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# Heap Sort in Data Structures

## Heap Sort

Building Heap

1. start with just one, element one element will always, satisfy heap property.
2. Insert next elements and make this a heap
3. Repeat step b until all elements are include in the heap

Sorting

1. Exchange the root name the last element in the heap
2. Make this a heap agar, but this time do not include the last node.
3. Repeat step a and b until there is no element left

#### Example

set the following elements in ascending order using heap sort 4,8,9,5.6

A

 4 8 3 9 5 6 1 2 3 4 5 6

### Sorting

Program :

Implementation of Heap Sort

# include<stdio.h>

void Heapsort(int a[],int n);

void Build Heap(int a[],int n);

void Reheap(int a[],int k);

void main()

{

in a[20],n,i;

printf(“Enter N value \n”);

scanf(“%d”,&n);

printf(“Enter those numbers: \n”);

for(int i=1; i<=n; i++)

{

scanf(“%d”,&a[i]);

}

Heap sort(a,n);

printf(“ The following are the sorted elements. \n”);

for(i=1;i<=n;i++)

{

printf(“%d”,a[i]);

}

}

void Heap sort(int a[],int n)

{

int fs,temp;

Build Heap(a,n);

for(pos=n;pos>=2;pos–)

{

temp=a[1];

a[1]=a[pos];

a[pos]=temp;

Reheap(a,pos-1);

}

}

void Build Heap(int a[],int n)

{

for(j=2;j<=n;j++)

{

key=a[i];

i=j/2;

while((i>0) && (a[i]<key))

{

a[j]=a[i];

j=i;

i=j/2;

}

a[j]=key;

}

a[j]=key;

}

}

void Reheap(int a[], int k)

{

int parent, child, key, heap;

parent=1;

child=2;

Key=a[parent];

heap=0;

while((child<=k) && (!heap))

{

if(child<k)

{

if(a[child+1]>a[child])

child=child+1;

}

if(a[child]>key)

{

a[parent]=a[child];

parent=child;

child=parent*2;

}

else

{

heap=1;

}

}

a[parent]=key;

}

### Time complexity :

Since each phase require time proportional to nlog2n, The running time to sort the n-element array using heap sort is proportional to nlog2n, that is

f(n)=0(nlog2n) the average running time of heap sort is o(nlog2n)