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Height of binary tree considering even level leaves only
• Difficulty Level : Hard
• Last Updated : 03 Nov, 2020

Find the height of the binary tree given that only the nodes on the even levels are considered as the valid leaf nodes.
The height of a binary tree is the number of edges between the tree’s root and its furthest leaf. But what if we bring a twist and change the definition of a leaf node. Let us define a valid leaf node as the node that has no children and is at an even level (considering root node as an odd level node). Output :Height of tree is 4

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Solution : The approach to this problem is slightly different from the normal height finding approach. In the return step, we check if the node is a valid root node or not. If it is valid, return 1, else we return 0. Now in the recursive step- if the left and the right sub-tree both yield 0, the current node yields 0 too, because in that case there is no path from current node to a valid leaf node. But in case at least one of the values returned by the children is non-zero, it means the leaf node on that path is a valid leaf node, and hence that path can contribute to the final result, so we return max of the values returned + 1 for the current node. ## C++

 `/* Program to find height of the tree considering``   ``only even level leaves. */``#include ``using` `namespace` `std;`` ` `/* A binary tree node has data, pointer to``   ``left child and a pointer to right child */``struct` `Node {``    ``int` `data;``    ``struct` `Node* left;``    ``struct` `Node* right;``};`` ` `int` `heightOfTreeUtil(Node* root, ``bool` `isEven)``{``    ``// Base Case``    ``if` `(!root)``        ``return` `0;`` ` `    ``if` `(!root->left && !root->right) {``        ``if` `(isEven)``            ``return` `1;``        ``else``            ``return` `0;``    ``}`` ` `    ``/*left stores the result of left subtree,``      ``and right stores the result of right subtree*/``    ``int` `left = heightOfTreeUtil(root->left, !isEven);``    ``int` `right = heightOfTreeUtil(root->right, !isEven);`` ` `    ``/*If both left and right returns 0, it means``      ``there is no valid path till leaf node*/``    ``if` `(left == 0 && right == 0)``        ``return` `0;`` ` `    ``return` `(1 + max(left, right));``}`` ` `/* Helper function that allocates a new node with the``   ``given data and NULL left and right pointers. */``struct` `Node* newNode(``int` `data)``{``    ``struct` `Node* node = ``              ``(``struct` `Node*)``malloc``(``sizeof``(``struct` `Node));``    ``node->data = data;``    ``node->left = NULL;``    ``node->right = NULL;`` ` `    ``return` `(node);``}`` ` `int` `heightOfTree(Node* root)``{``    ``return` `heightOfTreeUtil(root, ``false``);``}`` ` `/* Driver program to test above functions*/``int` `main()``{``    ``// Let us create binary tree shown in above diagram``    ``struct` `Node* root = newNode(1);`` ` `    ``root->left = newNode(2);``    ``root->right = newNode(3);``    ``root->left->left = newNode(4);``    ``root->left->right = newNode(5);``    ``root->left->right->left = newNode(6);``    ``cout << ``"Height of tree is "` `<< heightOfTree(root);``    ``return` `0;``}`

## Java

 `/* Java Program to find height of the tree considering ``only even level leaves. */``class` `GfG {`` ` `/* A binary tree node has data, pointer to ``left child and a pointer to right child */``static` `class` `Node { ``    ``int` `data; ``    ``Node left; `` ``Node right; ``}`` ` `static` `int` `heightOfTreeUtil(Node root, ``boolean` `isEven) ``{ ``    ``// Base Case ``    ``if` `(root == ``null``) ``        ``return` `0``; `` ` `    ``if` `(root.left == ``null` `&& root.right == ``null``) { ``        ``if` `(isEven == ``true``) ``            ``return` `1``; ``        ``else``            ``return` `0``; ``    ``} `` ` `    ``/*left stores the result of left subtree, ``    ``and right stores the result of right subtree*/``    ``int` `left = heightOfTreeUtil(root.left, !isEven); ``    ``int` `right = heightOfTreeUtil(root.right, !isEven); `` ` `    ``/*If both left and right returns 0, it means ``    ``there is no valid path till leaf node*/``    ``if` `(left == ``0` `&& right == ``0``) ``        ``return` `0``; `` ` `    ``return` `(``1` `+ Math.max(left, right)); ``} `` ` `/* Helper function that allocates a new node with the ``given data and NULL left and right pointers. */``static` `Node newNode(``int` `data) ``{ ``    ``Node node = ``new` `Node(); ``    ``node.data = data; ``    ``node.left = ``null``; ``    ``node.right = ``null``; `` ` `    ``return` `(node); ``} `` ` `static` `int` `heightOfTree(Node root) ``{ ``    ``return` `heightOfTreeUtil(root, ``false``); ``} `` ` `/* Driver program to test above functions*/``public` `static` `void` `main(String[] args) ``{ ``    ``// Let us create binary tree shown in above diagram ``    ``Node root = newNode(``1``); `` ` `    ``root.left = newNode(``2``); ``    ``root.right = newNode(``3``); ``    ``root.left.left = newNode(``4``); ``    ``root.left.right = newNode(``5``); ``    ``root.left.right.left = newNode(``6``); ``    ``System.out.println(``"Height of tree is "` `+ heightOfTree(root)); ``}``} `

## Python3

 `# Program to find height of the tree considering ``# only even level leaves.`` ` `# Helper class that allocates a new node with the ``# given data and None left and right pointers. ``class` `newNode:``    ``def` `__init__(``self``, data):``        ``self``.data ``=` `data ``        ``self``.left ``=` `None``        ``self``.right ``=` `None`` ` `def` `heightOfTreeUtil(root, isEven):``     ` `    ``# Base Case ``    ``if` `(``not` `root): ``        ``return` `0`` ` `    ``if` `(``not` `root.left ``and` `not` `root.right): ``        ``if` `(isEven): ``            ``return` `1``        ``else``:``            ``return` `0`` ` `    ``# left stores the result of left subtree, ``    ``# and right stores the result of right subtree``    ``left ``=` `heightOfTreeUtil(root.left, ``not` `isEven) ``    ``right ``=` `heightOfTreeUtil(root.right, ``not` `isEven) `` ` `    ``#If both left and right returns 0, it means ``    ``# there is no valid path till leaf node``    ``if` `(left ``=``=` `0` `and` `right ``=``=` `0``):``        ``return` `0`` ` `    ``return` `(``1` `+` `max``(left, right))`` ` `def` `heightOfTree(root):``    ``return` `heightOfTreeUtil(root, ``False``)`` ` `# Driver Code``if` `__name__ ``=``=` `'__main__'``: ``     ` `    ``# Let us create binary tree shown``    ``# in above diagram ``    ``root ``=` `newNode(``1``) `` ` `    ``root.left ``=` `newNode(``2``) ``    ``root.right ``=` `newNode(``3``) ``    ``root.left.left ``=` `newNode(``4``) ``    ``root.left.right ``=` `newNode(``5``) ``    ``root.left.right.left ``=` `newNode(``6``) ``    ``print``(``"Height of tree is"``,``           ``heightOfTree(root))`` ` `# This code is contributed by PranchalK`

## C#

 `/* C# Program to find height of the tree considering ``only even level leaves. */``using` `System;`` ` `class` `GfG``{ `` ` `    ``/* A binary tree node has data, pointer to ``    ``left child and a pointer to right child */``    ``class` `Node``    ``{ ``        ``public` `int` `data; ``        ``public` `Node left; ``        ``public` `Node right; ``    ``} `` ` `    ``static` `int` `heightOfTreeUtil(Node root,``                               ``bool` `isEven) ``    ``{ ``        ``// Base Case ``        ``if` `(root == ``null``) ``            ``return` `0; `` ` `        ``if` `(root.left == ``null` `&& ``            ``root.right == ``null``)``        ``{ ``            ``if` `(isEven == ``true``) ``                ``return` `1; ``            ``else``                ``return` `0; ``        ``} `` ` `        ``/*left stores the result of left subtree, ``        ``and right stores the result of right subtree*/``        ``int` `left = heightOfTreeUtil(root.left, !isEven); ``        ``int` `right = heightOfTreeUtil(root.right, !isEven); `` ` `        ``/*If both left and right returns 0, it means ``        ``there is no valid path till leaf node*/``        ``if` `(left == 0 && right == 0) ``            ``return` `0; `` ` `        ``return` `(1 + Math.Max(left, right)); ``    ``} `` ` `    ``/* Helper function that allocates a new node with the ``    ``given data and NULL left and right pointers. */``    ``static` `Node newNode(``int` `data) ``    ``{ ``        ``Node node = ``new` `Node(); ``        ``node.data = data; ``        ``node.left = ``null``; ``        ``node.right = ``null``; `` ` `        ``return` `(node); ``    ``} `` ` `    ``static` `int` `heightOfTree(Node root) ``    ``{ ``        ``return` `heightOfTreeUtil(root, ``false``); ``    ``} `` ` `    ``/* Driver code*/``    ``public` `static` `void` `Main(String[] args) ``    ``{ ``        ``// Let us create binary tree``        ``// shown in above diagram ``        ``Node root = newNode(1); `` ` `        ``root.left = newNode(2); ``        ``root.right = newNode(3); ``        ``root.left.left = newNode(4); ``        ``root.left.right = newNode(5); ``        ``root.left.right.left = newNode(6); ``        ``Console.WriteLine(``"Height of tree is "` `+``                            ``heightOfTree(root)); ``    ``} ``} `` ` `/* This code is contributed by Rajput-Ji*/`

Output:

```Height of tree is 4
```

Time Complexity:O(n) where n is number of nodes in given binary tree.

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