Shell Sort Vs Heap Sort Vs Quick Sort

[mackol]

i am having a debate as to which of the sort is more efficient in 2 cases:

when a 2d array of size 50, 100, or 1000 of randomly generated integers

and the same 2d array with all numbers sorted but only 2 indexes where their values have been exchanged.

for these 2 cases which of the 3 sorts seems more efficient.. i am pretty sure the quick sort is the best for the randomly generated array..

but what about the other case... the problem that is bugging me is that when the size is small the difference in the number of comparisons made with quick sort is very similar to the shell sort ...

any suggestions welcomed

:wacko:

[Gumboot]

In general, quicksort is the fastest known sort method.

However, if the array is presorted, or nearly presorted, then quicksort is no longer the best (the time taken is not much different from random data which is O(n log n)). Shell sort should be quite a bit quicker. Strangely enough, insertion sort and bubble sort - the two algorithms that are taught first 'cause they're so simple - do really well with presorted input (both O(n)). I suspect that in your case ("all numbers sorted but only 2 indexes where their values have been exchanged") insertion sort will be fastest, even faster than shell sort.

Of course I could be wrong ;)

BTW, Heap sort is never any good - don't use it :)

[xWeston]

Big O notation isnt as exact as you are talking about. The easiest way to try this is just to do it by hand and see how many moves it takes :)

[Gumboot]

  Quote

Big O notation isnt as exact as you are talking about.

Of course it's not exact. On the other hand, for large data sets, any difference in complexity (ie. big-oh) makes a huge difference. Anyway, for the case he's talking about (sorting an almost sorted array) I'm pretty sure shell sort, bubble sort and insertion sort are all O(n). Which makes big-oh notation somewhat useless really. But my guess is that insertion sort will perform the best, due to the simplicity of the algorithm.

[SimGuy]

Gumboot: Did you ever take "Discrete Structures?"

[Gumboot]

Also of note: according to my data structures book, shellsort (with Sedgewick's increments) performs better than quicksort when the data set is small (about 100 items or less).

The full results are posted below (the input data is random and the times are in seconds).

[AOXOMOXOA]

WOW! I must say i dont know wtf you guys are talking about.. :unsure: :unsure:

[Gumboot]

[AMD]-SimGuy: Discrete structures? What're they? :blink:

[mackol]

yeah, what are they

i am doing data structure and i have done discrete mathematics

but what is discrete structures?? :D

from my program it seems like quick sort performed the best in all the cases.

heap sort is disastrous

its time just explodes ...

btw, here is the program which performs these sorts and counts the number of times each sort does a compare and a move ..

#include <stdio.h>
#include <stdlib.h>
#include <memory.h>

#define ARYSIZE 1000
#define ROW 5
#define COL 10
#define SWAP1 19
#define	SWAP2 20
#define NUMTOPRINT 50
#define S "Shell Sort"
#define H "Heap Sort"
#define Q "Quick Sort"

void printSortLine (char *str);
void createAry (int *ary);
void printAry (int *ary, int size);
void shellSort (int list [], int last, int *compare, int *moves);
void printCmpAndMov (int compare, int moves, char *str);
void swap (int *ary);
void heapSort (int list[], int last, int *compare, int *move);
void quickSort (int sortData [], int left, int right, int *compare, int *move);

int main (void)
{
	int ary[ARYSIZE], heapAry [ARYSIZE], quickAry [ARYSIZE], compare = 0, moves = 0;

	createAry (ary);
	memcpy (heapAry, ary, ARYSIZE * sizeof (int));
	memcpy (quickAry, ary, ARYSIZE * sizeof (int));

	printf("Array size:\t%d\n\n", ARYSIZE);

	printSortLine (S);
	compare = moves = 0;
	shellSort (ary, ARYSIZE, &compare, &moves);
	printAry (ary, ARYSIZE);
	printCmpAndMov (compare, moves, "Random list Shell Sort:");
	swap (ary);
	compare = moves = 0;
	shellSort (ary, ARYSIZE, &compare, &moves);
	printCmpAndMov (compare, moves, "Nearly ordered list Shell Sort:");

	printSortLine (H);
	compare = moves = 0;
	heapSort (heapAry, ARYSIZE - 1, &compare, &moves);
	printAry (heapAry, ARYSIZE);
	printCmpAndMov (compare, moves, "Random list Heap Sort:");
	swap (heapAry);
	compare = moves = 0;
	heapSort (heapAry, ARYSIZE - 1, &compare, &moves);
	printCmpAndMov (compare, moves, "Nearly ordered list Heap Sort:");

	printSortLine (Q);
	compare = moves = 0;
	quickSort (quickAry, 0, ARYSIZE - 1, &compare, &moves);
	printAry (quickAry, ARYSIZE);
	printCmpAndMov (compare, moves, "Random list Quick Sort:");
	swap (quickAry);
	compare = moves = 0;
	quickSort (quickAry, 0, ARYSIZE - 1, &compare, &moves);
	printCmpAndMov (compare, moves, "Nearly ordered list Quick Sort:");

	return 0;
}

void printSortLine (char *str)
{
	printf("\nPerforming %s....\n\n", str);
	return;
}

void createAry (int *ary)
{
	int i;

	for (i = 0; i < ARYSIZE; i++)
	{
  ary[i] = rand () % 1001;
	}
	return;
}

void printAry (int *ary, int size)
{
	int i, j;

	if (size <= NUMTOPRINT)
	{
  for (i = 0; i < ROW; i++)
  {
 	 for (j = 0; j < COL; j++)
 	 {
    printf("%4d   ", ary[(i * COL) + j]);
 	 }
 	 printf("\n");
  }
	}
	printf("\n");
	return;
}

void printCmpAndMov (int compare, int moves, char *str)
{
	printf("%-25s\t|compares = %6d  |  moves = %6d|\n", str, compare, moves);
	return;
}

void swap (int *ary)
{
	int temp;

	temp = ary[SWAP1];
	ary [SWAP1] = ary [SWAP2];
	ary [SWAP2] = temp;
	return;
}

void shellSort (int list [], int last, int *compare, int *moves)
{
	int hold, incre, curr, walker;

	incre = last / 2;
	while (incre != 0)
	{
  for (curr = incre; curr <= last; curr++)
  {
 	 hold = list [curr];
 	 *moves += 1;
 	 walker = curr - incre;
 	 while (((*compare)++,walker >= 0 && hold < list [walker]))
 	 {
    list [walker + incre] = list [walker];
    *moves += 1;

    walker = (walker - incre);
 	 }

 	 list [walker + incre] = hold;
 	 *moves += 1;
  }
  incre /= 2;
	}
	return;
}


void heapSort (int list[], int last, int *compare, int *move)
{
	void reheapUp (int heap[], int newElem, int *compare, int *move);
	void reheapDown (int heap[], int current, int last, int *compare, int *move);

	int sorted, holdData, walker;

	for (walker = 1; walker <= last; walker++)
	{
  reheapUp (list, walker, compare, move);
	}

	sorted = last;
	while (sorted > 0)
	{
  holdData = list [0];
  list [0] = list [sorted];
  list [sorted] = holdData;
  *move += 3;
  sorted--;
  reheapDown (list, 0, sorted, compare, move);
	}
	return;
}

void reheapUp (int *heap, int newNode, int *compare, int *move)
{
	int parent, hold;

	if (newNode)
	{
  parent = (newNode - 1)/2;
  if ( *compare += 1, heap [newNode] > heap [parent])
  {
 	 hold = heap[parent];
 	 heap[parent] = heap[newNode];
 	 heap[newNode] = hold;
 	 *move += 3;
 	 reheapUp (heap, parent, compare, move);
  }
	}
	return;
}

void reheapDown (int *heap, int root, int last, int *compare, int *move)
{
	int hold, leftKey, rightKey, largeChildKey, largeChildIndex;

	if ((root * 2 + 1) <= last)
	{
  leftKey = heap [root * 2 + 1];
  *move += 1;

  if ((root * 2 + 2) <= last)
  {
 	 rightKey = heap [root * 2 + 2];
 	 *move += 1;
  }
  else
  {
 	 rightKey = -1;
  }

  if (leftKey > rightKey)
  {
 	 largeChildKey = leftKey;
 	 largeChildIndex = root * 2 + 1;
  }
  else
  {
 	 largeChildKey = rightKey;
 	 largeChildIndex = root * 2 + 2;
  }

  if (*compare += 1, heap[root] < heap [largeChildIndex])
  {
 	 hold = heap [root];
 	 heap [root] = heap [largeChildIndex];
 	 heap [largeChildIndex] = hold;
 	 *move += 3;
 	 reheapDown (heap, largeChildIndex, last, compare, move);
  }
	}
	return;
}

void quickSort (int sortData [], int left, int right, int *compare, int *move)
{
#define MIN_SIZE 16

	void quickInsertion (int sortData[], int first, int last, int *compare, int *move);
	void medianLeft (int sortData[], int left, int right, int *compare, int *move);

	int sortLeft;
	int sortRight;
	int pivot;
	int hold;

	if ( (right - left) > MIN_SIZE)
	{
  medianLeft (sortData, left, right, compare, move);
  pivot = sortData [left];
  *move += 1;
  sortLeft = left + 1;
  sortRight = right;

  while (sortLeft <= sortRight)
  {
 	 while (*compare += 1, sortData [sortLeft] < pivot)
    sortLeft = sortLeft + 1;

 	 while (*compare += 1, sortData[sortRight] >= pivot)
    sortRight = sortRight - 1;

 	 if (sortLeft <= sortRight)
 	 {
    hold = sortData [sortLeft];
    sortData [sortLeft] = sortData [sortRight];
    sortData [sortRight] = hold;
    *move += 3;
    sortLeft = sortLeft + 1;
    sortRight = sortRight - 1;
 	 }
  }

  sortData [left] = sortData [sortLeft - 1];

  sortData [sortLeft - 1] = pivot;

  *move += 2;

  if (left < sortRight)
 	 quickSort (sortData, left, sortRight - 1, compare, move);
  if (sortLeft < right)
 	 quickSort (sortData, sortLeft, right, compare, move);
	}
	else
  quickInsertion (sortData, left, right, compare, move);
	return;
}

void quickInsertion (int sortData[], int first, int last, int *compare, int *move)
{
	int current;
	int hold;
	int walker;

	for (current = first + 1; current <= last; current++)
	{
  hold = sortData [current];
  *move += 1;
  walker = current - 1;
  while (*compare += 1, walker >= first && hold < sortData [walker])
  {
 	 sortData [walker + 1] = sortData [walker];
 	 *move += 1;
 	 walker = walker - 1;
  }
  sortData[walker + 1] = hold;
  *move += 1;
	}
	return;
}

void medianLeft (int sortData[], int left, int right, int *compare, int *move)
{
	int mid;
	int hold;

	mid = (left + right) / 2;

	if (*compare += 1, sortData [left] > sortData [mid])
	{
  hold = sortData [left];
  sortData [left] = sortData [mid];
  sortData [mid] = hold;  
  *move += 3;
	}
	if (*compare += 1, sortData [left] > sortData [right])
	{
  hold = sortData [left];
  sortData [left] = sortData [right];
  sortData [right] = hold;
  *move += 3;
	}
	if (*compare += 1, sortData [mid] > sortData [right])
	{
  hold = sortData [mid];
  sortData [mid] = sortData [right];
  sortData [right] = hold;
  *move += 3;
	}

	hold = sortData [left];
	sortData [left] = sortData [mid];
	sortData [mid] = hold;
	*move += 3;

	return;
}

here is the output file

  Quote

output# 1

Array size:     50

Performing Shell Sort....

 18     41    117    126    150    153    225    258    273    291

292    303    328    329    359    370    404    431    440    442

449    467    474    491    527    590    642    656    660    675

698    699    700    704    705    709    757    788    811    823

862    868    876    885    893    899    931    936    952    993

Random list Shell Sort:         |compares =    372  |  moves =    580|

Nearly ordered list Shell Sort: |compares =    209  |  moves =    417|

Performing Heap Sort....

 18     41    117    126    150    153    225    258    273    291

292    303    328    329    359    370    404    431    440    442

449    467    474    491    527    590    642    656    660    675

698    699    700    704    705    709    757    788    811    823

862    868    876    885    893    899    931    936    952    993

Random list Heap Sort:          |compares =    269  |  moves =   1140|

Nearly ordered list Heap Sort:  |compares =    361  |  moves =   1467|

Performing Quick Sort....

 18     41    117    126    150    153    225    258    273    291

292    303    328    329    359    370    404    431    440    442

449    467    474    491    527    590    642    656    660    675

698    699    700    704    705    709    757    788    811    823

862    868    876    885    893    899    931    936    952    993

Random list Quick Sort:         |compares =    294  |  moves =    306|

Nearly ordered list Quick Sort: |compares =    155  |  moves =    105|

Output# 2

Array size:     100

Performing Shell Sort....

Random list Shell Sort:         |compares =    916  |  moves =   1425|

Nearly ordered list Shell Sort: |compares =    510  |  moves =   1019|

Performing Heap Sort....

Random list Heap Sort:          |compares =    642  |  moves =   2756|

Nearly ordered list Heap Sort:  |compares =    910  |  moves =   3685|

Performing Quick Sort....

Random list Quick Sort:         |compares =    712  |  moves =    731|

Nearly ordered list Quick Sort: |compares =    410  |  moves =    213|

Output# 3

Array size:     1000

Performing Shell Sort....

Random list Shell Sort:         |compares =  15493  |  moves =  23508|

Nearly ordered list Shell Sort: |compares =   8015  |  moves =  16030|

Performing Heap Sort....

Random list Heap Sort:          |compares =   9733  |  moves =  43757|

Nearly ordered list Heap Sort:  |compares =  15325  |  moves =  61177|

Performing Quick Sort....

Random list Quick Sort:         |compares =  10982  |  moves =   9177|

Nearly ordered list Quick Sort: |compares =   7032  |  moves =   2205|

[kyo116]

quick sort is the fastest when u have huge test cases. (i learnt that half way through a programming competition, bad day that was)

shell sort and merge sort would serve ur purpose the rest of the time.

heapsort, bubble sort, selection sort are practically useless.

thats wat i feel.