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Check whether a binary tree is a full binary tree or not

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  • Difficulty Level : Easy
  • Last Updated : 22 Nov, 2022
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A full binary tree is defined as a binary tree in which all nodes have either zero or two child nodes. Conversely, there is no node in a full binary tree, which has one child node. More information about full binary trees can be found here.

For Example : 
 

Full

Recommended Practice

To check whether a binary tree is a full binary tree we need to test the following cases:-

  1. If a binary tree node is NULL then it is a full binary tree. 
  2. If a binary tree node does have empty left and right sub-trees, then it is a full binary tree by definition. 
  3. If a binary tree node has left and right sub-trees, then it is a part of a full binary tree by definition. In this case recursively check if the left and right sub-trees are also binary trees themselves. 
  4. In all other combinations of right and left sub-trees, the binary tree is not a full binary tree.

Following is the implementation for checking if a binary tree is a full binary tree.

C++




// C++ program to check whether a given Binary Tree is full or not
#include <bits/stdc++.h>
 
using namespace std;
  
/*  Tree node structure */
struct Node
{
    int key;
    struct Node *left, *right;
};
  
/* Helper function that allocates a new node with the
   given key and NULL left and right pointer. */
struct Node *newNode(char k)
{
    struct Node *node = new  Node;
    node->key = k;
    node->right = node->left = NULL;
    return node;
}
  
/* This function tests if a binary tree is a full binary tree. */
bool isFullTree (struct Node* root)
{
    // If empty tree
    if (root == NULL)
        return true;
  
    // If leaf node
    if (root->left == NULL && root->right == NULL)
        return true;
  
    // If both left and right are not NULL, and left & right subtrees
    // are full
    if ((root->left) && (root->right))
        return (isFullTree(root->left) && isFullTree(root->right));
  
    // We reach here when none of the above if conditions work
    return false;
}
  
// Driver Program
int main()
{
    struct Node* root = NULL;
    root = newNode(10);
    root->left = newNode(20);
    root->right = newNode(30);
  
    root->left->right = newNode(40);
    root->left->left = newNode(50);
    root->right->left = newNode(60);
    root->right->right = newNode(70);
  
    root->left->left->left = newNode(80);
    root->left->left->right = newNode(90);
    root->left->right->left = newNode(80);
    root->left->right->right = newNode(90);
    root->right->left->left = newNode(80);
    root->right->left->right = newNode(90);
    root->right->right->left = newNode(80);
    root->right->right->right = newNode(90);
  
    if (isFullTree(root))
        cout << "The Binary Tree is full\n";
    else
        cout << "The Binary Tree is not full\n";
  
    return(0);
}
 
// This code is contributed by shubhamsingh10

C




// C program to check whether a given Binary Tree is full or not
#include<stdio.h>
#include<stdlib.h>
#include<stdbool.h>
 
/*  Tree node structure */
struct Node
{
    int key;
    struct Node *left, *right;
};
 
/* Helper function that allocates a new node with the
   given key and NULL left and right pointer. */
struct Node *newNode(char k)
{
    struct Node *node = (struct Node*)malloc(sizeof(struct Node));
    node->key = k;
    node->right = node->left = NULL;
    return node;
}
 
/* This function tests if a binary tree is a full binary tree. */
bool isFullTree (struct Node* root)
{
    // If empty tree
    if (root == NULL)
        return true;
 
    // If leaf node
    if (root->left == NULL && root->right == NULL)
        return true;
 
    // If both left and right are not NULL, and left & right subtrees
    // are full
    if ((root->left) && (root->right))
        return (isFullTree(root->left) && isFullTree(root->right));
 
    // We reach here when none of the above if conditions work
    return false;
}
 
// Driver Program
int main()
{
    struct Node* root = NULL;
    root = newNode(10);
    root->left = newNode(20);
    root->right = newNode(30);
 
    root->left->right = newNode(40);
    root->left->left = newNode(50);
    root->right->left = newNode(60);
    root->right->right = newNode(70);
 
    root->left->left->left = newNode(80);
    root->left->left->right = newNode(90);
    root->left->right->left = newNode(80);
    root->left->right->right = newNode(90);
    root->right->left->left = newNode(80);
    root->right->left->right = newNode(90);
    root->right->right->left = newNode(80);
    root->right->right->right = newNode(90);
 
    if (isFullTree(root))
        printf("The Binary Tree is full\n");
    else
        printf("The Binary Tree is not full\n");
 
    return(0);
}

Java




// Java program to check if binary tree is full or not
 
/*  Tree node structure */
class Node
{
    int data;
    Node left, right;
  
    Node(int item)
    {
        data = item;
        left = right = null;
    }
}
  
class BinaryTree
{
    Node root;
      
    /* this function checks if a binary tree is full or not */
    boolean isFullTree(Node node)
    {
        // if empty tree
        if(node == null)
        return true;
          
        // if leaf node
        if(node.left == null && node.right == null )
            return true;
          
        // if both left and right subtrees are not null
        // the are full
        if((node.left!=null) && (node.right!=null))
            return (isFullTree(node.left) && isFullTree(node.right));
          
        // if none work
        return false;
    }
  
      
    // Driver program
    public static void main(String args[])
    {
        BinaryTree tree = new BinaryTree();
        tree.root = new Node(10);
        tree.root.left = new Node(20);
        tree.root.right = new Node(30);
        tree.root.left.right = new Node(40);
        tree.root.left.left = new Node(50);
        tree.root.right.left = new Node(60);
        tree.root.left.left.left = new Node(80);
        tree.root.right.right = new Node(70);
        tree.root.left.left.right = new Node(90);
        tree.root.left.right.left = new Node(80);
        tree.root.left.right.right = new Node(90);
        tree.root.right.left.left = new Node(80);
        tree.root.right.left.right = new Node(90);
        tree.root.right.right.left = new Node(80);
        tree.root.right.right.right = new Node(90);
          
        if(tree.isFullTree(tree.root))
            System.out.print("The binary tree is full");
        else
            System.out.print("The binary tree is not full");
    }
}
  
// This code is contributed by Mayank Jaiswal

Python3




# Python program to check whether given Binary tree is full or not
 
# Tree node structure
class Node:
 
    # Constructor of the node class for creating the node
    def __init__(self , key):
        self.key = key
        self.left = None
        self.right = None
 
# Checks if the binary tree is full or not
def isFullTree(root):
 
    # If empty tree
    if root is None:   
        return True
     
    # If leaf node
    if root.left is None and root.right is None:
        return True
 
    # If both left and right subtress are not None and
    # left and right subtress are full
    if root.left is not None and root.right is not None:
        return (isFullTree(root.left) and isFullTree(root.right))
     
    # We reach here when none of the above if conditions work
    return False
 
# Driver Program
root = Node(10);
root.left = Node(20);
root.right = Node(30);
 
root.left.right = Node(40);
root.left.left = Node(50);
root.right.left = Node(60);
root.right.right = Node(70);
 
root.left.left.left = Node(80);
root.left.left.right = Node(90);
root.left.right.left = Node(80);
root.left.right.right = Node(90);
root.right.left.left = Node(80);
root.right.left.right = Node(90);
root.right.right.left = Node(80);
root.right.right.right = Node(90);
 
if isFullTree(root):
    print ("The Binary tree is full")
else:
    print ("Binary tree is not full")
 
# This code is contributed by Nikhil Kumar Singh(nickzuck_007)

C#




// C# program to check if binary tree
// is full or not
using System;
 
/* Tree node structure */
public class Node
{
    public int data;
    public Node left, right;
 
    public Node(int item)
    {
        data = item;
        left = right = null;
    }
}
 
class GFG
{
public Node root;
 
/* This function checks if a binary
tree is full or not */
public virtual bool isFullTree(Node node)
{
    // if empty tree
    if (node == null)
    {
    return true;
    }
 
    // if leaf node
    if (node.left == null && node.right == null)
    {
        return true;
    }
 
    // if both left and right subtrees
    // are not null they are full
    if ((node.left != null) && (node.right != null))
    {
        return (isFullTree(node.left) &&
                isFullTree(node.right));
    }
 
    // if none work
    return false;
}
 
// Driver Code
public static void Main(string[] args)
{
    GFG tree = new GFG();
    tree.root = new Node(10);
    tree.root.left = new Node(20);
    tree.root.right = new Node(30);
    tree.root.left.right = new Node(40);
    tree.root.left.left = new Node(50);
    tree.root.right.left = new Node(60);
    tree.root.left.left.left = new Node(80);
    tree.root.right.right = new Node(70);
    tree.root.left.left.right = new Node(90);
    tree.root.left.right.left = new Node(80);
    tree.root.left.right.right = new Node(90);
    tree.root.right.left.left = new Node(80);
    tree.root.right.left.right = new Node(90);
    tree.root.right.right.left = new Node(80);
    tree.root.right.right.right = new Node(90);
 
    if (tree.isFullTree(tree.root))
    {
        Console.Write("The binary tree is full");
    }
    else
    {
        Console.Write("The binary tree is not full");
    }
}
}
 
// This code is contributed by Shrikant13

Javascript




<script>
// javascript program to check if binary tree is full or not
 
/*  Tree node structure */
class Node {
    constructor(item) {
        this.data = item;
        this.left = this.right = null;
    }
}
 
 
    var root;
 
    /* this function checks if a binary tree is full or not */
    function isFullTree( node) {
        // if empty tree
        if (node == null)
            return true;
 
        // if leaf node
        if (node.left == null && node.right == null)
            return true;
 
        // if both left and right subtrees are not null
        // the are full
        if ((node.left != null) && (node.right != null))
            return (isFullTree(node.left) && isFullTree(node.right));
 
        // if none work
        return false;
    }
 
    // Driver program
     
     
        root = new Node(10);
        root.left = new Node(20);
        root.right = new Node(30);
        root.left.right = new Node(40);
        root.left.left = new Node(50);
        root.right.left = new Node(60);
        root.left.left.left = new Node(80);
        root.right.right = new Node(70);
        root.left.left.right = new Node(90);
        root.left.right.left = new Node(80);
        root.left.right.right = new Node(90);
        root.right.left.left = new Node(80);
        root.right.left.right = new Node(90);
        root.right.right.left = new Node(80);
        root.right.right.right = new Node(90);
         if(isFullTree(root))
            document.write("The binary tree is full");
        else
            document.write("The binary tree is not full");
             
// This code contributed by gauravrajput1
</script>

Output

The Binary Tree is full

Time complexity: O(n) where n is number of nodes in given binary tree.
Auxiliary Space: O(n) for call stack since using recursion

Iterative Approach:

To check whether a binary tree is a full binary tree we need to test the following cases:-

  1. Create a queue to store nodes
  2. Store the root of the tree in the queue
  3. Traverse until the queue is not empty
    1. If the current node is not a leaf insert root->left and root->right in the queue.
    2. If the current node is NULL return false.
  4. If the queue is empty return true.

Following is the implementation for checking if a binary tree is a full binary tree.

C++




// c++ program to check whether a given BT is full or not
#include <bits/stdc++.h>
using namespace std;
 
// Tree node structure
struct Node {
    int val;
    Node *left, *right;
};
 
// fun that creates and returns a new node
Node* newNode(int data)
{
    Node* node = new Node();
    node->val = data;
    node->left = node->right = NULL;
    return node;
}
 
// helper fun to check leafnode
bool isleafnode(Node* root)
{
    return !root->left && !root->right;
}
 
// fun checks whether the given BT is a full BT or not
bool isFullTree(Node* root)
{
    // if tree is empty
    if (!root)
        return true;
 
    queue<Node*> q;
    q.push(root);
 
    while (!q.empty()) {
 
        root = q.front();
        q.pop();
 
        // null indicates - not a full BT
        if (root == NULL)
            return false;
 
        // if its not a leafnode then the current node
        // should contain both left and right pointers.
        if (!isleafnode(root)) {
            q.push(root->left);
            q.push(root->right);
        }
    }
 
    return true;
}
 
int main()
{
    Node* root = newNode(1);
    root->left = newNode(2);
    root->right = newNode(3);
    root->left->left = newNode(4);
    root->left->right = newNode(5);
 
    if (isFullTree(root))
        cout << "The Binary Tree is full\n";
    else
        cout << "The Binary Tree is not full\n";
 
    return 0;
}
// This code is contributed by Modem Upendra.

Java




// Java program to check whether a given BT is full or not
import java.util.ArrayDeque;
import java.util.Queue;
 
public class GFG
{
 
  /*  Tree node structure */
  static class Node {
    int data;
    Node left, right;
 
    Node(int item)
    {
      data = item;
      left = right = null;
    }
  }
 
  // helper fun to check leafnode
  static boolean isleafnode(Node root)
  {
    return root.left == null && root.right == null;
  }
 
  // fun checks whether the given BT is a full BT or not
  static boolean isFullTree(Node root)
  {
 
    // if tree is empty
    if (root == null)
      return true;
 
    Queue<Node> q = new ArrayDeque<>();
    q.add(root);
 
    while (!q.isEmpty()) {
 
      root = q.peek();
      q.remove();
 
      // null indicates - not a full BT
      if (root == null)
        return false;
 
      // if its not a leafnode then the current node
      // should contain both left and right pointers.
      if (!isleafnode(root)) {
        q.add(root.left);
        q.add(root.right);
      }
    }
 
    return true;
  }
 
  // Driver Code
  public static void main(String[] args)
  {
    Node root = new Node(1);
    root.left = new Node(2);
    root.right = new Node(3);
    root.left.left = new Node(4);
    root.left.right = new Node(5);
 
    if (isFullTree(root))
      System.out.println("The Binary Tree is full");
    else
      System.out.println(
      "The Binary Tree is not full");
  }
}
 
// This code is contributed by karandeep1234

Output

The Binary Tree is full

Time Complexity: O(N), Where N is the total nodes in a given binary tree.
Auxiliary Space: O(N), in most cases the last level contains nodes as half of the total nodes. O(N/2) ~ O(N)


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