Gapped Insertion sort implementation - c++

Question

I'm trying to pull off a gapped insertion sort in C++, known as a Library sort. I understand the concept, but I'm having trouble pulling it off going from a regular old insertion sort. I don't know how I'd account for the gaps in the array. I've been using the integer 0 to specify a gap. The code I have so far is below, which is a working insertion sort modified abit. How would you go about implementing a library sort? I went through 20 pages of google, and I have not seen a single actual example of code, in any programming language.
#include <iostream>
#include <stdlib.h>
#include <time.h>
#include <vector>
using namespace std;
vector<int> librarySort(int arr[20])
{
int j,tmp;
vector<int> array;
for (int i=0;i<20;i++)
{
array.push_back(0);
array.push_back(arr[i]);
}
for (int i=0;i<40;i++) { cout << array[i] << ",";}
cout << endl;
for (int i = 1; i < 40; i++)
{
j = i;
while (j > 0 && array[j - 1] > array[j])
{
tmp = array[j];
array[j] = array[j - 1];
array[j - 1] = tmp;
j--;
}
}
for (int i=0;i<40;i++) { cout << array[i] << ",";}
return array;
}
int main()
{
srand(time(0));
int array[20]= {0};
for (int i=0;i<20;i++)
{
int n=rand()%19+1;
tmp=array[i];
array[i]=array[n];
array[n]=tmp;
}
for (int i=0;i<20;i++) { cout << array[i] << ",";}
cout << endl;
librarySort(array);
}

Answer 1

Here you have a complete description and implementation. The gap is defined as whatever value that you will not use. If you were using pointers, NULL is a good option.
In general cases you must create an auxiliary array to the one that has the original data. In this case:
#define MAX 20
#define MAX2 100//The size of the gapped array must be bigger
#define EMPTY -1//Use this constant instead of zeros.
bool isEmpty(int index, int gappedArray[MAX2]) {
return gappedArray[index]>=0;
}
vector<int> libSort(int arr[MAX]) {
int aux[MAX];
for(int i=0;i<MAX;i++) aux = i;
//Add your library sort algorithm here
//However instead of comparing arr[i] with arr[j], compare arr[aux[i]] with arr[aux[j]]
//Then, when you are going to insert sorted values, insert aux[pos], not arr[pos]
}
Here you have library sort pseudocode:
Rebalance(Array S, Integer iniLen, Integer finLen)
k = finLen-1
step = finLen/iniLen
for j=iniLen-1 to 0:
S[k] = S[j]
S[j] = NONE
k = k-step
end for
LibrarySort(Array A, Integer n, Float epsilon, Array S)
goal = 1
pos = 0
sLen = (Integer)(1+epsilon)*n
while pos<n://For each round do this:
for i=1 to goal://Insert 'goal' elements to the sorted array S
//Search a position to insert A[pos]
insPos = binarySearch(A[pos], S, sLen)
if not IS_EMPTY(S[insPos]):
//Move elements to the right or the left in order to free
//insPos
freeSpace(insPos, S, sLen)
end if
S[insPos] = A[pos]//Insert new element
pos = pos + 1
if pos>n://All elements have been inserted
return LibrarySort
end if
end for
prevLen = sLen
sLen = min( (2+2*epsilon)*goal, (1+epsilon)*n )
//Rebalance array S
Rebalance(S, prevLen, sLen)
goal = goal * 2
end while