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Check whether a binary tree is a complete tree or not | Set 2 (Recursive Solution)
• Difficulty Level : Medium
• Last Updated : 10 Feb, 2020

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.

For 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.

1. Calculate the number of nodes (count) in the binary tree.
2. 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).
3. If the current node under examination is NULL, then the tree is a complete binary tree. Return true.
4. 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.
5. 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.

## C++

 `/* C++ program to checks if a binary tree complete ot not */``#include``#include``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 the``given key and NULL left and right pointer. */`` ` ` ` `/* This function counts the number of nodes``in 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 tree ``is 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 code``int` `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

 `/* C program to checks if a binary tree complete ot not */``#include``#include``#include`` ` `/*  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 program``int` `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

 `// Java program to check if binay 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

 `# Python program to check if a binary tree complete or not`` ` `# Tree node structure``class` `Node:`` ` `    ``# Contructor 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 tree``def` `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 not``def` `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 subtress``    ``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#

 `// C# program to check if binay``// tree is complete or not ``using` `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*/`

Output:
`The Binary Tree is not complete `