Sorting Algorithm

Files
file	merge_sort.cpp
	Merege Sort Algorithm (MEREGE SORT) implementation

Functions
template<typename T >
void	heapify (T *arr, int n, int i)
template<typename T >
void	heapSort (T *arr, int n)
void	merge (int *arr, int l, int m, int r)
void	mergeSort (int *arr, int l, int r)
void	show (int *arr, int size)
int	main ()

Detailed Description

The heapify procedure can be thought of as building a heap from the bottom up by successively sifting downward to establish the heap property.

Parameters

arr	array to be sorted
n	size of array
i	node position in Binary Tress or element position in Array to be compared with it's childern

Function Documentation

heapSort()

template<typename T >

void heapSort	(	T *	arr,
		int	n
	)

Utilizes heapify procedure to sort the array

Parameters

arr	array to be sorted
n	size of array

                             {
    for (int i = n - 1; i >= 0; i--) heapify(arr, n, i);
 
    for (int i = n - 1; i >= 0; i--) {
        std::swap(arr[0], arr[i]);
        heapify(arr, i, 0);
    }
}

main()

int main

(

void

)

Main function

           {
    int size;
    std::cout << "Enter the number of elements : ";
    std::cin >> size;
    int *arr = new int[size];
    std::cout << "Enter the unsorted elements : ";
    for (int i = 0; i < size; ++i) {
        std::cin >> arr[i];
    }
    mergeSort(arr, 0, size - 1);
    std::cout << "Sorted array : ";
    show(arr, size);
    delete[] arr;
    return 0;
}

merge()

void merge	(	int *	arr,
		int	l,
		int	m,
		int	r
	)

The merge() function is used for merging two halves. The merge(arr, l, m, r) is key process that assumes that arr[l..m] and arr[m+1..r] are sorted and merges the two sorted sub-arrays into one.

Parameters

arr	- array with two halves arr[l...m] and arr[m+1...l]
l	- left index or start index of first half array
m	- right index or end index of first half array

(The second array starts form m+1 and goes till l)

Parameters

l	- end index or right index of second half array

                                          {
    int i, j, k;
    int n1 = m - l + 1;
    int n2 = r - m;
 
    int *L = new int[n1], *R = new int[n2];
 
    for (i = 0; i < n1; i++) L[i] = arr[l + i];
    for (j = 0; j < n2; j++) R[j] = arr[m + 1 + j];
 
    i = 0;
    j = 0;
    k = l;
    while (i < n1 || j < n2) {
        if (j >= n2 || (i < n1 && L[i] <= R[j])) {
            arr[k] = L[i];
            i++;
        } else {
            arr[k] = R[j];
            j++;
        }
        k++;
    }
 
    delete[] L;
    delete[] R;
}

mergeSort()

void mergeSort	(	int *	arr,
		int	l,
		int	r
	)

Merge sort is a divide and conquer algorithm, it divides the input array into two halves and calls itself for the two halves and then calls merge() to merge the two halves

Parameters

arr	- array to be sorted
l	- left index or start index of array
r	- right index or end index of array

                                       {
    if (l < r) {
        int m = l + (r - l) / 2;
        mergeSort(arr, l, m);
        mergeSort(arr, m + 1, r);
        merge(arr, l, m, r);
    }
}

Here is the call graph for this function:

show()

void show	(	int *	arr,
		int	size
	)

Utility function used to print the array after sorting

                              {
    for (int i = 0; i < size; i++) std::cout << arr[i] << " ";
    std::cout << "\n";
}