How to sort list of values using only one variable?
EDIT: according to @Igor's comment, I retitled the question.
How to sort list of values using only one variable?
EDIT: according to @Igor's comment, I retitled the question.
You dont, it is already sorted. (as the question is vague, I shall assume variable is a synonym for an object)
Do you mean list with only one element, or you mean sort it using only one additional variable?
You could generate/write a lot of sorting-networks for each possible list size. Inside the sorting network you use a single variable for the swap operation.
I wouldn't recommend that you do this in software, but it is possible nevertheless.
Here's a sorting-routine for all n up to 4 in C
// define a compare and swap macro
#define order(a,b) if ((a)<(b)) { temp=(a); (a) = (b); (b) = temp; }
static void sort2 (int *data)
// sort-network for two numbers
{
int temp;
order (data[0], data[1]);
}
static void sort3 (int *data)
// sort-network for three numbers
{
int temp;
order (data[0], data[1]);
order (data[0], data[2]);
order (data[1], data[2]);
}
static void sort4 (int *data)
// sort-network for four numbers
{
int temp;
order (data[0], data[2]);
order (data[1], data[3]);
order (data[0], data[1]);
order (data[2], data[3]);
order (data[1], data[2]);
}
void sort (int *data, int n)
{
switch (n)
{
case 0:
case 1:
break;
case 2:
sort2 (data);
break;
case 3:
sort3 (data);
break;
case 4:
sort4 (data);
break;
default:
// Sorts for n>4 are left as an exercise for the reader
abort();
}
}
Obviously you need a sorting-network code for each possible N.
More info here:
I suspect I'm doing your homework for you, but hey it's an interesting challenge. Here's a solution in Icon:
procedure mysort(thelist)
local n # the one integer variable
every n := (1 to *thelist & 1 to *thelist-1) do
if thelist[n] > thelist[n+1] then thelist[n] :=: thelist[n+1]
return thelist
end
procedure main(args)
every write(!mysort([4,7,2,4,1,10,3]))
end
The output:
1
2
3
4
4
7
10
#include <stdio.h>
int main()
{
int list[]={4,7,2,4,1,10,3};
int n; // the one int variable
startsort:
for (n=0; n< sizeof(list)/sizeof(int)-1; ++n)
if (list[n] > list[n+1]) {
list[n] ^= list[n+1];
list[n+1] ^= list[n];
list[n] ^= list[n+1];
goto startsort;
}
for (n=0; n< sizeof(list)/sizeof(int); ++n)
printf("%d\n",list[n]);
return 0;
}
Output is of course the same as for the Icon program.
In java:
import java.util.Arrays;
/**
* Does a bubble sort without allocating extra memory
*
*/
public class Sort {
// Implements bubble sort very inefficiently for CPU but with minimal variable declarations
public static void sort(int[] array) {
int index=0;
while(true) {
next:
{
// Scan for correct sorting. Wasteful, but avoids using a boolean parameter
for (index=0;index<array.length-1;index++) {
if (array[index]>array[index+1]) break next;
}
// Array is now correctly sorted
return;
}
// Now swap. We don't need to rescan from the start
for (;index<array.length-1;index++) {
if (array[index]>array[index+1]) {
// use xor trick to avoid using an extra integer
array[index]^=array[index+1];
array[index+1]^=array[index];
array[index]^=array[index+1];
}
}
}
}
public static void main(final String argv[]) {
int[] array=new int[] {4,7,2,4,1,10,3};
sort(array);
System.out.println(Arrays.toString(array));
}
}
Actually, by using the trick proposed by Nils, you can eliminate even the one remaining int allocation - though of course that would add to the stack instead...
If you have a list (1 5 3 7 4 2)
and a variable v
, you can exchange two values of the list, for example the 3 and the 7, by first assigning 3 to v
, then assigning 7 to the place of 3, finally assigning the value of v
to the original place of 7. After that, you can reuse v
for the next exchange. In order to sort, you just need an algorithm that tells which values to exchange. You can look for a suitable algorithm for example at http://en.wikipedia.org/wiki/Sorting_algorithm .