Check if a given Binary Tree is Heap

Given a binary tree, we need to check it has heap property or not, Binary tree need to fulfill the following two conditions for being a heap –

It should be a complete tree (i.e. all levels except last should be full).
Every node’s value should be greater than or equal to its child node (considering max-heap).

For example this tree contains heap property –

While this doesn’t –

Recommended: Please solve it on “PRACTICE” first, before moving on to the solution.

We check each of the above condition separately, for checking completeness isComplete and for checking heap isHeapUtil function are written.
Detail about isComplete function can be found here.

isHeapUtil function is written considering the following things –

Every Node can have 2 children, 0 child (last level nodes) or 1 child (there can be at most one such node).
If Node has No child then it’s a leaf node and returns true (Base case)
If Node has one child (it must be left child because it is a complete tree) then we need to compare this node with its single child only.
If the Node has both child then check heap property at Node at recur for both subtrees.
Complete code.

Implementation

C++

/* C++ program to checks if a binary tree is max heap or not */
#include <bits/stdc++.h> 
  
using namespace std; 
   
/*  Tree node structure */
struct Node 
{ 
    int key; 
    struct Node *left; 
    struct Node *right; 
}; 
   
/* Helper function that allocates a new node */
struct Node *newNode(int k) 
{ 
    struct Node *node = new Node; 
    node->key = k; 
    node->right = node->left = NULL; 
    return node; 
} 
   
/* This function counts the number of nodes in a binary tree */
unsigned int countNodes(struct Node* root) 
{ 
    if (root == NULL) 
        return (0); 
    return (1 + countNodes(root->left) + countNodes(root->right)); 
} 
   
/* This function checks if the binary tree is complete or not */
bool isCompleteUtil (struct Node* root, unsigned int index, 
                     unsigned int number_nodes) 
{ 
    // An empty tree is complete 
    if (root == NULL) 
        return (true); 
   
    // If index assigned to current node is more than 
    // number of nodes in tree, then tree is not complete 
    if (index >= number_nodes) 
        return (false); 
   
    // Recur for left and right subtrees 
    return (isCompleteUtil(root->left, 2*index + 1, number_nodes) && 
            isCompleteUtil(root->right, 2*index + 2, number_nodes)); 
} 
   
// This Function checks the heap property in the tree. 
bool isHeapUtil(struct Node* root) 
{ 
    //  Base case : single node satisfies property 
    if (root->left == NULL && root->right == NULL) 
        return (true); 
   
    //  node will be in second last level 
    if (root->right == NULL) 
    { 
        //  check heap property at Node 
        //  No recursive call , because no need to check last level 
        return (root->key >= root->left->key); 
    } 
    else
    { 
        //  Check heap property at Node and 
        //  Recursive check heap property at left and right subtree 
        if (root->key >= root->left->key && 
            root->key >= root->right->key) 
            return ((isHeapUtil(root->left)) && 
                    (isHeapUtil(root->right))); 
        else
            return (false); 
    } 
} 
   
//  Function to check binary tree is a Heap or Not. 
bool isHeap(struct Node* root) 
{ 
    // These two are used in isCompleteUtil() 
    unsigned int node_count = countNodes(root); 
    unsigned int index = 0; 
   
    if (isCompleteUtil(root, index, node_count) && isHeapUtil(root)) 
        return true; 
    return false; 
} 
   
// Driver program 
int main() 
{ 
    struct Node* root = NULL; 
    root = newNode(10); 
    root->left = newNode(9); 
    root->right = newNode(8); 
    root->left->left = newNode(7); 
    root->left->right = newNode(6); 
    root->right->left = newNode(5); 
    root->right->right = newNode(4); 
    root->left->left->left = newNode(3); 
    root->left->left->right = newNode(2); 
    root->left->right->left = newNode(1); 
   
    if (isHeap(root)) 
        cout << "Given binary tree is a Heap\n"; 
    else
        cout << "Given binary tree is not a Heap\n"; 
   
    return 0; 
} 
  
// This code is contributed by shubhamsingh10 

C

/* C program to checks if a binary tree is max heap or not */
#include<stdio.h> 
#include<stdlib.h> 
#include<stdbool.h> 
  
/*  Tree node structure */
struct Node 
{ 
    int key; 
    struct Node *left; 
    struct Node *right; 
}; 
  
/* Helper function that allocates a new node */
struct Node *newNode(int k) 
{ 
    struct Node *node = (struct Node*)malloc(sizeof(struct Node)); 
    node->key = k; 
    node->right = node->left = NULL; 
    return node; 
} 
  
/* This function counts the number of nodes in a binary tree */
unsigned int countNodes(struct Node* root) 
{ 
    if (root == NULL) 
        return (0); 
    return (1 + countNodes(root->left) + countNodes(root->right)); 
} 
  
/* This function checks if the binary tree is complete or not */
bool isCompleteUtil (struct Node* root, unsigned int index, 
                     unsigned int number_nodes) 
{ 
    // An empty tree is complete 
    if (root == NULL) 
        return (true); 
  
    // If index assigned to current node is more than 
    // number of nodes in tree, then tree is not complete 
    if (index >= number_nodes) 
        return (false); 
  
    // Recur for left and right subtrees 
    return (isCompleteUtil(root->left, 2*index + 1, number_nodes) && 
            isCompleteUtil(root->right, 2*index + 2, number_nodes)); 
} 
  
// This Function checks the heap property in the tree. 
bool isHeapUtil(struct Node* root) 
{ 
    //  Base case : single node satisfies property 
    if (root->left == NULL && root->right == NULL) 
        return (true); 
  
    //  node will be in second last level 
    if (root->right == NULL) 
    { 
        //  check heap property at Node 
        //  No recursive call , because no need to check last level 
        return (root->key >= root->left->key); 
    } 
    else
    { 
        //  Check heap property at Node and 
        //  Recursive check heap property at left and right subtree 
        if (root->key >= root->left->key && 
            root->key >= root->right->key) 
            return ((isHeapUtil(root->left)) && 
                    (isHeapUtil(root->right))); 
        else
            return (false); 
    } 
} 
  
//  Function to check binary tree is a Heap or Not. 
bool isHeap(struct Node* root) 
{ 
    // These two are used in isCompleteUtil() 
    unsigned int node_count = countNodes(root); 
    unsigned int index = 0; 
  
    if (isCompleteUtil(root, index, node_count) && isHeapUtil(root)) 
        return true; 
    return false; 
} 
  
// Driver program 
int main() 
{ 
    struct Node* root = NULL; 
    root = newNode(10); 
    root->left = newNode(9); 
    root->right = newNode(8); 
    root->left->left = newNode(7); 
    root->left->right = newNode(6); 
    root->right->left = newNode(5); 
    root->right->right = newNode(4); 
    root->left->left->left = newNode(3); 
    root->left->left->right = newNode(2); 
    root->left->right->left = newNode(1); 
  
    if (isHeap(root)) 
        printf("Given binary tree is a Heap\n"); 
    else
        printf("Given binary tree is not a Heap\n"); 
  
    return 0; 
} 

Java

/* Java program to checks if a binary tree is max heap or not */
  
// A Binary Tree node 
class Node 
{ 
    int key; 
    Node left, right; 
  
    Node(int k) 
    { 
        key = k; 
        left = right = null; 
    } 
} 
  
class Is_BinaryTree_MaxHeap 
{ 
    /* This function counts the number of nodes in a binary tree */
    int countNodes(Node root) 
    { 
        if(root==null) 
            return 0; 
        return(1 + countNodes(root.left) + countNodes(root.right)); 
    } 
      
    /* This function checks if the binary tree is complete or not */
    boolean isCompleteUtil(Node root, int index, int number_nodes) 
    { 
        // An empty tree is complete 
        if(root == null) 
            return true; 
          
        // If index assigned to current node is more than 
        // number of nodes in tree, then tree is not complete 
        if(index >= number_nodes) 
            return false; 
          
        // Recur for left and right subtrees 
        return isCompleteUtil(root.left, 2*index+1, number_nodes) &&  
               isCompleteUtil(root.right, 2*index+2, number_nodes); 
          
    } 
      
    // This Function checks the heap property in the tree. 
    boolean isHeapUtil(Node root) 
    { 
        //  Base case : single node satisfies property 
        if(root.left == null && root.right==null) 
            return true; 
          
        //  node will be in second last level 
        if(root.right == null) 
        { 
            //  check heap property at Node 
            //  No recursive call , because no need to check last level 
            return root.key >= root.left.key; 
        } 
        else
        { 
            //  Check heap property at Node and 
            //  Recursive check heap property at left and right subtree 
            if(root.key >= root.left.key && root.key >= root.right.key) 
                return isHeapUtil(root.left) && isHeapUtil(root.right); 
            else
                return false; 
        } 
    } 
      
    //  Function to check binary tree is a Heap or Not. 
    boolean isHeap(Node root) 
    { 
        if(root == null) 
            return true; 
          
        // These two are used in isCompleteUtil() 
        int node_count = countNodes(root); 
          
        if(isCompleteUtil(root, 0 , node_count)==true && isHeapUtil(root)==true) 
            return true; 
        return false; 
    } 
      
    // driver function to test the above functions 
    public static void main(String args[]) 
    { 
        Is_BinaryTree_MaxHeap bt = new Is_BinaryTree_MaxHeap(); 
          
        Node root = new Node(10); 
        root.left = new Node(9); 
        root.right = new Node(8); 
        root.left.left = new Node(7); 
        root.left.right = new Node(6); 
        root.right.left = new Node(5); 
        root.right.right = new Node(4); 
        root.left.left.left = new Node(3); 
        root.left.left.right = new Node(2); 
        root.left.right.left = new Node(1); 
  
        if(bt.isHeap(root) == true) 
            System.out.println("Given binary tree is a Heap"); 
        else 
            System.out.println("Given binary tree is not a Heap"); 
    } 
} 
  
// This code has been contributed by Amit Khandelwal  

Python

# To check if a binary tree 
# is a MAX Heap or not 
class GFG: 
    def __init__(self, value): 
        self.key = value 
        self.left = None
        self.right = None
      
    def count_nodes(self, root): 
        if root is None: 
            return 0
        else: 
            return (1 + self.count_nodes(root.left) + 
                        self.count_nodes(root.right)) 
      
    def heap_propert_util(self, root): 
      
        if (root.left is None and 
            root.right is None): 
            return True
      
        if root.right is None: 
            return root.key >= root.left.key 
        else: 
            if (root.key >= root.left.key and 
                root.key >= root.right.key): 
                return (self.heap_propert_util(root.left) and 
                        self.heap_propert_util(root.right)) 
            else: 
                return False
      
    def complete_tree_util(self, root,  
                           index, node_count): 
        if root is None: 
            return True
        if index >= node_count: 
            return False
        return (self.complete_tree_util(root.left, 2 * 
                                       index + 1, node_count) and 
               self.complete_tree_util(root.right, 2 * 
                                       index + 2, node_count)) 
      
    def check_if_heap(self): 
        node_count = self.count_nodes(self) 
        if (self.complete_tree_util(self, 0, node_count) and 
            self.heap_propert_util(self)): 
            return True
        else: 
            return False
  
# Driver Code 
root = GFG(5) 
root.left = GFG(2) 
root.right = GFG(3) 
root.left.left = GFG(1) 
  
if root.check_if_heap(): 
    print("Given binary tree is a heap") 
else: 
    print("Given binary tree is not a Heap") 
  
# This code has been  
# contributed by Yash Agrawal 

C#

/* C# program to checks if a binary tree is max heap or not */
using System; 
  
// A Binary Tree node  
public class Node  
{  
    public int key;  
    public Node left, right;  
  
    public Node(int k)  
    {  
        key = k;  
        left = right = null;  
    }  
}  
  
class Is_BinaryTree_MaxHeap  
{  
    /* This function counts the number 
    of nodes in a binary tree */
    int countNodes(Node root)  
    {  
        if(root == null)  
            return 0;  
        return(1 + countNodes(root.left) + countNodes(root.right));  
    }  
      
    /* This function checks if the  
    binary tree is complete or not */
    Boolean isCompleteUtil(Node root, int index, int number_nodes)  
    {  
        // An empty tree is complete  
        if(root == null)  
            return true;  
          
        // If index assigned to current node is more than  
        // number of nodes in tree, then tree is not complete  
        if(index >= number_nodes)  
            return false;  
          
        // Recur for left and right subtrees  
        return isCompleteUtil(root.left, 2*index+1, number_nodes) &&  
            isCompleteUtil(root.right, 2*index+2, number_nodes);  
          
    }  
      
    // This Function checks the heap property in the tree.  
    Boolean isHeapUtil(Node root)  
    {  
        // Base case : single node satisfies property  
        if(root.left == null && root.right==null)  
            return true;  
          
        // node will be in second last level  
        if(root.right == null)  
        {  
            // check heap property at Node  
            // No recursive call , because no need to check last level  
            return root.key >= root.left.key;  
        }  
        else
        {  
            // Check heap property at Node and  
            // Recursive check heap property at left and right subtree  
            if(root.key >= root.left.key && root.key >= root.right.key)  
                return isHeapUtil(root.left) && isHeapUtil(root.right);  
            else
                return false;  
        }  
    }  
      
    // Function to check binary tree is a Heap or Not.  
    Boolean isHeap(Node root)  
    {  
        if(root == null)  
            return true;  
          
        // These two are used in isCompleteUtil()  
        int node_count = countNodes(root);  
          
        if(isCompleteUtil(root, 0 , node_count)==true && isHeapUtil(root)==true)  
            return true;  
        return false;  
    }  
      
    // Driver code  
    public static void Main(String []args)  
    {  
        Is_BinaryTree_MaxHeap bt = new Is_BinaryTree_MaxHeap();  
          
        Node root = new Node(10);  
        root.left = new Node(9);  
        root.right = new Node(8);  
        root.left.left = new Node(7);  
        root.left.right = new Node(6);  
        root.right.left = new Node(5);  
        root.right.right = new Node(4);  
        root.left.left.left = new Node(3);  
        root.left.left.right = new Node(2);  
        root.left.right.left = new Node(1);  
  
        if(bt.isHeap(root) == true)  
            Console.WriteLine("Given binary tree is a Heap");  
        else
            Console.WriteLine("Given binary tree is not a Heap");  
    }  
}  
  
// This code has been contributed by Arnab Kundu 

Output:

Given binary tree is a Heap

This article is contributed by Utkarsh Trivedi. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above

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My Personal Notes

Recommended: Please solve it on “PRACTICE” first, before moving on to the solution.

C++

C

Java

Python

C#

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