Given a Binary Search Tree, convert it into a Min-Heap containing the same elements in O(n) time. Do this in-place.
Input: Binary Search Tree
8
/
4 12
/ /
2 6 10 14
Output - Min Heap
2
/
4 6
/ /
8 10 12 14
[Or any other tree that follows Min Heap
properties and has same keys]
If we are allowed to use extra space, we can perform inorder traversal of the tree and store the keys in an auxiliary array. As we’re doing inorder traversal on a BST, array will be sorted. Finally, we construct a complete binary tree from the sorted array. We construct the binary tree level by level and from left to right by taking next minimum element from sorted array. The constructed binary tree will be a min-Heap. This solution works in O(n) time, but is not in-place.
How to do it in-place?
The idea is to convert the binary search tree into a sorted linked list first. We can do this by traversing the BST in inorder fashion. We add nodes at the beginning of current linked list and update head of the list using pointer to head pointer. Since we insert at the beginning, to maintain sorted order, we first traverse the right subtree before the left subtree. i.e. do a reverse inorder traversal.
Finally we convert the sorted linked list into a min-Heap by setting the left and right pointers appropriately. We can do this by doing a Level order traversal of the partially built Min-Heap Tree using queue and traversing the linked list at the same time. At every step, we take the parent node from queue, make next two nodes of linked list as children of the parent node, and enqueue the next two nodes to queue. As the linked list is sorted, the min-heap property is maintained.
Below is the implementation of above idea –
C++
// Program to convert a BST into a Min-Heap // in O(n) time and in-place #include <iostream> #include <queue> using namespace std; // Node for BST/Min-Heap struct Node { int data; Node *left, *right; }; // Utility function for allocating node for BST Node* newNode(int data) { Node* node = new Node; node->data = data; node->left = node->right = NULL; return node; } // Utility function to print Min-heap level by level void printLevelOrder(Node *root) { // Base Case if (root == NULL) return; // Create an empty queue for level order traversal queue<Node *> q; q.push(root); while (!q.empty()) { int nodeCount = q.size(); while (nodeCount > 0) { Node *node = q.front(); cout << node->data << " "; q.pop(); if (node->left) q.push(node->left); if (node->right) q.push(node->right); nodeCount--; } cout << endl; } } // A simple recursive function to convert a given // Binary Search tree to Sorted Linked List // root --> Root of Binary Search Tree // head_ref --> Pointer to head node of created // linked list void BSTToSortedLL(Node* root, Node** head_ref) { // Base cases if(root == NULL) return; // Recursively convert right subtree BSTToSortedLL(root->right, head_ref); // insert root into linked list root->right = *head_ref; // Change left pointer of previous head // to point to NULL if (*head_ref != NULL) (*head_ref)->left = NULL; // Change head of linked list *head_ref = root; // Recursively convert left subtree BSTToSortedLL(root->left, head_ref); } // Function to convert a sorted Linked // List to Min-Heap. // root --> Root of Min-Heap // head --> Pointer to head node of sorted // linked list void SortedLLToMinHeap(Node* &root, Node* head) { // Base Case if (head == NULL) return; // queue to store the parent nodes queue<Node *> q; // The first node is always the root node root = head; // advance the pointer to the next node head = head->right; // set right child to NULL root->right = NULL; // add first node to the queue q.push(root); // run until the end of linked list is reached while (head) { // Take the parent node from the q and remove it from q Node* parent = q.front(); q.pop(); // Take next two nodes from the linked list and // Add them as children of the current parent node // Also in push them into the queue so that // they will be parents to the future nodes Node *leftChild = head; head = head->right; // advance linked list to next node leftChild->right = NULL; // set its right child to NULL q.push(leftChild); // Assign the left child of parent parent->left = leftChild; if (head) { Node *rightChild = head; head = head->right; // advance linked list to next node rightChild->right = NULL; // set its right child to NULL q.push(rightChild); // Assign the right child of parent parent->right = rightChild; } } } // Function to convert BST into a Min-Heap // without using any extra space Node* BSTToMinHeap(Node* &root) { // head of Linked List Node *head = NULL; // Convert a given BST to Sorted Linked List BSTToSortedLL(root, &head); // set root as NULL root = NULL; // Convert Sorted Linked List to Min-Heap SortedLLToMinHeap(root, head); } // Driver code int main() { /* Constructing below tree 8 / 4 12 / / 2 6 10 14 */ Node* root = newNode(8); root->left = newNode(4); root->right = newNode(12); root->right->left = newNode(10); root->right->right = newNode(14); root->left->left = newNode(2); root->left->right = newNode(6); BSTToMinHeap(root); /* Output - Min Heap 2 / 4 6 / / 8 10 12 14 */ printLevelOrder(root); return 0; } |
Python3
# Python3 prgroam to contrcut all unique # BSTs for keys from 1 to n # Binary Tree Node """ A utility function to create a new BST node """class newNode: # Construct to create a newNode def __init__(self, data): self.data = data self.left = None self.right = None # Utility function to print Min-heap # level by level def printLevelOrder(root): # Base Case if (root == None): return # Create an empty queue for level # order traversal q = [] q.append(root) while (len(q)): nodeCount = len(q) while (nodeCount > 0) : node = q[0] print(node.data, end = " " ) q.pop(0) if (node.left) : q.append(node.left) if (node.right) : q.append(node.right) nodeCount -= 1 print() # A simple recursive function to convert a # given Binary Search tree to Sorted Linked # List root -. Root of Binary Search Tree def BSTToSortedLL(root, head_ref): # Base cases if(root == None) : return # Recursively convert right subtree BSTToSortedLL(root.right, head_ref) # insert root into linked list root.right = head_ref[0] # Change left pointer of previous # head to point to None if (head_ref[0] != None): (head_ref[0]).left = None # Change head of linked list head_ref[0] = root # Recursively convert left subtree BSTToSortedLL(root.left, head_ref) # Function to convert a sorted Linked # List to Min-Heap. # root -. root[0] of Min-Heap # head -. Pointer to head node of # sorted linked list def SortedLLToMinHeap( root, head) : # Base Case if (head == None) : return # queue to store the parent nodes q = [] # The first node is always the # root node root[0] = head[0] # advance the pointer to the next node head[0] = head[0].right # set right child to None root[0].right = None # add first node to the queue q.append(root[0]) # run until the end of linked list # is reached while (head[0] != None) : # Take the parent node from the q # and remove it from q parent = q[0] q.pop(0) # Take next two nodes from the linked # list and Add them as children of the # current parent node. Also in push them # into the queue so that they will be # parents to the future nodes leftChild = head[0] head[0] = head[0].right # advance linked list to next node leftChild.right = None # set its right child to None q.append(leftChild) # Assign the left child of parent parent.left = leftChild if (head) : rightChild = head[0] head[0] = head[0].right # advance linked list to next node rightChild.right = None # set its right child to None q.append(rightChild) # Assign the right child of parent parent.right = rightChild # Function to convert BST into a Min-Heap # without using any extra space def BSTToMinHeap(root): # head of Linked List head = [None] # Convert a given BST to Sorted Linked List BSTToSortedLL(root, head) # set root as None root = [None] # Convert Sorted Linked List to Min-Heap SortedLLToMinHeap(root, head) return root # Driver Code if __name__ == '__main__': """ Constructing below tree 8 / 4 12 / / 2 6 10 14 """ root = newNode(8) root.left = newNode(4) root.right = newNode(12) root.right.left = newNode(10) root.right.right = newNode(14) root.left.left = newNode(2) root.left.right = newNode(6) root = BSTToMinHeap(root) """ Output - Min Heap 2 / 4 6 / / 8 10 12 14 """ printLevelOrder(*root) # This code is contributed by # Shubham Singh(SHUBHAMSINGH10) |
Output :
2 4 6 8 10 12 14
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