将BST转换为Max Heap

给定二叉搜索树，它也是完整的二叉树。问题是将给定的BST转换为“特殊最大堆”，其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。此条件适用于如此转换后的“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.执行BST的有序遍历，并按排序方式将节点值复制到arr []中
命令。
3.现在执行树的后置遍历。
4.在后遍历遍历中遍历根时，将值从数组arr []复制到节点。

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

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