Heap Sort

Heap Sort is a comparison-based sorting algorithm that uses a binary heap data structure to sort elements. It is an in-place algorithm and has a time complexity of O(n log n), making it efficient for large datasets.

Algorithm

The Heap Sort algorithm consists of the following steps:

1. Build a Max Heap from the input data.
2. Swap the root node with the last node and remove the last node from the heap.
3. Repeat steps 2 and 3 until the heap is empty.
4. Restore the heap property by comparing the swapped element with its children and swapping if necessary.

Example

To demonstrate the Heap Sort algorithm, consider the following array of integers:

1int[] arr = {4, 10, 3, 5, 1};

Step 1: Build a Max Heap

In the first step, we build a max heap from the given array. The max heap is represented as an array with the following values:

1{10, 5, 3, 4, 1}

Step 2: Swap and Remove the Root Node

Next, we swap the root node (the largest element) with the last node and remove the last node from the heap. After the first swap and removal, the heap becomes:

1{5, 4, 3, 1}

Step 3: Repeat Swapping and Removal

We repeat the swapping and removal process until the heap is empty. After each iteration, the largest element is moved to the end of the array. The sorted array at each step is as follows:

1{1, 5, 3, 4}
2{1, 4, 3}
3{1, 3}
4{1}

Step 4: Restore the Heap Property

After the sorting process, we restore the heap property by comparing the swapped element with its children and swapping if necessary. The final sorted array is:

1{1, 3, 4, 5, 10}

Java Implementation

Here is a Java implementation of the Heap Sort algorithm:

1${code}

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```java

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