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notes/fund-prog-3/some-sorts-2024-01-31.md

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+# 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]
+```