# 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); ` `    ``} ` ` `  `    ``// Funtion 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<``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); ` `} ` ` `  `// Funtion 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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