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Check whether a given binary tree is perfect or not

Given a Binary Tree, write a function to check whether the given Binary Tree is a prefect Binary Tree or not.

A Binary tree is Perfect Binary Tree in which all internal nodes have two children and all leaves are at same level.

Examples:
The following tree is a perfect binary tree

               10
           /         
         20         30  
        /          /  
      40    50    60   70


               18
           /         
         15         30  

The following tree is not a perfect binary tree

      1
    /    
   2       3
         /     
     4   5    6



A Perfect Binary Tree of height h (where height is number of nodes on path from root to leaf) has 2h – 1 nodes.

Below is an idea to check whether a given Binary Tree is perfect or not.

  1. Find depth of any node (in below tree we find depth of leftmost node). Let this depth be d.
  2. Now recursively traverse the tree and check for following two conditions.
    • Every internal node should have both children non-empty
    • All leaves are at depth ‘d’

C++

// C++ program to check whether a given
// Binary Tree is Perfect or not
#include<bits/stdc++.h>
  
/*  Tree node structure */
struct Node
{
    int key;
    struct Node *left, *right;
};
  
// Returns depth of leftmost leaf.
int findADepth(Node *node)
{
   int d = 0;
   while (node != NULL)
   {
      d++;
      node = node->left;
   }
   return d;
}
  
/* This function tests if a binary tree is perfect
   or not. It basically checks for two things :
   1) All leaves are at same level
   2) All internal nodes have two children */
bool isPerfectRec(struct Node* root, int d, int level = 0)
{
    // An empty tree is perfect
    if (root == NULL)
        return true;
  
    // If leaf node, then its depth must be same as
    // depth of all other leaves.
    if (root->left == NULL && root->right == NULL)
        return (d == level+1);
  
    // If internal node and one child is empty
    if (root->left == NULL || root->right == NULL)
        return false;
  
    // Left and right subtrees must be perfect.
    return isPerfectRec(root->left, d, level+1) &&
           isPerfectRec(root->right, d, level+1);
}
  
// Wrapper over isPerfectRec()
bool isPerfect(Node *root)
{
   int d = findADepth(root);
   return isPerfectRec(root, d);
}
  
/* Helper function that allocates a new node with the
   given key and NULL left and right pointer. */
struct Node *newNode(int k)
{
    struct Node *node = new Node;
    node->key = k;
    node->right = node->left = NULL;
    return node;
}
  
// Driver Program
int main()
{
    struct Node* root = NULL;
    root = newNode(10);
    root->left = newNode(20);
    root->right = newNode(30);
  
    root->left->left = newNode(40);
    root->left->right = newNode(50);
    root->right->left = newNode(60);
    root->right->right = newNode(70);
  
    if (isPerfect(root))
        printf("Yes ");
    else
        printf("No ");
  
    return(0);
}

Java

// Java program to check whether a given 
// Binary Tree is Perfect or not 
class GfG { 
  
/* Tree node structure */
static class Node 
    int key; 
    Node left, right; 
}
  
// Returns depth of leftmost leaf. 
static int findADepth(Node node) 
int d = 0
while (node != null
    d++; 
    node = node.left; 
return d; 
  
/* This function tests if a binary tree is perfect 
or not. It basically checks for two things : 
1) All leaves are at same level 
2) All internal nodes have two children */
static boolean isPerfectRec(Node root, int d, int level) 
    // An empty tree is perfect 
    if (root == null
        return true
  
    // If leaf node, then its depth must be same as 
    // depth of all other leaves. 
    if (root.left == null && root.right == null
        return (d == level+1); 
  
    // If internal node and one child is empty 
    if (root.left == null || root.right == null
        return false
  
    // Left and right subtrees must be perfect. 
    return isPerfectRec(root.left, d, level+1) && isPerfectRec(root.right, d, level+1); 
  
// Wrapper over isPerfectRec() 
static boolean isPerfect(Node root) 
int d = findADepth(root); 
return isPerfectRec(root, d, 0); 
  
/* Helper function that allocates a new node with the 
given key and NULL left and right pointer. */
static Node newNode(int k) 
    Node node = new Node(); 
    node.key = k; 
    node.right = null;
    node.left = null
    return node; 
  
// Driver Program 
public static void main(String args[]) 
    Node root = null
    root = newNode(10); 
    root.left = newNode(20); 
    root.right = newNode(30); 
  
    root.left.left = newNode(40); 
    root.left.right = newNode(50); 
    root.right.left = newNode(60); 
    root.right.right = newNode(70); 
  
    if (isPerfect(root) == true
        System.out.println("Yes"); 
    else
        System.out.println("No"); 
}

Python3

# Python3 program to check whether a 
# given Binary Tree is Perfect or not
  
# Helper class that allocates a new 
# node with the given key and None 
# left and right pointer. 
class newNode:
    def __init__(self, k):
        self.key =
        self.right = self.left = None
  
# Returns depth of leftmost leaf. 
def findADepth(node):
    d = 0
    while (node != None):
        d += 1
        node = node.left
    return d
  
# This function tests if a binary tree
# is perfect or not. It basically checks 
# for two things : 
# 1) All leaves are at same level 
# 2) All internal nodes have two children 
def isPerfectRec(root, d, level = 0):
      
    # An empty tree is perfect 
    if (root == None): 
        return True
  
    # If leaf node, then its depth must 
    # be same as depth of all other leaves. 
    if (root.left == None and root.right == None): 
        return (d == level + 1
  
    # If internal node and one child is empty 
    if (root.left == None or root.right == None): 
        return False
  
    # Left and right subtrees must be perfect. 
    return (isPerfectRec(root.left, d, level + 1) and 
            isPerfectRec(root.right, d, level + 1))
  
# Wrapper over isPerfectRec() 
def isPerfect(root):
    d = findADepth(root) 
    return isPerfectRec(root, d)
  
# Driver Code 
if __name__ == '__main__':
    root = None
    root = newNode(10
    root.left = newNode(20
    root.right = newNode(30
  
    root.left.left = newNode(40
    root.left.right = newNode(50
    root.right.left = newNode(60
    root.right.right = newNode(70
  
    if (isPerfect(root)): 
        print("Yes"
    else:
        print("No")
          
# This code is contributed by pranchalK

C#

// C# program to check whether a given 
// Binary Tree is Perfect or not 
using System;
  
class GfG 
  
/* Tree node structure */
class Node 
    public int key; 
    public Node left, right; 
  
// Returns depth of leftmost leaf. 
static int findADepth(Node node) 
    int d = 0; 
    while (node != null
    
        d++; 
        node = node.left; 
    
    return d; 
  
/* This function tests if a binary tree is perfect 
or not. It basically checks for two things : 
1) All leaves are at same level 
2) All internal nodes have two children */
static bool isPerfectRec(Node root, 
                    int d, int level) 
    // An empty tree is perfect 
    if (root == null
        return true
  
    // If leaf node, then its depth must be same as 
    // depth of all other leaves. 
    if (root.left == null && root.right == null
        return (d == level+1); 
  
    // If internal node and one child is empty 
    if (root.left == null || root.right == null
        return false
  
    // Left and right subtrees must be perfect. 
    return isPerfectRec(root.left, d, level+1) && 
            isPerfectRec(root.right, d, level+1); 
  
// Wrapper over isPerfectRec() 
static bool isPerfect(Node root) 
    int d = findADepth(root); 
    return isPerfectRec(root, d, 0); 
  
/* Helper function that allocates a new node with the 
given key and NULL left and right pointer. */
static Node newNode(int k) 
    Node node = new Node(); 
    node.key = k; 
    node.right = null
    node.left = null
    return node; 
  
// Driver code 
public static void Main() 
    Node root = null
    root = newNode(10); 
    root.left = newNode(20); 
    root.right = newNode(30); 
  
    root.left.left = newNode(40); 
    root.left.right = newNode(50); 
    root.right.left = newNode(60); 
    root.right.right = newNode(70); 
  
    if (isPerfect(root) == true
        Console.WriteLine("Yes"); 
    else
        Console.WriteLine("No"); 
  
/* This code is contributed by Rajput-Ji*/


Output:

Yes

Time complexity : O(n)

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.



This article is attributed to GeeksforGeeks.org

tags:

Tree Tree

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