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### Arrays and Sorting: Heap Sort ( with C Program source code, a tutorial and an MCQ Quiz )

Basic Sorting and Searching Algorithms for Arrays, at a glance
 Bubble Sort Insertion Sort Selection Sort Shell Sort Merge Sort Quick Sort Heap Sort Binary Search Algorithm

### Heap Sort

Heapsort uses the property of Heaps to sort an array. The Heap data structure is an array object that can be viewed as a complete and balanced binary tree. Min (Max)-Heap has a property that for every node other than the root, the value of the node is at least (at most) the value of its parent. Thus, the smallest (largest) element in a heap is stored at the root, and the subtrees rooted at a node contain larger (smaller) values than does the node itself.

### Algorithm:

It starts with building a heap by inserting the elements entered by the user, in its place.
1. Increase the size of the heap as a value is inserted.
2. Insert the entered value in the last place.
3. Compare the inserted value with its parent, until it satisfies the heap property and then
place it at its right position.

Now once the heap is built remove the elements from top to bottom, while maintaining the heap property to obtain the sorted list of entered values.

1. heap is the minimum element. So we remove heap. Size of the heap is decreased.
2. Now heap has to be filled. We put the last element in its place and see if it fits. If it does not fit, take minimum element among both its children and replaces parent with it.
3. Again see if the last element fits in that place.

### Property:

Best case performance – when the input array is already sorted O(nlogn).
Worst case performance – when the input array is in reverse order O(nlogn).
Average case performance – O(nlogn)
It does not require any extra space for sorting, hence O(1) extra space.
It is not stable.

## Heap Sort - C Program Source Code

`#include<stdio.h>#include<limits.h>/*Declaring heap globally so that we do not need to pass it as an argument every time*//* Heap used here is Min Heap */int heap,heapSize;/*Initialize Heap*/void Init(){        heapSize = 0;        heap = -INT_MAX;}/*Insert an element into the heap */void Insert(int element){        heapSize++;        heap[heapSize] = element; /*Insert in the last place*/        /*Adjust its position*/        int now = heapSize;        while(heap[now/2] > element)         {                heap[now] = heap[now/2];                now /= 2;        }        heap[now] = element;}int DeleteMin(){        /* heap is the minimum element. So we remove heap. Size of the heap is decreased.            Now heap has to be filled. We put the last element in its place and see if it fits.           If it does not fit, take minimum element among both its children and replaces parent with it.           Again See if the last element fits in that place.*/        int minElement,lastElement,child,now;        minElement = heap;        lastElement = heap[heapSize--];        /* now refers to the index at which we are now */        for(now = 1; now*2 <= heapSize ;now = child)        {                /* child is the index of the element which is minimum among both the children */                 /* Indexes of children are i*2 and i*2 + 1*/                child = now*2;                /*child!=heapSize beacuse heap[heapSize+1] does not exist, which means it has only one                   child */                if(child != heapSize && heap[child+1] < heap[child] )                 {                        child++;                }                /* To check if the last element fits ot not it suffices to check if the last element                   is less than the minimum element among both the children*/                if(lastElement > heap[child])                {                        heap[now] = heap[child];                }                else /* It fits there */                {                        break;                }        }        heap[now] = lastElement;        return minElement;}int main(){        int number_of_elements;        scanf("%d",&number_of_elements);        int iter, element;        Init();        for(iter = 0;iter < number_of_elements;iter++)        {                scanf("%d",&element);                Insert(element);        }        for(iter = 0;iter < number_of_elements;iter++)        {                printf("%d ",DeleteMin());        }        printf("\n");        return 0;}`

`MCQ Quiz: Efficient Sorting Algorithms- Quick sort, Merge Sort, Heap Sort- Check how much you can score!Your score will be e-mailed to the address filled up by you.MCQ Quiz- More efficient sorting algorithms `
Related Tutorials :

 Bubble Sort One of the most elementary sorting algorithms to implement - and also very inefficient. Runs in quadratic time. A good starting point to understand sorting in general, before moving on to more advanced techniques and algorithms. A general idea of how the algorithm works and a the code for a C program. Insertion Sort Another quadratic time sorting algorithm - an example of dynamic programming. An explanation and step through of how the algorithm works, as well as the source code for a C program which performs insertion sort. Selection Sort Another quadratic time sorting algorithm - an example of a greedy algorithm. An explanation and step through of how the algorithm works, as well as the source code for a C program which performs selection sort. Shell Sort An inefficient but interesting algorithm, the complexity of which is not exactly known. Merge Sort An example of a Divide and Conquer algorithm. Works in O(n log n) time. The memory complexity for this is a bit of a disadvantage. Quick Sort In the average case, this works in O(n log n) time. No additional memory overhead - so this is better than merge sort in this regard. A partition element is selected, the array is restructured such that all elements greater or less than the partition are on opposite sides of the partition. These two parts of the array are then sorted recursively. Heap Sort Efficient sorting algorithm which runs in O(n log n) time. Uses the Heap data structure. Binary Search Algorithm Commonly used algorithm used to find the position of an element in a sorted array. Runs in O(log n) time.

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