docs: Add type hints and improve documentation for pancake_sort

sorts/pancake_sort.py

@@ -1,12 +1,23 @@
-"""
-This is a pure Python implementation of the pancake sort algorithm
+"""Pancake Sort Algorithm Implementation.
+
+A pure Python implementation of the Pancake Sort algorithm.
+Pancake sort is a sorting algorithm that sorts an array by repeatedly flipping
+subsections of the array, similar to how you might sort a stack of pancakes
+by inserting a spatula and flipping the top portion.
+
+The algorithm works by finding the maximum element, flipping it to the top,
+then flipping it down to its correct position. This process is repeated for
+the remaining unsorted portion.
+
+Time Complexity: O(n^2) - We perform n iterations, each with up to 2 flips
+Space Complexity: O(1) - In-place sorting, only uses a constant amount of extra space
 
 For doctests run following command:
-python3 -m doctest -v pancake_sort.py
+    python3 -m doctest -v pancake_sort.py
 or
-python -m doctest -v pancake_sort.py
+    python -m doctest -v pancake_sort.py
 For manual testing run:
-python pancake_sort.py
+    python pancake_sort.py
 """
 
 from collections.abc import Sequence
@@ -51,12 +62,13 @@ def pancake_sort[T: Comparable](arr: Sequence[T]) -> list[T]:
     arr = list(arr)
     cur = len(arr)
     while cur > 1:
-        # Find the maximum number in arr
-        mi = arr.index(max(arr[0:cur]))
-        # Reverse from 0 to mi
-        arr = arr[mi::-1] + arr[mi + 1 : len(arr)]
-        # Reverse whole list
-        arr = arr[cur - 1 :: -1] + arr[cur : len(arr)]
+        # Find the index of maximum element in arr[0:cur]
+        max_index = arr.index(max(arr[:cur]))
+        # Move maximum element to end of current unsorted portion:
+        # 1. Flip to bring max to the beginning
+        arr[: max_index + 1] = reversed(arr[: max_index + 1])
+        # 2. Flip to send max to position cur-1
+        arr[:cur] = reversed(arr[:cur])
         cur -= 1
     return arr
 
@@ -67,4 +79,4 @@ def pancake_sort[T: Comparable](arr: Sequence[T]) -> list[T]:
     doctest.testmod()
     user_input = input("Enter numbers separated by a comma:\n").strip()
     unsorted = [int(item) for item in user_input.split(",")]
-    print(f"{pancake_sort(unsorted) = }")
+    print(f"{unsorted = }, {pancake_sort(unsorted) = }")