Convert BST to Min Heap

Given a binary search tree which is also a complete binary tree. The problem is to convert the given BST into a Min Heap with the condition that all the values in the left subtree of a node should be less than all the values in the right subtree of the node. This condition is applied to all the nodes, in the resultant converted Min Heap.

Examples:

Input:

Output:

Explanation: The given BST has been transformed into a Min Heap. All the nodes in the Min Heap satisfies the given condition, that is, values in the left subtree of a node should be less than the values in the right subtree of the node.

Approach:

The idea is to store the inorder traversal of the BST in array and then do preorder traversal of the BST and while doing preorder traversal copy the values of inorder traversal into the current node, as copying the sorted elements while doing preorder traversal will make sure that a min-heap is constructed with the condition that all the values in the left subtree of a node are less than all the values in the right subtree of the node.

Follow the below steps to solve the problem:

Create an array arr of size n, where n is the number of nodes in the given BST.
Perform the inorder traversal of the BST and copy the node values in the arr[] in sorted order.
Now perform the preorder traversal of the tree.
While traversing the root during the preorder traversal, one by one copy the values from the array arr[] to the nodes of the BST.

Below is the implementation of the above approach:

C++

// C++ implementation to convert the given
// BST to Min Heap
#include <bits/stdc++.h>
using namespace std;

class Node {
public:
    int data;
    Node* left;
    Node* right;

    Node(int x) {
        data = x;
        left = right = nullptr;
    }
};

// Function to perform inorder traversal of BST
// and store the node values in a vector
void inorderTraversal(Node* root, 
                        vector<int>& inorderArr) {
    if (root == nullptr) {
        return;
    }
  
    // Traverse the left subtree Store the current 
    // node value Traverse the right subtree
    inorderTraversal(root->left, inorderArr);  
    inorderArr.push_back(root->data);          
    inorderTraversal(root->right, inorderArr); 
}

// Function to perform preorder traversal of the tree
// and copy the values from the inorder array to nodes
void preorderFill(Node* root, vector<int>& inorderArr, 
                                          int& index) {
    if (root == nullptr) {
        return;
    }

    // Copy the next element from the inorder array
    root->data = inorderArr[index++];

    // Fill left and right subtree
    preorderFill(root->left, inorderArr, index);  
    preorderFill(root->right, inorderArr, index);
}

// Function to convert BST to Min Heap
void convertBSTtoMinHeap(Node* root) {
  
    vector<int> inorderArr;

    // Step 1: Perform inorder traversal 
    // to store values in sorted order
    inorderTraversal(root, inorderArr);

    int index = 0;

    // Step 2: Perform preorder traversal and 
    // fill nodes with inorder values
    preorderFill(root, inorderArr, index);
}

// Function to print preorder traversal of the tree
void preorderPrint(Node* root) {
    if (root == nullptr) {
        return;
    }

    cout << root->data << " "; 
    preorderPrint(root->left); 
    preorderPrint(root->right); 
}

int main() {
  
    // Constructing the Binary Search Tree (BST)
    //          4
    //        /   \
    //       2     6
    //      / \   / \
    //     1   3 5   7
    Node* root = new Node(4);
    root->left = new Node(2);
    root->right = new Node(6);
    root->left->left = new Node(1);
    root->left->right = new Node(3);
    root->right->left = new Node(5);
    root->right->right = new Node(7);

    convertBSTtoMinHeap(root);
    preorderPrint(root);

    return 0;
}

Java

// Java implementation to convert the given
// BST to Min Heap
import java.util.ArrayList;

class Node {
    int data;
    Node left, right;

    Node(int x) {
        data = x;
        left = right = null;
    }
}

class GfG {

    // Function to perform inorder traversal of the BST
    // and store node values in an ArrayList
    static void inorderTraversal(Node root, 
                      ArrayList<Integer> inorderArr) {
        if (root == null) {
            return;
        }

        // Traverse the left subtree, store 
        // the current node value,
        // and traverse the right subtree
        inorderTraversal(root.left, inorderArr);
        inorderArr.add(root.data);
        inorderTraversal(root.right, inorderArr);
    }

    // Function to perform preorder traversal of the tree
    // and copy the values from the inorder 
    // ArrayList to the nodes
    static void preorderFill(Node root, 
            ArrayList<Integer> inorderArr, int[] index) {
        if (root == null) {
            return;
        }

        // Copy the next element from the inorder array
        root.data = inorderArr.get(index[0]++);

        // Fill left and right subtree
        preorderFill(root.left, inorderArr, index);
        preorderFill(root.right, inorderArr, index);
    }

    // Function to convert BST to Min Heap
    static void convertBSTtoMinHeap(Node root) {
        ArrayList<Integer> inorderArr 
                             = new ArrayList<>();

        // Step 1: Perform inorder traversal to
        // store values in sorted order
        inorderTraversal(root, inorderArr);

        // Using array to keep index as a reference
        int[] index = {0};  

        // Step 2: Perform preorder traversal and 
        // fill nodes with inorder values
        preorderFill(root, inorderArr, index);
    }

    static void preorderPrint(Node root) {
        if (root == null) {
            return;
        }

        System.out.print(root.data + " ");
        preorderPrint(root.left);
        preorderPrint(root.right);
    }

    public static void main(String[] args) {
      
        // Constructing the Binary Search Tree (BST)
        //          4
        //        /   \
        //       2     6
        //      / \   / \
        //     1   3 5   7
        Node root = new Node(4);
        root.left = new Node(2);
        root.right = new Node(6);
        root.left.left = new Node(1);
        root.left.right = new Node(3);
        root.right.left = new Node(5);
        root.right.right = new Node(7);

        convertBSTtoMinHeap(root);
        preorderPrint(root);
    }
}

Python

# Python implementation to convert the given
# BST to Min Heap
class Node:
    def __init__(self, data):
        self.data = data
        self.left = None
        self.right = None

# Function to perform inorder traversal of the BST
# and store the node values in a list
def inorder_traversal(root, inorder_arr):
    if root is None:
        return

    # Traverse the left subtree, store the current
    # node value, and traverse the right subtree
    inorder_traversal(root.left, inorder_arr)
    inorder_arr.append(root.data)
    inorder_traversal(root.right, inorder_arr)

# Function to perform preorder traversal of the tree
# and copy the values from the inorder list to the nodes
def preorder_fill(root, inorder_arr, index):
    if root is None:
        return index

    # Copy the next element from the inorder list
    root.data = inorder_arr[index]
    index += 1

    # Fill left and right subtree
    index = preorder_fill(root.left, inorder_arr, index)
    index = preorder_fill(root.right, inorder_arr, index)
    return index

# Function to convert BST to Min Heap
def bstToMinHeap(root):
    inorder_arr = []

    # Step 1: Perform inorder traversal to 
    # store values in sorted order
    inorder_traversal(root, inorder_arr)

    # Step 2: Perform preorder traversal 
    # and fill nodes with inorder values
    preorder_fill(root, inorder_arr, 0)

# Function to print preorder traversal of the tree
def preorder_print(root):
    if root is None:
        return

    print(root.data, end=" ")
    preorder_print(root.left)
    preorder_print(root.right)

if __name__ == "__main__":
  
    # Constructing the Binary Search Tree (BST)
    #          4
    #        /   \
    #       2     6
    #      / \   / \
    #     1   3 5   7
    root = Node(4)
    root.left = Node(2)
    root.right = Node(6)
    root.left.left = Node(1)
    root.left.right = Node(3)
    root.right.left = Node(5)
    root.right.right = Node(7)

    bstToMinHeap(root)
    preorder_print(root)

// C# implementation to convert the given
// BST to Min Heap
using System;
using System.Collections.Generic;

class Node {
    public int data;
    public Node left, right;

    public Node(int x) {
        data = x;
        left = right = null;
    }
}

class GfG {

    // Function to perform inorder traversal of the BST
    // and store the node values in a List
    static void InorderTraversal(Node root, 
                             List<int> inorderArr) {
        if (root == null) {
            return;
        }

        // Traverse the left subtree, store the 
        // current node value, and traverse 
        // the right subtree
        InorderTraversal(root.left, inorderArr);
        inorderArr.Add(root.data);
        InorderTraversal(root.right, inorderArr);
    }

    // Function to perform preorder traversal 
    // of the tree and copy the values from the inorder 
    // list to the nodes
    static void PreorderFill(Node root,
                   List<int> inorderArr, ref int index) {
        if (root == null) {
            return;
        }

        // Copy the next element from the inorder list
        root.data = inorderArr[index++];
        
        // Fill left and right subtree
        PreorderFill(root.left, inorderArr, ref index);
        PreorderFill(root.right, inorderArr, ref index);
    }

    // Function to convert BST to Min Heap
    static void ConvertBSTToMinHeap(Node root) {
        List<int> inorderArr = new List<int>();

        // Step 1: Perform inorder traversal to
        // store values in sorted order
        InorderTraversal(root, inorderArr);

        int index = 0;  

        // Step 2: Perform preorder traversal 
        // and fill nodes with inorder values
        PreorderFill(root, inorderArr, ref index);
    }

    // Function to print preorder traversal of the tree
    static void PreorderPrint(Node root) {
        if (root == null) {
            return;
        }

        Console.Write(root.data + " ");
        PreorderPrint(root.left);
        PreorderPrint(root.right);
    }

    public static void Main() {
      
        // Constructing the Binary Search Tree (BST)
        //          4
        //        /   \
        //       2     6
        //      / \   / \
        //     1   3 5   7
        Node root = new Node(4);
        root.left = new Node(2);
        root.right = new Node(6);
        root.left.left = new Node(1);
        root.left.right = new Node(3);
        root.right.left = new Node(5);
        root.right.right = new Node(7);

        ConvertBSTToMinHeap(root);
        PreorderPrint(root);
    }
}

JavaScript

// Javascript implementation to convert the given
// BST to Min Heap
class Node {
    constructor(data) {
        this.data = data;
        this.left = null;
        this.right = null;
    }
}

// Function to perform inorder traversal of the BST
// and store the node values in an array
function inorderTraversal(root, inorderArr) {
    if (root === null) {
        return;
    }

    // Traverse the left subtree, store the 
    // current node value, and traverse
    // the right subtree
    inorderTraversal(root.left, inorderArr);
    inorderArr.push(root.data);
    inorderTraversal(root.right, inorderArr);
}

// Function to perform preorder traversal of the tree
// and copy the values from the inorder 
// array to the nodes
function preorderFill(root, inorderArr, index) {
    if (root === null) {
        return index;
    }

    // Copy the next element from the inorder array
    root.data = inorderArr[index];
    index += 1;

    // Fill left and right subtree
    index = preorderFill(root.left, inorderArr, index);
    index = preorderFill(root.right, inorderArr, index);
    
    return index;
}

// Function to convert BST to Min Heap
function convertBSTtoMinHeap(root) {
    let inorderArr = [];

    // Step 1: Perform inorder traversal to 
    // store values in sorted order
    inorderTraversal(root, inorderArr);

    // Step 2: Perform preorder traversal 
    // and fill nodes with inorder values
    preorderFill(root, inorderArr, 0);
}

// Function to print preorder traversal of the tree
function preorderPrint(root) {
    if (root === null) {
        return;
    }

    console.log(root.data + " ");
    preorderPrint(root.left);
    preorderPrint(root.right);
}

// Constructing the Binary Search Tree (BST)
//          4
//        /   \
//       2     6
//      / \   / \
//     1   3 5   7
let root = new Node(4);
root.left = new Node(2);
root.right = new Node(6);
root.left.left = new Node(1);
root.left.right = new Node(3);
root.right.left = new Node(5);
root.right.right = new Node(7);

convertBSTtoMinHeap(root);
preorderPrint(root);

Output

1 2 3 4 5 6 7

Time Complexity: O(n), since inorder traversal and preorder filling both take O(n), where n is the number of nodes in the tree.
Auxiliary Space: O(n), space is used for storing the inorder traversal in the array, also recursion stack uses O(h) space, where h is the height of the tree (O(log n) for balanced trees, O(n) for skewed trees).

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