Use c or java please 1 Heapsort Implement in the language of

Use c++ or java please!!!

1 Heapsort

Implement in the language of your choice a function or method which takes in a vector or list of

integers and sorts the list using the heap sort algorithm. You can either modify

the list given (past by reference) or produce a new sorted list (pass by value). The worst case

run time for this function must be O(n log(n)).

2 Quicksort

Implement a function or method in the language of your choice which takes in a vector or list

of integers and sorts the list using the quicksort algorithm. Your function must either modify the given list, or return a new sorted list. The average run time for this function must be O(n log(n)). The worst case run time can be O(n).

3 Mixsort

Implement a function or method in the language of your choice which takes in a vector or list

Of integers and also takes in another integer d which we will refer to as depth. The function will

Recursively call quicksort similar to problem 2 while decrementing depth until the depth has

Reached 0. At which point the algorithm will switch over to the heapsort you implemented in

problem 1 to finish the sorting of the vector. For this problem also comment in the code what

the value of d needs to with respect to the size of the vector n for the algorithm to have worst

case run time of O(n log(n)).

4 Program

You should have the above 3 problems implemented as functions. You also should have an

implementation of a heap included in your code. Make a basic main function that does a test

run for each of the 3 functions above.

Solution

1) Answer:-

Heap Sort:

Heap sort is a comparison based sorting technique based on Binary Heap data structure. It is similar to selection sort where we first find the maximum element and place the maximum element at the end. We repeat the same process for remaining element.

Binary Heap:

Let us first define a Complete Binary Tree. A complete binary tree is a binary tree in which every level, except possibly the last, is completely filled, and all nodes are as far left as possible.
A Binary Heap is a Complete Binary Tree where items are stored in a special order such that value in a parent node is greater(or smaller) than the values in its two children nodes. The former is called as max heap and the latter is called min heap. The heap can be represented by binary tree or array.

Heap Sort Algorithm for sorting in increasing order:
1. Build a max heap from the input data.
2. At this point, the largest item is stored at the root of the heap. Replace it with the last item of the heap followed by reducing the size of heap by 1. Finally, heapify the root of tree.
3. Repeat above steps until size of heap is greater than 1.

How to build the heap?
Heapify procedure can be applied to a node only if its children nodes are heapified. So the heapification must be performed in the bottom up order.

Example:

Program :

#include <iostream>
using namespace std;

void max_heapify(int *a, int i, int n)
{
int j, temp;
temp = a[i];
j = 2*i;
while (j <= n)
{
if (j < n && a[j+1] > a[j])
j = j+1;
if (temp > a[j])
break;
else if (temp <= a[j])
{
a[j/2] = a[j];
j = 2*j;
}
}
a[j/2] = temp;
return;
}
void heapsort(int *a, int n)
{
int i, temp;
for (i = n; i >= 2; i--)
{
temp = a[i];
a[i] = a[1];
a[1] = temp;
max_heapify(a, 1, i - 1);
}
}
void build_maxheap(int *a, int n)
{
int i;
for(i = n/2; i >= 1; i--)
{
max_heapify(a, i, n);
}
}
int main()
{
int n, i, x;
cout<<\"Enter no of elements of arrayn\";
cin>>n;
int a[20];
for (i = 1; i <= n; i++)
{
cout<<\"Enter element\"<<(i)<<endl;
cin>>a[i];
}
build_maxheap(a,n);
heapsort(a, n);
cout<<\"nnSorted Arrayn\";
for (i = 1; i <= n; i++)
{
cout<<a[i]<<endl;
}
return 0;
}

Output :