将 BST 转换为最小堆

给定一个二叉搜索树，它也是一棵完全二叉树。问题是将给定的 BST 转换为最小堆，条件是节点左子树中的所有值都应小于节点右子树中的所有值。此条件应用于如此转换的最小堆中的所有节点。
例子：

Input :          4
               /   \
              2     6
            /  \   /  \
           1   3  5    7  

Output :        1
              /   \
             2     5
           /  \   /  \
          3   4  6    7 

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. 

1. 创建一个大小为n的数组arr[] ，其中 n 是给定 BST 中的节点数。
2. 执行 BST 的中序遍历并按排序顺序复制arr[]中的节点值。
3. 现在执行树的前序遍历。
4. 在前序遍历过程中遍历根的同时，将数组arr[]中的值一一复制到节点中。

C++

// C++ implementation to convert the given
// BST to Min Heap
#include 
using namespace std;
 
// structure of a node of BST
struct Node
{
    int data;
    Node *left, *right;
};
 
/* Helper function that allocates a new node
   with the given data and NULL left and right
   pointers. */
struct Node* getNode(int data)
{
    struct Node *newNode = new Node;
    newNode->data = data;
    newNode->left = newNode->right = NULL;
    return newNode;
}
 
// function prototype for preorder traversal
// of the given tree
void preorderTraversal(Node*);
 
// function for the inorder traversal of the tree
// so as to store the node values in 'arr' in
// sorted order
void inorderTraversal(Node *root, vector& arr)
{
    if (root == NULL)
        return;
 
    // first recur on left subtree
    inorderTraversal(root->left, arr);
 
    // then copy the data of the node
    arr.push_back(root->data);
 
    // now recur for right subtree
    inorderTraversal(root->right, arr);
}
 
// function to convert the given BST to MIN HEAP
// performs preorder traversal of the tree
void BSTToMinHeap(Node *root, vector arr, int *i)
{
    if (root == NULL)
        return;
 
    // first copy data at index 'i' of 'arr' to
    // the node
    root->data = arr[++*i];
 
    // then recur on left subtree
    BSTToMinHeap(root->left, arr, i);
 
    // now recur on right subtree
    BSTToMinHeap(root->right, arr, i);
}
 
// utility function to convert the given BST to
// MIN HEAP
void convertToMinHeapUtil(Node *root)
{
    // vector to store the data of all the
    // nodes of the BST
    vector arr;
    int i = -1;
 
    // inorder traversal to populate 'arr'
    inorderTraversal(root, arr);
 
    // BST to MIN HEAP conversion
    BSTToMinHeap(root, arr, &i);
}
 
// function for the preorder traversal of the tree
void preorderTraversal(Node *root)
{
    if (!root)
        return;
 
    // first print the root's data
    cout << root->data << " ";
 
    // then recur on left subtree
    preorderTraversal(root->left);
 
    // now recur on right subtree
    preorderTraversal(root->right);
}
 
// Driver program to test above
int main()
{
    // BST formation
    struct Node *root = getNode(4);
    root->left = getNode(2);
    root->right = getNode(6);
    root->left->left = getNode(1);
    root->left->right = getNode(3);
    root->right->left = getNode(5);
    root->right->right = getNode(7);
 
    convertToMinHeapUtil(root);
    cout << "Preorder Traversal:" << endl;
    preorderTraversal(root);
 
    return 0;
}

Java

// Java implementation to convert the given
// BST to Min Heap
import java.util.ArrayList;
 
class Gfg {
     
    static class Node{
 
 
        int data;
        Node left,right;
         
        // Constructor
        Node(){
            this.data = 0;
            this.left = this.right = null;
        }
 
        Node(int data)
        {
            this.data = data;
            this.left = this.right = null;
 
        }
    }
 
 
    private static void preOrder(Node root)
    {
        if(root==null)
            return ;
        System.out.print(root.data + " ");
        preOrder(root.left);
        preOrder(root.right);
    }
 
    private static void bstToArray(Node root, ArrayList arr){
       // ArrayLIst stores elements in inorder fashion
        if(root==null)
            return;
         
            bstToArray(root.left, arr);
        
            arr.add(root.data);
         
            bstToArray(root.right, arr);
 
 
    }
 
    static int  index = 0;
    private static void arrToMinHeap(Node root, ArrayList arr){
        if(root== null)
            return;
        root.data = arr.get(index++);
 
        arrToMinHeap(root.left, arr);
        arrToMinHeap(root.right, arr);
 
         
    }
    static void convertToMinHeap(Node root)
    {
        ArrayList arr = new ArrayList();
        bstToArray(root, arr);
         
        arrToMinHeap(root,arr);
 
 
    }
 
     
// Driver program to test above
public static void main(String[] args)
{
    
    // BST formation
    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);
     
    System.out.print("Preorder Traversal Before Conversion :" +"\n");
    preOrder(root);
    convertToMinHeap(root);
     
    System.out.print("\nPreorder Traversal After Conversion :" +"\n");
    preOrder(root);
  
    }
}
 
// Contributed by : @mahi_07
 
/*
Tip : If interviewer ask not to use global index variable you can use LinkedList Instead of ArrayList
    and  use LinkedList's removeFirst() method
    So instead of this
        root.data = arr.get(index++);
    you can write
        root.data = list.removeFirst();  
    Do not forget to initialize list in converttoMinHeap function
*/

Python3

# C++ implementation to convert the
# given BST to Min Heap
 
# structure of a node of BST
class Node:
 
    # Constructor to create a new node
    def __init__(self, data):
        self.data = data
        self.left = None
        self.right = None
 
# function for the inorder traversal
# of the tree so as to store the node
# values in 'arr' in sorted order
def inorderTraversal(root, arr):
    if root == None:
        return
 
    # first recur on left subtree
    inorderTraversal(root.left, arr)
 
    # then copy the data of the node
    arr.append(root.data)
 
    # now recur for right subtree
    inorderTraversal(root.right, arr)
     
# function to convert the given
# BST to MIN HEAP performs preorder
# traversal of the tree
def BSTToMinHeap(root, arr, i):
    if root == None:
        return
 
    # first copy data at index 'i' of
    # 'arr' to the node
    i[0] += 1
    root.data = arr[i[0]]
 
    # then recur on left subtree
    BSTToMinHeap(root.left, arr, i)
 
    # now recur on right subtree
    BSTToMinHeap(root.right, arr, i)
 
# utility function to convert the
# given BST to MIN HEAP
def convertToMinHeapUtil(root):
     
    # vector to store the data of
    # all the nodes of the BST
    arr = []
    i = [-1]
 
    # inorder traversal to populate 'arr'
    inorderTraversal(root, arr);
 
    # BST to MIN HEAP conversion
    BSTToMinHeap(root, arr, i)
     
# function for the preorder traversal
# of the tree
def preorderTraversal(root):
    if root == None:
        return
 
    # first print the root's data
    print(root.data, end = " ")
 
    # then recur on left subtree
    preorderTraversal(root.left)
 
    # now recur on right subtree
    preorderTraversal(root.right)
     
# Driver Code
if __name__ == '__main__':
     
    # BST formation
    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)
 
    convertToMinHeapUtil(root)
    print("Preorder Traversal:")
    preorderTraversal(root)
 
# This code is contributed
# by PranchalK

C#

// C# implementation to convert the given
// BST to Min Heap
using System;
using System.Collections.Generic;
public class GFG
{
 
// structure of a node of BST
public
 
 class Node
{
    public
 int data;
    public
 Node left, right;
};
 
/* Helper function that allocates a new node
   with the given data and null left and right
   pointers. */
static Node getNode(int data)
{
    Node newNode = new Node();
    newNode.data = data;
    newNode.left = newNode.right = null;
    return newNode;
}
 
// function prototype for preorder traversal
// of the given tree
 
// function for the inorder traversal of the tree
// so as to store the node values in 'arr' in
// sorted order
static void inorderTraversal(Node root)
{
    if (root == null)
        return;
 
    // first recur on left subtree
    inorderTraversal(root.left);
 
    // then copy the data of the node
    arr.Add(root.data);
 
    // now recur for right subtree
    inorderTraversal(root.right);
}
 
// function to convert the given BST to MIN HEAP
// performs preorder traversal of the tree
static void BSTToMinHeap(Node root)
{
    if (root == null)
        return;
 
    // first copy data at index 'i' of 'arr' to
    // the node
    root.data = arr[++i];
 
    // then recur on left subtree
    BSTToMinHeap(root.left);
 
    // now recur on right subtree
    BSTToMinHeap(root.right);
}
static  List arr = new List();
static int i;
   
// utility function to convert the given BST to
// MIN HEAP
static void convertToMinHeapUtil(Node root)
{
   
    // vector to store the data of all the
    // nodes of the BST
     i = -1;
 
    // inorder traversal to populate 'arr'
    inorderTraversal(root);
 
    // BST to MIN HEAP conversion
    BSTToMinHeap(root);
}
 
// function for the preorder traversal of the tree
static void preorderTraversal(Node root)
{
    if (root == null)
        return;
 
    // first print the root's data
    Console.Write(root.data + " ");
 
    // then recur on left subtree
    preorderTraversal(root.left);
 
    // now recur on right subtree
    preorderTraversal(root.right);
}
 
// Driver program to test above
public static void Main(String[] args)
{
   
    // BST formation
    Node root = getNode(4);
    root.left = getNode(2);
    root.right = getNode(6);
    root.left.left = getNode(1);
    root.left.right = getNode(3);
    root.right.left = getNode(5);
    root.right.right = getNode(7);
 
    convertToMinHeapUtil(root);
    Console.Write("Preorder Traversal:" +"\n");
    preorderTraversal(root);
}
}
 
// This code contributed by Rajput-Ji

Javascript

 
      // JavaScript implementation to convert the given
      // BST to Min Heap
      // structure of a node of BST
      class Node {
        constructor() {
          this.data = 0;
          this.left = null;
          this.right = null;
        }
      }
 
      /* Helper function that allocates a new node
      with the given data and null left and right
      pointers. */
      function getNode(data) {
        var newNode = new Node();
        newNode.data = data;
        newNode.left = newNode.right = null;
        return newNode;
      }
 
      // function prototype for preorder traversal
      // of the given tree
 
      // function for the inorder traversal of the tree
      // so as to store the node values in 'arr' in
      // sorted order
      function inorderTraversal(root) {
        if (root == null) return;
 
        // first recur on left subtree
        inorderTraversal(root.left);
 
        // then copy the data of the node
        arr.push(root.data);
 
        // now recur for right subtree
        inorderTraversal(root.right);
      }
 
      // function to convert the given BST to MIN HEAP
      // performs preorder traversal of the tree
      function BSTToMinHeap(root) {
        if (root == null) return;
 
        // first copy data at index 'i' of 'arr' to
        // the node
        root.data = arr[++i];
 
        // then recur on left subtree
        BSTToMinHeap(root.left);
 
        // now recur on right subtree
        BSTToMinHeap(root.right);
      }
      var arr = [];
      var i;
 
      // utility function to convert the given BST to
      // MIN HEAP
      function convertToMinHeapUtil(root) {
        // vector to store the data of all the
        // nodes of the BST
        i = -1;
 
        // inorder traversal to populate 'arr'
        inorderTraversal(root);
 
        // BST to MIN HEAP conversion
        BSTToMinHeap(root);
      }
 
      // function for the preorder traversal of the tree
      function preorderTraversal(root) {
        if (root == null) {
          return;
        }
 
        // first print the root's data
        document.write(root.data + " ");
 
        // then recur on left subtree
        preorderTraversal(root.left);
 
        // now recur on right subtree
        preorderTraversal(root.right);
      }
 
      // Driver program to test above
      // BST formation
      var root = getNode(4);
      root.left = getNode(2);
      root.right = getNode(6);
      root.left.left = getNode(1);
      root.left.right = getNode(3);
      root.right.left = getNode(5);
      root.right.right = getNode(7);
 
      convertToMinHeapUtil(root);
      document.write("Preorder Traversal:" + "<br>");
      preorderTraversal(root);
       

输出：

Preorder Traversal:
1 2 3 4 5 6 7

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