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
Explanation:
1
/     \
2       3
/   \    / \
4      5 6   7
/   \   /
8     9 10
Leaf Nodes of the Binary Heap are:
6 7 8 9 10

Approach: The key observation in the problem is that the every leaf node of the Binary  Heap will be at the Height H or H -1, If H is the height of the Binary Heap. Therefore, the leaf nodes can be computed as follows:

• Calculate the total height of the binary heap.
• Traverse the array in reverse order and compare the height of each node to the compute height H of the Binary Heap.
• If the height of the current node is H, then add the current node to the leaf nodes.
• Otherwise, If the height of current node is H-1 and there are no child nodes, then also add the node as leaf node.

Below is the implementation of the above approach:

Java

 // Java implementation to print // the leaf nodes of a Binary Heap    import java.lang.*; import java.util.*; class GFG {        // Function to calculate height     // of the Binary heap with given     // the count of the nodes     static int height(int N)     {         return (int)Math.ceil(                    Math.log(N + 1)                    / Math.log(2))             - 1;     }        // Function to find the leaf     // nodes of binary heap     static void findLeafNodes(         int arr[], int n)     {         // Calculate the height of         // the complete binary tree         int h = height(n);            ArrayList arrlist             = new ArrayList<>();            for (int i = n - 1; i >= 0; i--) {             if (height(i + 1) == h) {                 arrlist.add(arr[i]);             }             else if (height(i + 1) == h - 1                      && n <= ((2 * i) + 1)) {                    // if the height if h-1,                 // then there should not                 // be any child nodes                 arrlist.add(arr[i]);             }             else {                 break;             }         }         printLeafNodes(arrlist);     }        // Function to print the leaf nodes     static void printLeafNodes(         ArrayList arrlist)     {         for (int i = arrlist.size() - 1;              i >= 0; i--) {             System.out.print(                 arrlist.get(i) + " ");         }     }        // Driver Code     public static void main(String[] args)     {         int arr[] = { 1, 2, 3, 4, 5,                       6, 7, 8, 9, 10 };         findLeafNodes(arr, arr.length);     } }

C#

 // C# implementation to print // the leaf nodes of a Binary Heap using System; using System.Collections.Generic; class GFG{    // Function to calculate height // of the Binary heap with given // the count of the nodes static int height(int N) {     return (int)Math.Ceiling(                 Math.Log(N + 1) /                 Math.Log(2)) - 1; }    // Function to find the leaf // nodes of binary heap static void findLeafNodes(int []arr,                            int n) {     // Calculate the height of     // the complete binary tree     int h = height(n);        List arrlist = new List();        for (int i = n - 1; i >= 0; i--)      {         if (height(i + 1) == h)         {             arrlist.Add(arr[i]);         }         else if (height(i + 1) == h - 1 &&                   n <= ((2 * i) + 1))          {                // if the height if h-1,             // then there should not             // be any child nodes             arrlist.Add(arr[i]);         }         else         {             break;         }     }     printLeafNodes(arrlist); }    // Function to print the leaf nodes static void printLeafNodes(List arrlist) {     for (int i = arrlist.Count - 1; i >= 0; i--)      {         Console.Write(arrlist[i] + " ");     } }    // Driver Code public static void Main(String[] args) {     int []arr = { 1, 2, 3, 4, 5,                   6, 7, 8, 9, 10 };     findLeafNodes(arr, arr.Length); } }    // This code is contributed by Princi Singh

Output:

6 7 8 9 10

Performance Analysis:

• Time Complexity: O(L), where L is the number of leaf nodes.
• Auxiliary Space: O(1)

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