Leaf starting point in a Binary Heap data structure

Last Updated : 21 Jul, 2022

Binary Heap is a complete tree (All levels are completely filled except possibly the last level and the last level has all keys as left as possible). In other words, we can say that it’s an almost complete binary tree. A Binary heap is typically represented as array. If we take a closer look, we can noticed that in a Heap with number of nodes n, the leaves start from a particular index and following it, all the nodes are leaves till index n. Let’s see an example to observe this:

            10 
         /      \               
       20        100          
      /                      
    30

Let us represent this in the form of an array Arr whose index starts from 1 : we have: Arr[1] = 10 Arr[2] = 20 Arr[3] = 100 Arr[4] = 30 If we observe, the first leaf (i.e. 100) starts from the index 3. Following it Arr[4] is also a leaf. By carefully analyzing, the following conclusion is observed:

The first leaf in a Heap starts from [floor(n/2)]+1 and all the nodes following it till n are leaves.

Conclusion: In a Heap having n elements, Elements from indexes [(floor(n/2)+1) to n] are leaves. What is starting index of leaves if indexes start from 0 instead of 1? The above explanation assumes indexes starting from 1, but in most of the programming languages, index starts with 0.

If we consider 0 as starting index, then leaves starts from floor(n/2) and exist till end, i.e., (n-1).

GeeksforGeeks

Improve

Previous Article

Minimum product of k integers in an array of positive Integers

Sum of all elements between k1'th and k2'th smallest elements

Similar Reads

Difference between Binary Heap, Binomial Heap and Fibonacci Heap

Binary Heap:A Binary Heap is a Binary Tree with following properties. It’s a complete binary tree i.e., all levels are completely filled except possibly the last level and the last level has all keys as left as possible. This property of Binary Heap makes them suitable to be stored in an array. A Binary Heap is either Min Heap or Max Heap. In a Min

When building a Heap, is the structure of Heap unique?

What is Heap? A heap is a tree based data structure where the tree is a complete binary tree that maintains the property that either the children of a node are less than itself (max heap) or the children are greater than the node (min heap). Properties of Heap: Structural Property: This property states that it should be A Complete Binary Tree. For

Sum of Bitwise AND of the sum of all leaf and non-leaf nodes for each level of a Binary Tree

Given a Binary Tree consisting of N nodes, the task is to find the sum of Bitwise AND of the sum of all leaf nodes and the sum of all non-leaf nodes for each level in the given Tree. Examples: Input: Below is the given tree: 5 / \ 3 9 / \ 6 4 \ 7Output: 5Explanation: For Level 1: leaf node sum = 0, non-leaf node sum = 5. So, 0&5 = 0. For Level

Print the longest leaf to leaf path in a Binary tree

C/C++ Code // C++ program to print the longest leaf to leaf // path #include <bits/stdc++.h> using namespace std; // Tree node structure used in the program struct Node { int data; Node *left, *right; }; struct Node* newNode(int data) { struct Node* node = new Node; node->data = data; node->left = node->right = NULL; return (node); }

Print all the leaf nodes of Binary Heap

Given an array of N elements which denotes the array representation of binary heap, the task is to find the leaf nodes of this binary heap. Examples: Input: arr[] = {1, 2, 3, 4, 5, 6, 7} Output: 4 5 6 7 Explanation: 1 / \ 2 3 / \ / \ 4 5 6 7 Leaf nodes of the Binary Heap are: 4 5 6 7 Input: arr[] = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} Output: 6 7 8 9 10

Find min and max values among all maximum leaf nodes from all possible Binary Max Heap

Given a positive integer N, the task is to find the largest and smallest elements, from the maximum leaf nodes of every possible binary max-heap formed by taking the first N natural numbers as the nodes' value of the binary max-heap. Examples: Input: N = 2Output: 1 1Explanation: There is only one maximum binary heap with the nodes {1, 2}: In the ab

Minimum time to burn a Tree starting from a Leaf node

Given a binary tree and a leaf node from this tree. It is known that in 1s all nodes connected to a given node (left child, right child, and parent) get burned in 1 second. Then all the nodes which are connected through one intermediate get burned in 2 seconds, and so on. The task is to find the minimum time required to burn the complete binary tre

Convert Min Heap to Max Heap

Given an array representation of min Heap, convert it to max Heap. Examples: Input: arr[] = {3, 5, 9, 6, 8, 20, 10, 12, 18, 9} 3 / \ 5 9 / \ / \ 6 8 20 10 / \ /12 18 9 Output: arr[] = {20, 18, 10, 12, 9, 9, 3, 5, 6, 8} 20 / \ 18 10 / \ / \ 12 9 9 3 / \ /5 6 8 Input: arr[] = {3, 4, 8, 11, 13}Output: arr[] = {13, 11, 8, 4, 3} Approach: To solve the p

Heap Sort for decreasing order using min heap

Given an array of elements, sort the array in decreasing order using min heap. Examples: Input : arr[] = {5, 3, 10, 1} Output : arr[] = {10, 5, 3, 1} Input : arr[] = {1, 50, 100, 25} Output : arr[] = {100, 50, 25, 1} Prerequisite: Heap sort using min heap. Algorithm : Build a min heap from the input data. At this point, the smallest item is stored

Difference between Min Heap and Max Heap

A Heap is a special Tree-based data structure in which the tree is a complete binary tree. Since a heap is a complete binary tree, a heap with N nodes has log N height. It is useful to remove the highest or lowest priority element. It is typically represented as an array. There are two types of Heaps in the data structure. Min-HeapIn a Min-Heap the

Article Tags :

DSA
Heap

Practice Tags :

Heap