将 BST 转换为最大堆

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 转换为特殊最大堆，条件是节点左子树中的所有值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大堆中的所有节点。
例子：

Input :          4
               /   \
              2     6
            /  \   /  \
           1   3  5    7  
 
Output :       7
             /   \
            3     6
          /   \  /   \
         1    2 4     5
The given BST has been transformed into a
Max Heap.
All the nodes in the Max 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. 

先决条件：二叉搜索树 |堆
方法
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.进行BST的中序遍历，将arr[]中的节点值复制到sorted
命令。
3. 现在执行树的后序遍历。
4.在后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 a given
// BST to Max Heap
#include 
using namespace std;
 
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 postorder traversal
// of the given tree
void postorderTraversal(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);
}
 
void BSTToMaxHeap(Node* root, vector arr, int* i)
{
    if (root == NULL)
        return;
 
    // recur on left subtree
    BSTToMaxHeap(root->left, arr, i);
 
    // recur on right subtree
    BSTToMaxHeap(root->right, arr, i);
 
    // copy data at index 'i' of 'arr' to
    // the node
    root->data = arr[++*i];
}
 
// Utility function to convert the given BST to
// MAX HEAP
void convertToMaxHeapUtil(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 MAX HEAP conversion
    BSTToMaxHeap(root, arr, &i);
}
 
// Function to Print Postorder Traversal of the tree
void postorderTraversal(Node* root)
{
    if (!root)
        return;
 
    // recur on left subtree
    postorderTraversal(root->left);
 
    // then recur on right subtree
    postorderTraversal(root->right);
 
    // print the root's data
    cout << root->data << " ";
}
 
// Driver Code
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);
 
    convertToMaxHeapUtil(root);
    cout << "Postorder Traversal of Tree:" << endl;
    postorderTraversal(root);
 
    return 0;
}

Java

// Java implementation to convert a given
// BST to Max Heap
import java.util.*;
 
class GFG
{
 
static int i;
static class Node
{
    int data;
    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 for the inorder traversal of the tree
// so as to store the node values in 'arr' in
// sorted order
static 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.add(root.data);
 
    // now recur for right subtree
    inorderTraversal(root.right, arr);
}
 
static void BSTToMaxHeap(Node root, Vector arr)
{
    if (root == null)
        return;
 
    // recur on left subtree
    BSTToMaxHeap(root.left, arr);
 
    // recur on right subtree
    BSTToMaxHeap(root.right, arr);
 
    // copy data at index 'i' of 'arr' to
    // the node
    root.data = arr.get(i++);
}
 
// Utility function to convert the given BST to
// MAX HEAP
static void convertToMaxHeapUtil(Node root)
{
    // vector to store the data of all the
    // nodes of the BST
    Vector arr = new Vector();
    int i = -1;
 
    // inorder traversal to populate 'arr'
    inorderTraversal(root, arr);
 
    // BST to MAX HEAP conversion
    BSTToMaxHeap(root, arr);
}
 
// Function to Print Postorder Traversal of the tree
static void postorderTraversal(Node root)
{
    if (root == null)
        return;
 
    // recur on left subtree
    postorderTraversal(root.left);
 
    // then recur on right subtree
    postorderTraversal(root.right);
 
    // print the root's data
    System.out.print(root.data + " ");
}
 
// Driver Code
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);
 
    convertToMaxHeapUtil(root);
    System.out.print("Postorder Traversal of Tree:" +"\n");
    postorderTraversal(root);
 
}
}
 
// This code is contributed by 29AjayKumar

Python3

# Python3 implementation to convert a given
# BST to Max Heap
i = 0
class Node:
    def __init__(self):
        self.data = 0
        self.left = None
        self.right = None
 
# Helper function that allocates a new node
# with the given data and None left and right
# pointers.
def getNode(data):
 
    newNode = Node()
    newNode.data = data
    newNode.left = newNode.right = None
    return newNode
 
arr = []
 
# Function for the inorder traversal of the tree
# so as to store the node values in 'arr' in
# sorted order
def inorderTraversal( root):
 
    if (root == None):
        return arr
 
    # first recur on left subtree
    inorderTraversal(root.left)
 
    # then copy the data of the node
    arr.append(root.data)
 
    # now recur for right subtree
    inorderTraversal(root.right)
 
def BSTToMaxHeap(root):
 
    global i
    if (root == None):
        return None
 
    # recur on left subtree
    root.left = BSTToMaxHeap(root.left)
 
    # recur on right subtree
    root.right = BSTToMaxHeap(root.right)
 
    # copy data at index 'i' of 'arr' to
    # the node
    root.data = arr[i]
    i = i + 1
    return root
 
# Utility function to convert the given BST to
# MAX HEAP
def convertToMaxHeapUtil( root):
    global i
     
    # vector to store the data of all the
    # nodes of the BST
    i = 0
 
    # inorder traversal to populate 'arr'
    inorderTraversal(root)
 
    # BST to MAX HEAP conversion
    root = BSTToMaxHeap(root)
    return root
 
# Function to Print Postorder Traversal of the tree
def postorderTraversal(root):
 
    if (root == None):
        return
 
    # recur on left subtree
    postorderTraversal(root.left)
 
    # then recur on right subtree
    postorderTraversal(root.right)
 
    # print the root's data
    print(root.data ,end= " ")
 
# Driver Code
 
# BST formation
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)
 
root = convertToMaxHeapUtil(root)
print("Postorder Traversal of Tree:" )
postorderTraversal(root)
 
# This code is contributed by Arnab Kundu

Javascript

// Javascript implementation to convert a given
// BST to Max Heap
 
let i = 0;
 
class Node
{
    constructor()
    {
        this.data = 0;
        this.left = this.right = null;
    }
}
 
/* Helper function that allocates a new node
   with the given data and null left and right
   pointers. */
function getNode(data)
{
    let newNode = new Node();
    newNode.data = data;
    newNode.left = newNode.right = null;
    return newNode;
}
 
// Function for the inorder traversal of the tree
// so as to store the node values in 'arr' in
// sorted order
function inorderTraversal(root, arr)
{
    if (root == null)
        return;
    
    // first recur on left subtree
    inorderTraversal(root.left, arr);
    
    // then copy the data of the node
    arr.push(root.data);
    
    // now recur for right subtree
    inorderTraversal(root.right, arr);
}
 
function BSTToMaxHeap(root,arr)
{
     
    if (root == null)
        return;
    
    // recur on left subtree
    BSTToMaxHeap(root.left, arr);
    
    // recur on right subtree
    BSTToMaxHeap(root.right, arr);
    
    // copy data at index 'i' of 'arr' to
    // the node
     
    root.data = arr[i++];
     
}
 
// Utility function to convert the given BST to
// MAX HEAP
function convertToMaxHeapUtil(root)
{
    // vector to store the data of all the
    // nodes of the BST
    let arr = [];
     
    
    // inorder traversal to populate 'arr'
    inorderTraversal(root, arr);
    
    // BST to MAX HEAP conversion
    BSTToMaxHeap(root, arr);
     
}
 
// Function to Print Postorder Traversal of the tree
function postorderTraversal(root)
{
    if (root == null)
        return;
    
    // recur on left subtree
    postorderTraversal(root.left);
    
    // then recur on right subtree
    postorderTraversal(root.right);
    
    // print the root's data
    document.write(root.data + " ");
}
 
// Driver Code
// BST formation
let 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);
 
convertToMaxHeapUtil(root);
document.write("Postorder Traversal of Tree:" +"\n");
postorderTraversal(root);
 
// This code is contributed by rag2127

输出：

Postorder Traversal of Tree:
1 2 3 4 5 6 7 

时间复杂度：O(n)
辅助空间：O(n)
其中，n 是树中的节点数

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