# Split a BST into two balanced BSTs based on a value K

Given a Binary Search tree and an integer K, we have to split the tree into two Balanced Binary Search Tree, where BST-1 consists of all the nodes which are less than K and BST-2 consists of all the nodes which are greater than or equal to K.

Note: Arrangement of the nodes may be anything but both BST should be Balanced.

Examples:

```Input:
40
/   \
20     50
/  \      \
10   35     60
/      /
25      55
K = 35
Output:
First BST: 10 20 25
Second BST: 35 40 50 55 60
Explanation:
After splitting above BST
about given value K = 35
First Balanced Binary Search Tree is
20
/   \
10     25
Second Balanced Binary Search Tree is
50
/   \
35     55
\      \
40     60
OR
40
/   \
35     55
/   \
50    60

Input:
100
/   \
20     500
/  \
10   30
\
40
K = 50
Output:
First BST: 10 20 30 40
Second BST: 100 500
Explanation:
After splitting above BST
about given value K = 50
First Balanced Binary Search Tree is
20
/   \
10     30
\
40
Second Balanced Binary Search Tree is
100
\
500
```

Approach:

1. First store the inorder traversal of given BST in an array
2. Then, split this array about given value K
3. Now construct first balanced BST by first splitting part and second BST by second splitting part, using the approach used in this article.

Below is the implementation of the above approach:

 `// C++ program to split a BST into ` `// two balanced BSTs based on a value K ` ` `  `#include ` `using` `namespace` `std; ` ` `  `// Structure of each node of BST ` `struct` `node { ` `    ``int` `key; ` `    ``struct` `node *left, *right; ` `}; ` ` `  `// A utility 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; ` `} ` ` `  `// A utility function to insert a new ` `// node with given key in BST ` `struct` `node* insert(``struct` `node* node, ` `                    ``int` `key) ` `{ ` `    ``// If the tree is empty, return a new node ` `    ``if` `(node == NULL) ` `        ``return` `newNode(key); ` ` `  `    ``// Otherwise, recur down the tree ` `    ``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 return the splitting ` `// index of the array ` `int` `getSplittingIndex(``int` `inOrder[], ` `                      ``int` `index, ``int` `k) ` `{ ` `    ``for` `(``int` `i = 0; i < index; i++) { ` `        ``if` `(inOrder[i] >= k) { ` `            ``return` `i - 1; ` `        ``} ` `    ``} ` `    ``return` `index - 1; ` `} ` ` `  `// Function to create the Balanced ` `// Binary search tree ` `node* createBST(``int` `inOrder[], ` `                ``int` `start, ``int` `end) ` `{ ` `    ``// Base Condition ` `    ``if` `(start > end) { ` `        ``return` `NULL; ` `    ``} ` ` `  `    ``// Calculate the mid of the array ` `    ``int` `mid = (start + end) / 2; ` `    ``node* t = newNode(inOrder[mid]); ` ` `  `    ``// Recursive call for left child ` `    ``t->left = createBST(inOrder, ` `                        ``start, mid - 1); ` ` `  `    ``// Recursive call for right child ` `    ``t->right = createBST(inOrder, ` `                         ``mid + 1, end); ` ` `  `    ``// Return newly created Balanced ` `    ``// Binary Search Tree ` `    ``return` `t; ` `} ` ` `  `// Function to traverse the tree ` `// in inorder fashion ` `void` `inorderTrav(node* root) ` `{ ` `    ``if` `(root == NULL) ` `        ``return``; ` `    ``inorderTrav(root->left); ` `    ``cout << root->key << ``" "``; ` `    ``inorderTrav(root->right); ` `} ` ` `  `// Function to split the BST ` `// into two Balanced BST ` `void` `splitBST(node* root, ``int` `k) ` `{ ` ` `  `    ``// Print the original BST ` `    ``cout << ``"Original BST : "``; ` `    ``if` `(root != NULL) { ` `        ``inorderTrav(root); ` `    ``} ` `    ``else` `{ ` `        ``cout << ``"NULL"``; ` `    ``} ` `    ``cout << endl; ` ` `  `    ``// Store the size of BST1 ` `    ``int` `numNode = sizeOfTree(root); ` ` `  `    ``// Take auxiliary array for storing ` `    ``// The inorder traversal of BST1 ` `    ``int` `inOrder[numNode + 1]; ` `    ``int` `index = 0; ` ` `  `    ``// Function call for storing ` `    ``// inorder traversal of BST1 ` `    ``storeInorder(root, inOrder, index); ` ` `  `    ``// Function call for getting ` `    ``// splitting index ` `    ``int` `splitIndex ` `        ``= getSplittingIndex(inOrder, ` `                            ``index, k); ` ` `  `    ``node* root1 = NULL; ` `    ``node* root2 = NULL; ` ` `  `    ``// Creation of first Balanced ` `    ``// Binary Search Tree ` `    ``if` `(splitIndex != -1) ` `        ``root1 = createBST(inOrder, 0, ` `                          ``splitIndex); ` ` `  `    ``// Creation of Second Balanced ` `    ``// Binary Search Tree ` `    ``if` `(splitIndex != (index - 1)) ` `        ``root2 = createBST(inOrder, ` `                          ``splitIndex + 1, ` `                          ``index - 1); ` ` `  `    ``// Print two Balanced BSTs ` `    ``cout << ``"First BST : "``; ` `    ``if` `(root1 != NULL) { ` `        ``inorderTrav(root1); ` `    ``} ` `    ``else` `{ ` `        ``cout << ``"NULL"``; ` `    ``} ` `    ``cout << endl; ` ` `  `    ``cout << ``"Second BST : "``; ` `    ``if` `(root2 != NULL) { ` `        ``inorderTrav(root2); ` `    ``} ` `    ``else` `{ ` `        ``cout << ``"NULL"``; ` `    ``} ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``/*  BST  ` `             ``5 ` `           ``/   \       ` `          ``3     7      ` `         ``/ \   / \     ` `         ``2  4  6  8   ` `    ``*/` `    ``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 = 5; ` ` `  `    ``// Function to split BST ` `    ``splitBST(root, k); ` ` `  `    ``return` `0; ` `} `

Output:

```Original BST : 2 3 4 5 6 7 8
First BST : 2 3 4
Second BST : 5 6 7 8
```

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