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Add all greater values to every node in a given BST

Given a Binary Search Tree (BST), modify it so that all greater values in the given BST are added to every node. For example, consider the following BST.

`              50           /      \         30        70        /   \      /  \      20    40    60   80 The above tree should be modified to following               260           /      \         330        150        /   \       /  \      350   300    210   80`

A simple method for solving this is to find the sum of all greater values for every node. This method would take O(n^2) time.

The method discussed in this article uses the technique of reverse in-order tree traversal of BST which optimizes the problem to be solved in a single traversal.

Approach: In this problem as we could notice that the largest node would remain the same. The value of 2nd largest node = value of largest + value of second largest node. Similarly, the value of nth largest node will be the sum of the n-th node and value of (n-1)th largest node after modification. So if we traverse the tree in descending order and simultaneously update the sum value at every step while adding the value to the root node, the problem would be solved.

So to traverse the BST in descending order we use reverse in-order traversal of BST. This takes a global variable sum which is updated at every node and once the root node is reached it is added to the value of root node and value of the root node is updated.

C++

 `// C++ program to add all greater``// values in every node of BST``#include ``using` `namespace` `std;` `class` `Node {``public``:``    ``int` `data;``    ``Node *left, *right;``};` `// A utility function to create``// a new BST node``Node* newNode(``int` `item)``{``    ``Node* temp = ``new` `Node();``    ``temp->data = item;``    ``temp->left = temp->right = NULL;``    ``return` `temp;``}` `// Recursive function to add all``// greater values in every node``void` `modifyBSTUtil(Node* root, ``int``* sum)``{``    ``// Base Case``    ``if` `(root == NULL)``        ``return``;` `    ``// Recur for right subtree``    ``modifyBSTUtil(root->right, sum);` `    ``// Now *sum has sum of nodes``    ``// in right subtree, add``    ``// root->data to sum and``    ``// update root->data``    ``*sum = *sum + root->data;``    ``root->data = *sum;` `    ``// Recur for left subtree``    ``modifyBSTUtil(root->left, sum);``}` `// A wrapper over modifyBSTUtil()``void` `modifyBST(Node* root)``{``    ``int` `sum = 0;``    ``modifyBSTUtil(root, &sum);``}` `// A utility function to do``// inorder traversal of BST``void` `inorder(Node* root)``{``    ``if` `(root != NULL) {``        ``inorder(root->left);``        ``cout << root->data << ``" "``;``        ``inorder(root->right);``    ``}``}` `/* A utility function to insert``a new node with given data in BST */``Node* insert(Node* node, ``int` `data)``{``    ``/* If the tree is empty,``       ``return a new node */``    ``if` `(node == NULL)``        ``return` `newNode(data);` `    ``/* Otherwise, recur down the tree */``    ``if` `(data <= node->data)``        ``node->left = insert(node->left, data);``    ``else``        ``node->right = insert(node->right, data);` `    ``/* return the (unchanged) node pointer */``    ``return` `node;``}` `// Driver code``int` `main()``{``    ``/* Let us create following BST``            ``50``        ``/ \``        ``30 70``        ``/ \ / \``    ``20 40 60 80 */``    ``Node* root = NULL;``    ``root = insert(root, 50);``    ``insert(root, 30);``    ``insert(root, 20);``    ``insert(root, 40);``    ``insert(root, 70);``    ``insert(root, 60);``    ``insert(root, 80);` `    ``modifyBST(root);` `    ``// print inorder traversal of the modified BST``    ``inorder(root);` `    ``return` `0;``}` `// This code is contributed by rathbhupendra`

C

 `// C program to add all greater``// values in every node of BST``#include ``#include ` `struct` `Node {``    ``int` `data;``    ``struct` `Node *left, *right;``};` `// A utility function to create a new BST node``struct` `Node* newNode(``int` `item)``{``    ``struct` `Node* temp``        ``= (``struct` `Node*)``malloc``(``            ``sizeof``(``struct` `Node));``    ``temp->data = item;``    ``temp->left = temp->right = NULL;``    ``return` `temp;``}` `// Recursive function to add``// all greater values in every node``void` `modifyBSTUtil(``    ``struct` `Node* root, ``int``* sum)``{``    ``// Base Case``    ``if` `(root == NULL)``        ``return``;` `    ``// Recur for right subtree``    ``modifyBSTUtil(root->right, sum);` `    ``// Now *sum has sum of nodes``    ``// in right subtree, add``    ``// root->data to sum and``    ``// update root->data``    ``*sum = *sum + root->data;``    ``root->data = *sum;` `    ``// Recur for left subtree``    ``modifyBSTUtil(root->left, sum);``}` `// A wrapper over modifyBSTUtil()``void` `modifyBST(``struct` `Node* root)``{``    ``int` `sum = 0;``    ``modifyBSTUtil(root, &sum);``}` `// A utility function to do``// inorder traversal of BST``void` `inorder(``struct` `Node* root)``{``    ``if` `(root != NULL) {``        ``inorder(root->left);``        ``printf``(``"%d "``, root->data);``        ``inorder(root->right);``    ``}``}` `/* A utility function to insert``a new node with given data in BST */``struct` `Node* insert(``    ``struct` `Node* node, ``int` `data)``{``    ``/* If the tree is empty, return a new node */``    ``if` `(node == NULL)``        ``return` `newNode(data);` `    ``/* Otherwise, recur down the tree */``    ``if` `(data <= node->data)``        ``node->left = insert(node->left, data);``    ``else``        ``node->right = insert(node->right, data);` `    ``/* return the (unchanged) node pointer */``    ``return` `node;``}` `// Driver Program to test above functions``int` `main()``{``    ``/* Let us create following BST``              ``50``           ``/     \``          ``30      70``         ``/  \    /  \``       ``20   40  60   80 */``    ``struct` `Node* root = NULL;``    ``root = insert(root, 50);``    ``insert(root, 30);``    ``insert(root, 20);``    ``insert(root, 40);``    ``insert(root, 70);``    ``insert(root, 60);``    ``insert(root, 80);` `    ``modifyBST(root);` `    ``// print inorder traversal of the modified BST``    ``inorder(root);` `    ``return` `0;``}`

Java

 `// Java code to add all greater values to``// every node in a given BST` `// A binary tree node``class` `Node {` `    ``int` `data;``    ``Node left, right;` `    ``Node(``int` `d)``    ``{``        ``data = d;``        ``left = right = ``null``;``    ``}``}` `class` `BinarySearchTree {` `    ``// Root of BST``    ``Node root;` `    ``// Constructor``    ``BinarySearchTree()``    ``{``        ``root = ``null``;``    ``}` `    ``// Inorder traversal of the tree``    ``void` `inorder()``    ``{``        ``inorderUtil(``this``.root);``    ``}` `    ``// Utility function for inorder traversal of``    ``// the tree``    ``void` `inorderUtil(Node node)``    ``{``        ``if` `(node == ``null``)``            ``return``;` `        ``inorderUtil(node.left);``        ``System.out.print(node.data + ``" "``);``        ``inorderUtil(node.right);``    ``}` `    ``// adding new node``    ``public` `void` `insert(``int` `data)``    ``{``        ``this``.root = ``this``.insertRec(``this``.root, data);``    ``}` `    ``/* A utility function to insert a new node with``    ``given data in BST */``    ``Node insertRec(Node node, ``int` `data)``    ``{``        ``/* If the tree is empty, return a new node */``        ``if` `(node == ``null``) {``            ``this``.root = ``new` `Node(data);``            ``return` `this``.root;``        ``}` `        ``/* Otherwise, recur down the tree */``        ``if` `(data <= node.data) {``            ``node.left = ``this``.insertRec(node.left, data);``        ``}``        ``else` `{``            ``node.right = ``this``.insertRec(node.right, data);``        ``}``        ``return` `node;``    ``}` `    ``// This class initialises the value of sum to 0``    ``public` `class` `Sum {``        ``int` `sum = ``0``;``    ``}` `    ``// Recursive function to add all greater values in``    ``// every node``    ``void` `modifyBSTUtil(Node node, Sum S)``    ``{``        ``// Base Case``        ``if` `(node == ``null``)``            ``return``;` `        ``// Recur for right subtree``        ``this``.modifyBSTUtil(node.right, S);` `        ``// Now *sum has sum of nodes in right subtree, add``        ``// root->data to sum and update root->data``        ``S.sum = S.sum + node.data;``        ``node.data = S.sum;` `        ``// Recur for left subtree``        ``this``.modifyBSTUtil(node.left, S);``    ``}` `    ``// A wrapper over modifyBSTUtil()``    ``void` `modifyBST(Node node)``    ``{``        ``Sum S = ``new` `Sum();``        ``this``.modifyBSTUtil(node, S);``    ``}` `    ``// Driver Function``    ``public` `static` `void` `main(String[] args)``    ``{``        ``BinarySearchTree tree = ``new` `BinarySearchTree();` `        ``/* Let us create following BST``              ``50``           ``/     \``          ``30      70``         ``/  \    /  \``       ``20   40  60   80 */` `        ``tree.insert(``50``);``        ``tree.insert(``30``);``        ``tree.insert(``20``);``        ``tree.insert(``40``);``        ``tree.insert(``70``);``        ``tree.insert(``60``);``        ``tree.insert(``80``);` `        ``tree.modifyBST(tree.root);` `        ``// print inorder traversal of the modified BST``        ``tree.inorder();``    ``}``}` `// This code is contributed by Kamal Rawal`

Python3

 `# Python3 program to add all greater values``# in every node of BST` `# A utility function to create a``# new BST node``class` `newNode:` `    ``# Constructor to create a new node``    ``def` `__init__(``self``, data):``        ``self``.data ``=` `data``        ``self``.left ``=` `None``        ``self``.right ``=` `None` `# Recursive function to add all greater``# values in every node``def` `modifyBSTUtil(root, ``Sum``):``    ` `    ``# Base Case``    ``if` `root ``=``=` `None``:``        ``return` `    ``# Recur for right subtree``    ``modifyBSTUtil(root.right, ``Sum``)` `    ``# Now Sum[0] has sum of nodes in right``    ``# subtree, add root.data to sum and``    ``# update root.data``    ``Sum``[``0``] ``=` `Sum``[``0``] ``+` `root.data``    ``root.data ``=` `Sum``[``0``]` `    ``# Recur for left subtree``    ``modifyBSTUtil(root.left, ``Sum``)` `# A wrapper over modifyBSTUtil()``def` `modifyBST(root):``    ``Sum` `=` `[``0``]``    ``modifyBSTUtil(root, ``Sum``)` `# A utility function to do inorder``# traversal of BST``def` `inorder(root):``    ``if` `root !``=` `None``:``        ``inorder(root.left)``        ``print``(root.data, end ``=``" "``)``        ``inorder(root.right)` `# A utility function to insert a new node``# with given data in BST``def` `insert(node, data):``    ` `    ``# If the tree is empty, return a new node``    ``if` `node ``=``=` `None``:``        ``return` `newNode(data)` `    ``# Otherwise, recur down the tree``    ``if` `data <``=` `node.data:``        ``node.left ``=` `insert(node.left, data)``    ``else``:``        ``node.right ``=` `insert(node.right, data)` `    ``# return the (unchanged) node pointer``    ``return` `node` `# Driver Code``if` `__name__ ``=``=` `'__main__'``:``    ` `    ``# Let us create following BST``    ``# 50``    ``#     /     \``    ``# 30     70``    ``#     / \ / \``    ``# 20 40 60 80``    ``root ``=` `None``    ``root ``=` `insert(root, ``50``)``    ``insert(root, ``30``)``    ``insert(root, ``20``)``    ``insert(root, ``40``)``    ``insert(root, ``70``)``    ``insert(root, ``60``)``    ``insert(root, ``80``)` `    ``modifyBST(root)` `    ``# print inorder traversal of the``    ``# modified BST``    ``inorder(root)``    ` `# This code is contributed by PranchalK`

C#

 `using` `System;` `// C# code to add all greater values to``// every node in a given BST` `// A binary tree node``public` `class` `Node {` `    ``public` `int` `data;``    ``public` `Node left, right;` `    ``public` `Node(``int` `d)``    ``{``        ``data = d;``        ``left = right = ``null``;``    ``}``}` `public` `class` `BinarySearchTree {` `    ``// Root of BST``    ``public` `Node root;` `    ``// Constructor``    ``public` `BinarySearchTree()``    ``{``        ``root = ``null``;``    ``}` `    ``// Inorder traversal of the tree``    ``public` `virtual` `void` `inorder()``    ``{``        ``inorderUtil(``this``.root);``    ``}` `    ``// Utility function for inorder traversal of``    ``// the tree``    ``public` `virtual` `void` `inorderUtil(Node node)``    ``{``        ``if` `(node == ``null``) {``            ``return``;``        ``}` `        ``inorderUtil(node.left);``        ``Console.Write(node.data + ``" "``);``        ``inorderUtil(node.right);``    ``}` `    ``// adding new node``    ``public` `virtual` `void` `insert(``int` `data)``    ``{``        ``this``.root = ``this``.insertRec(``this``.root, data);``    ``}` `    ``/* A utility function to insert a new node with ``    ``given data in BST */``    ``public` `virtual` `Node insertRec(Node node, ``int` `data)``    ``{``        ``/* If the tree is empty, return a new node */``        ``if` `(node == ``null``) {``            ``this``.root = ``new` `Node(data);``            ``return` `this``.root;``        ``}` `        ``/* Otherwise, recur down the tree */``        ``if` `(data <= node.data) {``            ``node.left = ``this``.insertRec(node.left, data);``        ``}``        ``else` `{``            ``node.right = ``this``.insertRec(node.right, data);``        ``}``        ``return` `node;``    ``}` `    ``// This class initialises the value of sum to 0``    ``public` `class` `Sum {``        ``private` `readonly` `BinarySearchTree outerInstance;` `        ``public` `Sum(BinarySearchTree outerInstance)``        ``{``            ``this``.outerInstance = outerInstance;``        ``}` `        ``public` `int` `sum = 0;``    ``}` `    ``// Recursive function to add all greater values in``    ``// every node``    ``public` `virtual` `void` `modifyBSTUtil(Node node, Sum S)``    ``{``        ``// Base Case``        ``if` `(node == ``null``) {``            ``return``;``        ``}` `        ``// Recur for right subtree``        ``this``.modifyBSTUtil(node.right, S);` `        ``// Now *sum has sum of nodes in right subtree, add``        ``// root->data to sum and update root->data``        ``S.sum = S.sum + node.data;``        ``node.data = S.sum;` `        ``// Recur for left subtree``        ``this``.modifyBSTUtil(node.left, S);``    ``}` `    ``// A wrapper over modifyBSTUtil()``    ``public` `virtual` `void` `modifyBST(Node node)``    ``{``        ``Sum S = ``new` `Sum(``this``);``        ``this``.modifyBSTUtil(node, S);``    ``}` `    ``// Driver Function``    ``public` `static` `void` `Main(``string``[] args)``    ``{``        ``BinarySearchTree tree = ``new` `BinarySearchTree();` `        ``/* Let us create following BST``              ``50``           ``/     \``          ``30      70``         ``/  \    /  \``       ``20   40  60   80 */` `        ``tree.insert(50);``        ``tree.insert(30);``        ``tree.insert(20);``        ``tree.insert(40);``        ``tree.insert(70);``        ``tree.insert(60);``        ``tree.insert(80);` `        ``tree.modifyBST(tree.root);` `        ``// print inorder traversal of the modified BST``        ``tree.inorder();``    ``}``}` `// This code is contributed by Shrikant13`

Javascript

 ``

Output

```350 330 300 260 210 150 80

```

Complexity Analysis:

• Time Complexity: O(n).
As this problem uses an in-order tree traversal technique
• Auxiliary Space: O(1).
As no data structure has been used for storing values.

Approach 2: Recursive Inorder Traversal

In this approach, we traverse the BST in reverse inorder traversal, which gives us the nodes in descending order. While traversing, we maintain a variable sum that keeps track of the sum of all greater nodes than the current node. We add the sum to the current node’s value and update the sum to the new value. This way, we update all nodes with the sum of all greater nodes.

Initialize a variable sum to 0.
Traverse the given BST in reverse inorder (right, root, left) and for each node:
a. Add the node’s value to sum.
b. Replace the node’s value with sum.
Return the modified BST.

The reverse inorder traversal ensures that we visit the nodes in descending order, which allows us to calculate the sum of all greater values for each node. By keeping track of the running sum, we can easily update each node’s value with the sum of all greater values.

C++

 `#include ``using` `namespace` `std;` `struct` `Node {``    ``int` `data;``    ``Node *left, *right;``};` `Node* newNode(``int` `data) {``    ``Node* node = ``new` `Node;``    ``node->data = data;``    ``node->left = node->right = NULL;``    ``return` `node;``}` `void` `modifyBSTUtil(Node* root, ``int``* sum) {``    ``if` `(root == NULL) ``return``;` `    ``modifyBSTUtil(root->right, sum);` `    ``*sum = *sum + root->data;``    ``root->data = *sum;` `    ``modifyBSTUtil(root->left, sum);``}` `void` `modifyBST(Node* root) {``    ``int` `sum = 0;``    ``modifyBSTUtil(root, &sum);``}` `void` `inorder(Node* root) {``    ``if` `(root == NULL) ``return``;` `    ``inorder(root->left);``    ``cout << root->data << ``" "``;``    ``inorder(root->right);``}` `int` `main() {``    ``Node* root = newNode(50);``    ``root->left = newNode(30);``    ``root->right = newNode(70);``    ``root->left->left = newNode(20);``    ``root->left->right = newNode(40);``    ``root->right->left = newNode(60);``    ``root->right->right = newNode(80);``    `    `    ``modifyBST(root);` `  ` `    ``inorder(root);` `    ``return` `0;``}`

Java

 `class` `Node {``    ``int` `data;``    ``Node left, right;` `    ``Node(``int` `data) {``        ``this``.data = data;``        ``left = right = ``null``;``    ``}``}` `public` `class` `Main{``    ``static` `void` `modifyBSTUtil(Node root, ``int``[] sum) {``        ``if` `(root == ``null``)``            ``return``;` `        ``modifyBSTUtil(root.right, sum);` `        ``sum[``0``] = sum[``0``] + root.data;``        ``root.data = sum[``0``];` `        ``modifyBSTUtil(root.left, sum);``    ``}` `    ``static` `void` `modifyBST(Node root) {``        ``int``[] sum = ``new` `int``[``1``];``        ``modifyBSTUtil(root, sum);``    ``}` `    ``static` `void` `inorder(Node root) {``        ``if` `(root == ``null``)``            ``return``;` `        ``inorder(root.left);``        ``System.out.print(root.data + ``" "``);``        ``inorder(root.right);``    ``}` `    ``public` `static` `void` `main(String[] args) {``        ``Node root = ``new` `Node(``50``);``        ``root.left = ``new` `Node(``30``);``        ``root.right = ``new` `Node(``70``);``        ``root.left.left = ``new` `Node(``20``);``        ``root.left.right = ``new` `Node(``40``);``        ``root.right.left = ``new` `Node(``60``);``        ``root.right.right = ``new` `Node(``80``);` `        ``modifyBST(root);` `        ``inorder(root);``    ``}``}`

Python3

 `class` `Node:``    ``def` `__init__(``self``, data):``        ``self``.data ``=` `data``        ``self``.left ``=` `None``        ``self``.right ``=` `None` `def` `newNode(data):``    ``node ``=` `Node(data)``    ``return` `node` `def` `modifyBSTUtil(root, ``sum``):``    ``if` `root ``is` `None``:``        ``return``    ` `    ``modifyBSTUtil(root.right, ``sum``)``    ` `    ``sum``[``0``] ``+``=` `root.data``    ``root.data ``=` `sum``[``0``]``    ` `    ``modifyBSTUtil(root.left, ``sum``)` `def` `modifyBST(root):``    ``sum` `=` `[``0``]``    ``modifyBSTUtil(root, ``sum``)` `def` `inorder(root):``    ``if` `root ``is` `None``:``        ``return``    ` `    ``inorder(root.left)``    ``print``(root.data, end``=``' '``)``    ``inorder(root.right)` `if` `__name__ ``=``=` `'__main__'``:``    ``root ``=` `newNode(``50``)``    ``root.left ``=` `newNode(``30``)``    ``root.right ``=` `newNode(``70``)``    ``root.left.left ``=` `newNode(``20``)``    ``root.left.right ``=` `newNode(``40``)``    ``root.right.left ``=` `newNode(``60``)``    ``root.right.right ``=` `newNode(``80``)``    ` `    ``modifyBST(root)``    ` `    ``inorder(root)`

C#

 `using` `System;` `public` `class` `Node {``    ``public` `int` `data;``    ``public` `Node left, right;` `    ``public` `Node(``int` `data) {``        ``this``.data = data;``        ``left = right = ``null``;``    ``}``}` `public` `class` `GFG {``    ``static` `void` `ModifyBSTUtil(Node root, ``ref` `int` `sum) {``        ``if` `(root == ``null``)``            ``return``;` `        ``ModifyBSTUtil(root.right, ``ref` `sum);` `        ``sum = sum + root.data;``        ``root.data = sum;` `        ``ModifyBSTUtil(root.left, ``ref` `sum);``    ``}` `    ``static` `void` `ModifyBST(Node root) {``        ``int` `sum = 0;``        ``ModifyBSTUtil(root, ``ref` `sum);``    ``}` `    ``static` `void` `Inorder(Node root) {``        ``if` `(root == ``null``)``            ``return``;` `        ``Inorder(root.left);``        ``Console.Write(root.data + ``" "``);``        ``Inorder(root.right);``    ``}` `    ``public` `static` `void` `Main(``string``[] args) {``        ``Node root = ``new` `Node(50);``        ``root.left = ``new` `Node(30);``        ``root.right = ``new` `Node(70);``        ``root.left.left = ``new` `Node(20);``        ``root.left.right = ``new` `Node(40);``        ``root.right.left = ``new` `Node(60);``        ``root.right.right = ``new` `Node(80);` `        ``ModifyBST(root);` `        ``Inorder(root);``    ``}``}`

Javascript

 `// Define a Node class with a constructor that sets the data, left, and right properties.``class Node {``    ``constructor(data) {``        ``this``.data = data;``        ``this``.left = ``this``.right = ``null``;``    ``}``}` `// Create a new Node with the given data.``function` `newNode(data) {``    ``let node = ``new` `Node(data);``    ``return` `node;``}` `// Utility function to modify the BST (binary search tree).``function` `modifyBSTUtil(root, sum) {``    ``// If the root node is null, return.``    ``if` `(root == ``null``) ``return``;` `    ``// Recursively call modifyBSTUtil on the right subtree.``    ``modifyBSTUtil(root.right, sum);` `    ``// Add the data value of the current node to the sum.``    ``sum[0] = sum[0] + root.data;``    ``// Set the data value of the current node to the sum.``    ``root.data = sum[0];` `    ``// Recursively call modifyBSTUtil on the left subtree.``    ``modifyBSTUtil(root.left, sum);``}` `// Function to modify the BST by calling modifyBSTUtil with an initial sum of 0.``function` `modifyBST(root) {``    ``let sum = [0];``    ``modifyBSTUtil(root, sum);``}` `// Function to perform an inorder traversal of the BST and print the values.``function` `inorder(root) {``    ``// If the root node is null, return.``    ``if` `(root == ``null``) ``return``;` `    ``// Recursively call inorder on the left subtree.``    ``inorder(root.left);``    ``// Print the data value of the current node.``    ``console.log(root.data + ``" "``);``    ``// Recursively call inorder on the right subtree.``    ``inorder(root.right);``}` `// Create a new BST with the given nodes.``let root = newNode(50);``root.left = newNode(30);``root.right = newNode(70);``root.left.left = newNode(20);``root.left.right = newNode(40);``root.right.left = newNode(60);``root.right.right = newNode(80);` `// Modify the BST.``modifyBST(root);` `// Perform an inorder traversal and print the values.``inorder(root);`

Output

```350 330 300 260 210 150 80

```

Time Complexity: O(n), where n is the number of nodes in the BST.
Auxiliary Space: O(h), where h is the height of the BST.