# Some sorts

In pseudocode, but python syntax highlighting fits decently so that's what I'm using.

## Insertion sort (for shell sort)

```py
InsertionSortForShell(array, start, gap)
    for i = start + gap to len(array) - 1 # inclusive
        j = i
        while (j - gap >= start) and (array[j] < array[j - gap])
            swap(array[j], array[j - gap])
            j = j - gap
```

## Shell sort

```py
ShellSort(array, gapList)
    for gap in gapList
        for i = = 0 to gap - 1
            InsertionSortForShell(array, i, gap)
```

## Hibbard

2<sup>k</sup> - 1 where k is 1 to p where └ k<sup>p</sup> ┐ = N

## Pratt

For a Z-tuples for (0, 0) -> (k, k) create all the cartesian pairs

```txt
(0, 0), (0, 1), (0, 2), ..., (0, k)
(1, 0), (1, 1), (1, 2), ..., (1, k)
(2, 0), (2, 1), (2, 2), ..., (2, k)
...
(k, 0), (k, 1), (k, 2), ..., (k, k)
```

## Naive gap values

N/2<sup>k</sup>, k = 1 to p where N/2<sup>p</sup> => 1

```py
for i, j in S
    value = 2<sup>i</sup> * 3<sup>j</sup>
    gapList.append(value)
    sort(gapList)
    gapValues[0 ... N]
```