Print all the leaf nodes of Binary Heap

Difficulty Level : Medium
Last Updated : 20 Aug, 2020

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<Integer> 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<Integer> 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<int> arrlist = new List<int>(); 
  
    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<int> 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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