Check whether a binary tree is a complete tree or not | Set 2 (Recursive Solution)

24 Jun, 2022
A complete binary tree is a binary tree whose all levels except the last level are completely filled and all the leaves in the last level are all to the left side. More information about complete binary trees can be found here.
Example:Below tree is a Complete Binary Tree (All nodes till the second last nodes are filled and all leaves are to the left side) 
An iterative solution for this problem is discussed in below post. Check whether a given Binary Tree is Complete or not | Set 1 (Using Level Order Traversal)In this post a recursive solution is discussed.
In the array representation of a binary tree, if the parent node is assigned an index of ‘i’ and left child gets assigned an index of ‘2*i + 1’ while the right child is assigned an index of ‘2*i + 2’. If we represent the above binary tree as an array with the respective indices assigned to the different nodes of the tree above from top to down and left to right.
Hence we proceed in the following manner in order to check if the binary tree is complete binary tree. 
Calculate the number of nodes (count) in the binary tree.Start recursion of the binary tree from the root node of the binary tree with index (i) being set as 0 and the number of nodes in the binary (count).If the current node under examination is NULL, then the tree is a complete binary tree. Return true.If index (i) of the current node is greater than or equal to the number of nodes in the binary tree (count) i.e. (i>= count), then the tree is not a complete binary. Return false.Recursively check the left and right sub-trees of the binary tree for same condition. For the left sub-tree use the index as (2*i + 1) while for the right sub-tree use the index as (2*i + 2).
Calculate the number of nodes (count) in the binary tree.
Start recursion of the binary tree from the root node of the binary tree with index (i) being set as 0 and the number of nodes in the binary (count).
If the current node under examination is NULL, then the tree is a complete binary tree. Return true.
If index (i) of the current node is greater than or equal to the number of nodes in the binary tree (count) i.e. (i>= count), then the tree is not a complete binary. Return false.
Recursively check the left and right sub-trees of the binary tree for same condition. For the left sub-tree use the index as (2*i + 1) while for the right sub-tree use the index as (2*i + 2).
The time complexity of the above algorithm is O(n). Following is the code for checking if a binary tree is a complete binary tree. 
Implementation:
C++
C
Java
Python3
C#
Javascript
/* C++ program to checks if a binary tree complete ot not */#include<bits/stdc++.h>#include<stdbool.h>using namespace std; /* Tree node structure */class Node{    public:    int key;    Node *left, *right;         Node *newNode(char k)    {        Node *node = ( Node*)malloc(sizeof( Node));        node->key = k;        node->right = node->left = NULL;        return node;    }     }; /* Helper function that allocates a new node with thegiven key and NULL left and right pointer. */  /* This function counts the number of nodesin a binary tree */unsigned int countNodes(Node* root){    if (root == NULL)        return (0);    return (1 + countNodes(root->left) +            countNodes(root->right));} /* This function checks if the binary treeis complete or not */bool isComplete ( 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 (isComplete(root->left, 2*index + 1, number_nodes) &&            isComplete(root->right, 2*index + 2, number_nodes));} // Driver codeint main(){    Node n1;         // Let us create tree in the last diagram above    Node* root = NULL;    root = n1.newNode(1);    root->left = n1.newNode(2);    root->right = n1.newNode(3);    root->left->left = n1.newNode(4);    root->left->right = n1.newNode(5);    root->right->right = n1.newNode(6);     unsigned int node_count = countNodes(root);    unsigned int index = 0;     if (isComplete(root, index, node_count))        cout << "The Binary Tree is complete\n";    else        cout << "The Binary Tree is not complete\n";    return (0);} // This code is contributed by SoumikMondal
/* C program to checks if a binary tree complete ot 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 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 isComplete (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 (isComplete(root->left, 2*index + 1, number_nodes) &&            isComplete(root->right, 2*index + 2, number_nodes));} // Driver programint main(){    // Le us create tree in the last diagram above    struct Node* root = NULL;    root = newNode(1);    root->left = newNode(2);    root->right = newNode(3);    root->left->left = newNode(4);    root->left->right = newNode(5);    root->right->right = newNode(6);     unsigned int node_count = countNodes(root);    unsigned int index = 0;     if (isComplete(root, index, node_count))        printf("The Binary Tree is complete\n");    else        printf("The Binary Tree is not complete\n");    return (0);}
// Java program to check if binary tree is complete 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 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 isComplete(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 (isComplete(root.left, 2 * index + 1, number_nodes)            && isComplete(root.right, 2 * index + 2, number_nodes));      }      // Driver program    public static void main(String args[])    {        BinaryTree tree = new BinaryTree();                 // Le us create tree in the last diagram above        Node NewRoot = null;        tree.root = new Node(1);        tree.root.left = new Node(2);        tree.root.right = new Node(3);        tree.root.left.right = new Node(5);        tree.root.left.left = new Node(4);        tree.root.right.right = new Node(6);                  int node_count = tree.countNodes(tree.root);        int index = 0;                  if (tree.isComplete(tree.root, index, node_count))            System.out.print("The binary tree is complete");        else            System.out.print("The binary tree is not complete");    }}  // This code is contributed by Mayank Jaiswal
# Python program to check if a binary tree complete or not # Tree node structureclass Node:     # Constructor to create a new node    def __init__(self, key):        self.key = key        self.left = None        self.right = None  # This function counts the number of nodes in a binary treedef countNodes(root):    if root is None:        return 0    return (1+ countNodes(root.left) + countNodes(root.right)) # This function checks if binary tree is complete or notdef isComplete(root, index, number_nodes):         # An empty is complete    if root is None:        return True         # If index assigned to current nodes 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 (isComplete(root.left , 2*index+1 , number_nodes)        and isComplete(root.right, 2*index+2, number_nodes)          ) # Driver Program root = Node(1)root.left = Node(2)root.right = Node(3)root.left.left = Node(4)root.left.right = Node(5)root.right.right = Node(6) node_count = countNodes(root)index = 0 if isComplete(root, index, node_count):    print ("The Binary Tree is complete")else:    print ("The Binary Tree is not complete") # This code is contributed by Nikhil Kumar Singh(nickzuck_007)
// C# program to check if binary// tree is complete or notusing System; /* Tree node structure */class Node{    public int data;    public Node left, right;     public Node(int item)    {        data = item;        left = right = null;    }} public class BinaryTree{    Node root;     /* 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 */    bool isComplete(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 (isComplete(root.left, 2 * index + 1, number_nodes)            && isComplete(root.right, 2 * index + 2, number_nodes));     }     // Driver code    public static void Main()    {        BinaryTree tree = new BinaryTree();                 // Let us create tree in the last diagram above        tree.root = new Node(1);        tree.root.left = new Node(2);        tree.root.right = new Node(3);        tree.root.left.right = new Node(5);        tree.root.left.left = new Node(4);        tree.root.right.right = new Node(6);                 int node_count = tree.countNodes(tree.root);        int index = 0;                 if (tree.isComplete(tree.root, index, node_count))            Console.WriteLine("The binary tree is complete");        else            Console.WriteLine("The binary tree is not complete");    }} /* This code is contributed by Rajput-Ji*/
<script> // JavaScript program to check if// binary tree is complete or not /*  Tree node structure */class Node {        constructor(val) {            this.data = val;            this.left = null;            this.right = null;        }    }     var root;     /* This function counts the number of    nodes in a binary tree */    function countNodes(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 */    function isComplete(root , index , 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 (isComplete(root.left, 2 * index + 1, number_nodes)            && isComplete(root.right, 2 * index + 2, number_nodes));     }     // Driver program         // Le us create tree in the last diagram above        var NewRoot = null;        root = new Node(1);        root.left = new Node(2);        root.right = new Node(3);        root.left.right = new Node(5);        root.left.left = new Node(4);        root.right.right = new Node(6);         var node_count = countNodes(root);        var index = 0;         if (isComplete(root, index, node_count))            document.write("The binary tree is complete");        else            document.write("The binary tree is not complete"); // This code contributed by umadevi9616 </script>
The Binary Tree is not complete
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SoumikMondal
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umadevi9616
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