# Count pairs in BST with sum greater than K

• Last Updated : 28 Sep, 2021

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 pairâ€™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:

## C++

 `// C++ program to Count` `// pair in BST whose Sum` `// is greater than K`   `#include ` `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;` `}`

## Java

 `// 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`

## Python3

 `# Python3 program to count pair in` `# BST whose sum is greater than K` `index ``=` `0`   `# Structure of each node of BST` `class` `newNode:` `    `  `    ``# Function to create a new BST node` `    ``def` `__init__(``self``, item):` `        `  `        ``self``.key ``=` `item` `        ``self``.left ``=` `None` `        ``self``.right ``=` `None`   `# Function to insert a new ` `# node with given key in BST` `def` `insert(node, key):` `    `  `    ``# Check if the tree is empty` `    ``if` `(node ``=``=` `None``):` `        ``return` `newNode(key)`   `    ``if` `(key < node.key):` `        ``node.left ``=` `insert(node.left, key)`   `    ``elif``(key > node.key):` `        ``node.right ``=` `insert(node.right, key)`   `    ``# Return the (unchanged) node pointer ` `    ``return` `node`   `# Function to return the size of the tree` `def` `sizeOfTree(root):` `    `  `    ``if` `(root ``=``=` `None``):` `        ``return` `0`   `    ``# Calculate left size recursively` `    ``left ``=` `sizeOfTree(root.left)`   `    ``# Calculate right size recursively` `    ``right ``=` `sizeOfTree(root.right)`   `    ``# Return total size recursively` `    ``return` `(left ``+` `right ``+` `1``)`   `# Function to store inorder traversal of BST` `def` `storeInorder(root, inOrder):` `    `  `    ``global` `index` `    `  `    ``# Base condition` `    ``if` `(root ``=``=` `None``):` `        ``return`   `    ``# Left recursive call` `    ``storeInorder(root.left, inOrder)`   `    ``# Store elements in inorder array` `    ``inOrder[index] ``=` `root.key` `    ``index ``+``=` `1`   `    ``# Right recursive call` `    ``storeInorder(root.right, inOrder)`   `# Function to count the pair of BST` `# whose sum is greater than k` `def` `countPairUtil(inOrder, j, k):` `    `  `    ``i ``=` `0` `    ``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 ``-``=` `1` `        ``else``:` `            ``i ``+``=` `1`   `    ``# Return number of total pair` `    ``return` `pair`   `# Function to count the` `# pair of BST whose sum is` `# greater than k` `def` `countPair(root, k):` `    `  `    ``global` `index` `    `  `    ``# Store the size of BST` `    ``numNode ``=` `sizeOfTree(root)`   `    ``# Auxiliary array for storing` `    ``# the inorder traversal of BST` `    ``inOrder ``=` `[``0` `for` `i ``in` `range``(numNode ``+` `1``)]`   `    ``storeInorder(root, inOrder)`   `    ``# Function call to count the pair` `    ``return` `countPairUtil(inOrder, index ``-` `1``, k)`   `# Driver code` `if` `__name__ ``=``=` `'__main__'``:` `    `  `    ``# Create tree` `    ``root ``=` `None` `    ``root ``=` `insert(root, ``5``)` `    ``insert(root, ``3``)` `    ``insert(root, ``2``)` `    ``insert(root, ``4``)` `    ``insert(root, ``7``)` `    ``insert(root, ``6``)` `    ``insert(root, ``8``)`   `    ``k ``=` `11`   `    ``# Print the number of pair` `    ``print``(countPair(root, k))`   `# This code is contributed by ipg2016107`

## C#

 `// 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`

## Javascript

 ``

Output:

`6`

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