Given level order traversal of a Binary Tree, check if the Tree is a Min-Heap Last Updated : 17 Mar, 2025 Comments Improve Suggest changes Like Article Like Report Given the level order traversal of a Complete Binary Tree, determine whether the Binary Tree is a valid Min-HeapExamples:Input: level = [10, 15, 14, 25, 30]Output: TrueExplanation: The tree of the given level order traversal isGiven Tree is Min-HeapWe see that each parent has a value less than its child, and hence satisfies the min-heap property Input: level = [30, 56, 22, 49, 30, 51, 2, 67]Output: FalseExplanation: The tree of the given level order traversal isGiven Tree is not min-heapWe observe that at level 0, 30 > 22, and hence min-heap property is not satisfiedTo verify the heap property, we ensure that each non-leaf node (parent) is smaller than its children. For every parent at index i, we compare it with its left child at 2*i + 1 and, if present, its right child at 2*i + 2. If a parent has only one child, we check against the left child alone. C++ #include <bits/stdc++.h> using namespace std; // Checks if the given level order traversal represents a Min Heap bool isMinHeap(vector<int> level) { int n = level.size(); // Verify each parent node is smaller than its children for (int i = (n / 2 - 1); i >= 0; i--) { if (level[i] > level[2 * i + 1]) return false; if (2 * i + 2 < n && level[i] > level[2 * i + 2]) return false; } return true; } // Driver code int main() { vector<int> level = {10, 15, 14, 25, 30}; cout << (isMinHeap(level) ? "True" : "False"); return 0; } Java // Java program to check if a given tree is a Min Heap public class GfG { // Checks if the given level order traversal represents a Min Heap static boolean isMinHeap(int[] level) { int n = level.length - 1; // Verify each parent node is smaller than its children for (int i = (n / 2 - 1); i >= 0; i--) { if (level[i] > level[2 * i + 1]) return false; if (2 * i + 2 < n && level[i] > level[2 * i + 2]) return false; } return true; } // Driver code public static void main(String[] args) { int[] level = {10, 15, 14, 25, 30}; System.out.println(isMinHeap(level) ? "True" : "False"); } } Python # Checks if the given level order traversal represents a Min Heap def isMinHeap(level): n = len(level) # Verify each parent node is smaller than its children for i in range((n // 2) - 1, -1, -1): if level[i] > level[2 * i + 1]: return False if 2 * i + 2 < n and level[i] > level[2 * i + 2]: return False return True # Driver code if __name__ == '__main__': level = [10, 15, 14, 25, 30] print("True" if isMinHeap(level) else "False") C# using System; class GfG { // Checks if the given level order traversal represents a Min Heap public static bool isMinHeap(int[] level) { int n = level.Length - 1; // Verify each parent node is smaller than its children for (int i = (n / 2 - 1); i >= 0; i--) { if (level[i] > level[2 * i + 1]) { return false; } if (2 * i + 2 < n && level[i] > level[2 * i + 2]) { return false; } } return true; } public static void Main(string[] args) { int[] level = { 10, 15, 14, 25, 30 }; Console.WriteLine(isMinHeap(level) ? "True" : "False"); } } JavaScript // Checks if the given level order traversal represents a Min Heap function isMinHeap(level) { var n = level.length - 1; // Check if each parent node is smaller than its children for (var i = (n / 2 - 1); i >= 0; i--) { if (level[i] > level[2 * i + 1]) { return false; } if (2 * i + 2 < n && level[i] > level[2 * i + 2]) { return false; } } return true; } // Driver code var level = [10, 15, 14, 25, 30]; console.log(isMinHeap(level) ? "True" : "False"); OutputTrue Comment More infoAdvertise with us Next Article Given level order traversal of a Binary Tree, check if the Tree is a Min-Heap D Deepak Srivatsav Improve Article Tags : Tree Heap DSA tree-level-order Practice Tags : HeapTree Similar Reads Heap Data Structure A Heap is a complete binary tree data structure that satisfies the heap property: for every node, the value of its children is greater than or equal to its own value. Heaps are usually used to implement priority queues, where the smallest (or largest) element is always at the root of the tree.Basics 2 min read Introduction to Heap - Data Structure and Algorithm Tutorials A Heap is a special tree-based data structure with the following properties:It is a complete binary tree (all levels are fully filled except possibly the last, which is filled from left to right).It satisfies either the max-heap property (every parent node is greater than or equal to its children) o 15+ min read Binary Heap A Binary Heap is a complete binary tree that stores data efficiently, allowing quick access to the maximum or minimum element, depending on the type of heap. It can either be a Min Heap or a Max Heap. In a Min Heap, the key at the root must be the smallest among all the keys in the heap, and this pr 13 min read Advantages and Disadvantages of Heap Advantages of Heap Data StructureTime Efficient: Heaps have an average time complexity of O(log n) for inserting and deleting elements, making them efficient for large datasets. We can convert any array to a heap in O(n) time. The most important thing is, we can get the min or max in O(1) timeSpace 2 min read Time Complexity of building a heap Consider the following algorithm for building a Heap of an input array A. A quick look over the above implementation suggests that the running time is O(n * lg(n)) since each call to Heapify costs O(lg(n)) and Build-Heap makes O(n) such calls. This upper bound, though correct, is not asymptotically 2 min read Applications of Heap Data Structure Heap Data Structure is generally taught with Heapsort. Heapsort algorithm has limited uses because Quicksort is better in practice. Nevertheless, the Heap data structure itself is enormously used. Priority Queues: Heaps are commonly used to implement priority queues, where elements with higher prior 2 min read Comparison between Heap and Tree What is Heap? A Heap is a special Tree-based data structure in which the tree is a complete binary tree. Types of Heap Data Structure: Generally, Heaps can be of two types: Max-Heap: In a Max-Heap the key present at the root node must be greatest among the keys present at all of its children. The sa 3 min read 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 sta 4 min read Some other type of HeapBinomial HeapThe main application of Binary Heap is to implement a priority queue. 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Examples:Input: arr[] = {7, 10, 4, 3, 20, 15}, K = 3 Output: 7Input: arr[] = {7, 10, 4, 3, 20, 15}, K = 4 Output: 10 Table of Content[Naive Ap 15 min read Height of a complete binary tree (or Heap) with N nodesConsider a Binary Heap of size N. We need to find the height of it. Examples: Input : N = 6 Output : 2 () / \ () () / \ / () () () Input : N = 9 Output : 3 () / \ () () / \ / \ () () () () / \ () ()Recommended PracticeHeight of HeapTry It! Let the size of the heap be N and the height be h. If we tak 3 min read Heap Sort for decreasing order using min heapGiven 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.Using Min Heap Implementation - O(n Log n) Time 11 min read Like