(root->right, inOrder, index);
}
  
// function to count the pair of BST
// whose sum is greater than k
int countPairUtil(int inOrder[], int j, int k)
{
    int i = 0;
    int pair = 0;
    while (i < j) {
  
        // check if sum of value at index
        // i and j is greater than k
        if (inOrder[i] + inOrder[j] > k) {
            pair += j - i;
  
            j--;
        }
        else {
            i++;
        }
    }
  
    // Return number of total pair
    return pair;
}
  
// Function to count the
// pair of BST whose sum is
// greater than k
int countPair(node* root, int k)
{
  
    // Store the size of BST
    int numNode = sizeOfTree(root);
  
    // Auxiliary array for storing
    // the inorder traversal of BST
    int inOrder[numNode + 1];
  
    int index = 0;
  
    storeInorder(root, inOrder, index);
  
    // Function call to count the pair
    return countPairUtil(inOrder, index - 1, k);
}
  
// Driver code
int main()
{
  
    // create tree
    struct node* root = NULL;
    root = insert(root, 5);
    insert(root, 3);
    insert(root, 2);
    insert(root, 4);
    insert(root, 7);
    insert(root, 6);
    insert(root, 8);
  
    int k = 11;
  
    // Print the number of pair
    cout << countPair(root, k);
  
    return 0;
}

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Java

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// Java program to Count
// pair in BST whose Sum
// is greater than K
class GFG{
   
// Structure of each node of BST
static class node {
    int key;
    node left, right;
};
static int index;
  
// 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;
}
   
/* Function to insert a new 
node with given key in BST */
static node insert(node node, int key)
{
   
    // check if the tree is empty
    if (node == null)
        return newNode(key);
   
    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;
}
   
// Function to return the size of the tree
static int sizeOfTree(node root)
{
    if (root == null) {
        return 0;
    }
   
    // Calculate left size recursively
    int left = sizeOfTree(root.left);
   
    // Calculate right size recursively
    int right = sizeOfTree(root.right);
   
    // Return total size recursively
    return (left + right + 1);
}
   
// Function to store inorder traversal of BST
static void storeInorder(node root, int inOrder[])
{
   
    // Base condition
    if (root == null) {
        return;
    }
   
    // Left recursive call
    storeInorder(root.left, inOrder);
   
    // Store elements in inorder array
    inOrder[index++] = root.key;
   
    // Right recursive call
    storeInorder(root.right, inOrder);
}
   
// function to count the pair of BST
// whose sum is greater than k
static int countPairUtil(int inOrder[], int j, int k)
{
    int i = 0;
    int pair = 0;
    while (i < j) {
   
        // check if sum of value at index
        // i and j is greater than k
        if (inOrder[i] + inOrder[j] > k) {
            pair += j - i;
   
            j--;
        }
        else {
            i++;
        }
    }
   
    // Return number of total pair
    return pair;
}
   
// Function to count the
// pair of BST whose sum is
// greater than k
static int countPair(node root, int k)
{
   
    // Store the size of BST
    int numNode = sizeOfTree(root);
   
    // Auxiliary array for storing
    // the inorder traversal of BST
    int []inOrder = new int[numNode + 1];
   
    index = 0;
   
    storeInorder(root, inOrder);
   
    // Function call to count the pair
    return countPairUtil(inOrder, index - 1, k);
}
   
// Driver code
public static void main(String[] args)
{
   
    // create tree
    node root = null;
    root = insert(root, 5);
    insert(root, 3);
    insert(root, 2);
    insert(root, 4);
    insert(root, 7);
    insert(root, 6);
    insert(root, 8);
   
    int k = 11;
   
    // Print the number of pair
    System.out.print(countPair(root, k));
   
}
}
  
// This code is contributed by Princi Singh

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C#

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// C# program to Count
// pair in BST whose Sum
// is greater than K
using System;
  
class GFG{
    
// Structure of each node of BST
class node {
    public int key;
    public node left, right;
};
static int index;
   
// 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;
}
    
/* Function to insert a new 
node with given key in BST */
static node insert(node node, int key)
{
    
    // check if the tree is empty
    if (node == null)
        return newNode(key);
    
    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;
}
    
// Function to return the size of the tree
static int sizeOfTree(node root)
{
    if (root == null) {
        return 0;
    }
    
    // Calculate left size recursively
    int left = sizeOfTree(root.left);
    
    // Calculate right size recursively
    int right = sizeOfTree(root.right);
    
    // Return total size recursively
    return (left + right + 1);
}
    
// Function to store inorder traversal of BST
static void storeInorder(node root, int []inOrder)
{
    
    // Base condition
    if (root == null) {
        return;
    }
    
    // Left recursive call
    storeInorder(root.left, inOrder);
    
    // Store elements in inorder array
    inOrder[index++] = root.key;
    
    // Right recursive call
    storeInorder(root.right, inOrder);
}
    
// function to count the pair of BST
// whose sum is greater than k
static int countPairUtil(int []
                           
                           
                         inOrder, int j, int k)
{
    int i = 0;
    int pair = 0;
    while (i < j) {
    
        // check if sum of value at index
        // i and j is greater than k
        if (inOrder[i] + inOrder[j] > k) {
            pair += j - i;
    
            j--;
        }
        else {
            i++;
        }
    }
    
    // Return number of total pair
    return pair;
}
    
// Function to count the
// pair of BST whose sum is
// greater than k
static int countPair(node root, int k)
{
    
    // Store the size of BST
    int numNode = sizeOfTree(root);
    
    // Auxiliary array for storing
    // the inorder traversal of BST
    int []inOrder = new int[numNode + 1];
    
    index = 0;
    
    storeInorder(root, inOrder);
    
    // Function call to count the pair
    return countPairUtil(inOrder, index - 1, k);
}
    
// Driver code
public static void Main(String[] args)
{
    
    // create tree
    node root = null;
    root = insert(root, 5);
    insert(root, 3);
    insert(root, 2);
    insert(root, 4);
    insert(root, 7);
    insert(root, 6);
    insert(root, 8);
    
    int k = 11;
    
    // Print the number of pair
    Console.Write(countPair(root, k));
    
}
}
  
// This code is contributed by Rajput-Ji

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Output:

6

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