Given the level order traversal of a Complete Binary Tree, determine whether the Binary Tree is a valid Min-Heap
Examples:
Input : level = [10, 15, 14, 25, 30]
Output : True
The tree of the given level order traversal is
10
/ \
15 14
/ \
25 30
We 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 : False
The tree of the given level order traversal is
30
/ \
56 22
/ \ / \
49 30 51 2
/
67
We observe that at level 0, 30 > 22, and hence
min-heap property is not satisfied
We need to check whether each non-leaf node (parent) satisfies the heap property. For this, we check whether each parent (at index i) is smaller than its children (at indices 2*i+1 and 2*i+2, if the parent has two children). If only one child, we only check the parent against index 2*i+1.
C++
// C++ program to check if a given tree is // Binary Heap or not #include <bits/stdc++.h> using namespace std; // Returns true if given level order traversal // is Min Heap. bool isMinHeap(int level[], int n) { // First non leaf node is at index (n/2-1). // Check whether each parent is greater than child for (int i=(n/2-1) ; i>=0 ; i--) { // Left child will be at index 2*i+1 // Right child will be at index 2*i+2 if (level[i] > level[2 * i + 1]) return false; if (2*i + 2 < n) { // If parent is greater than right child if (level[i] > level[2 * i + 2]) return false; } } return true; } // Driver code int main() { int level[] = {10, 15, 14, 25, 30}; int n = sizeof(level)/sizeof(level[0]); if (isMinHeap(level, n)) cout << "True"; else cout << "False"; return 0; } |
chevron_right
filter_none
Java
// Java program to check if a given tree is // Binary Heap or not import java.io.*; import java.util.*; public class detheap { // Returns true if given level order traversal // is Min Heap. static boolean isMinHeap(int []level) { int n = level.length - 1; // First non leaf node is at index (n/2-1). // Check whether each parent is greater than child for (int i=(n/2-1) ; i>=0 ; i--) { // Left child will be at index 2*i+1 // Right child will be at index 2*i+2 if (level[i] > level[2 * i + 1]) return false; if (2*i + 2 < n) { // If parent is greater than right child if (level[i] > level[2 * i + 2]) return false; } } return true; } // Driver code public static void main(String[] args) throws IOException { // Level order traversal int[] level = new int[]{10, 15, 14, 25, 30}; if (isMinHeap(level)) System.out.println("True"); else System.out.println("False"); } } |
chevron_right
filter_none
Python3
# Python3 program to check if a given # tree is Binary Heap or not # Returns true if given level order # traversal is Min Heap. def isMinHeap(level, n): # First non leaf node is at index # (n/2-1). Check whether each parent # is greater than child for i in range(int(n / 2) - 1, -1, -1): # Left child will be at index 2*i+1 # Right child will be at index 2*i+2 if level[i] > level[2 * i + 1]: return False if 2 * i + 2 < n: # If parent is greater than right child if level[i] > level[2 * i + 2]: return False return True # Driver code if __name__ == '__main__': level = [10, 15, 14, 25, 30] n = len(level) if isMinHeap(level, n): print("True") else: print("False") # This code is contributed by PranchalK |
chevron_right
filter_none
C#
// C# program to check if a given tree // is Binary Heap or not using System; class GFG { // Returns true if given level // order traversal is Min Heap. public static bool isMinHeap(int[] level) { int n = level.Length - 1; // First non leaf node is at // index (n/2-1). Check whether // each parent is greater than child for (int i = (n / 2 - 1) ; i >= 0 ; i--) { // Left child will be at index 2*i+1 // Right child will be at index 2*i+2 if (level[i] > level[2 * i + 1]) { return false; } if (2 * i + 2 < n) { // If parent is greater than right child if (level[i] > level[2 * i + 2]) { return false; } } } return true; } // Driver code public static void Main(string[] args) { // Level order traversal int[] level = new int[]{10, 15, 14, 25, 30}; if (isMinHeap(level)) { Console.WriteLine("True"); } else { Console.WriteLine("False"); } } } // This code is contributed by Shrikant13 |
chevron_right
filter_none
PHP
<?php // PHP program to check if a given tree // is Binary Heap or not // Returns true if given level order // traversal is Min Heap. function isMinHeap($level, $n) { // First non leaf node is at index // (n/2-1). Check whether each parent // is greater than child for ($i = ($n / 2 - 1); $i >= 0; $i--) { // Left child will be at index 2*i+1 // Right child will be at index 2*i+2 if ($level[$i] > $level[2 * $i + 1]) return false; if (2 * $i + 2 < $n) { // If parent is greater than right child if ($level[$i] > $level[2 * $i + 2]) return false; } } return true; } // Driver code $level = array(10, 15, 14, 25, 30); $n = sizeof($level); if (isMinHeap($level, $n)) echo "True"; else echo "False"; // This code is contributed // by Akanksha Rai |
chevron_right
filter_none
Output:
True
These algorithms run with worse case O(n) complexity
This article is contributed by Deepak Srivatsav. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.
Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.
Recommended Posts:
- Level order traversal of Binary Tree using Morris Traversal
- Flatten Binary Tree in order of Level Order Traversal
- Print a Binary Tree in Vertical Order | Set 3 (Using Level Order Traversal)
- Print nodes of a Binary Search Tree in Top Level Order and Reversed Bottom Level Order alternately
- Check if the given array can represent Level Order Traversal of Binary Search Tree
- Insertion in n-ary tree in given order and Level order traversal
- Check if the level order traversal of a Binary Tree results in a palindrome
- Connect Nodes at same Level (Level Order Traversal)
- Deletion of a given node K in a Binary Tree using Level Order Traversal
- Perfect Binary Tree Specific Level Order Traversal
- Perfect Binary Tree Specific Level Order Traversal | Set 2
- Build Binary Tree from BST such that it's level order traversal prints sorted data
- Density of Binary Tree using Level Order Traversal
- Calculate height of Binary Tree using Inorder and Level Order Traversal
- Specific Level Order Traversal of Binary Tree
- Boundary Level order traversal of a Binary Tree
- Level Order Binary Tree Traversal
- Flatten binary tree in order of post-order traversal
- Check if two trees are mirror of each other using level order traversal
- General Tree (Each node can have arbitrary number of children) Level Order Traversal
