Add smooth algorithm

sorts/smooth_sort.py

@@ -0,0 +1,118 @@
+"""
+This is a pure Python implementation of the smoothSort algorithm
+Smooth Sort is an algorithm combine the concept of heap sort and the
+concept of merge sort It was designed by Edsger W. Dijkstra
+and later refined by Steven J. Ross.
+
+More info on: https://en.wikipedia.org/wiki/Smoothsort
+
+For doctests run following command:
+python -m doctest -v smooth_sort.py
+or
+python3 -m doctest -v smooth_sort.py
+For manual testing run:
+python bogo_sort.py
+"""
+
+
+def smooth_sort(unsorted):
+    """
+    Pure implementation of the smooth sort algorithm using Leonardo numbers in Python
+    :param unsorted: unordered mutable collection
+    :return: the same collection ordered in ascending order
+
+    Examples:
+    >>> smooth_sort([0, 5, 3, 2, 2])
+    [0, 2, 2, 3, 5]
+
+    >>> smooth_sort([])
+    []
+
+    >>> smooth_sort([-2, -5, -45])
+    [-45, -5, -2]
+    """
+
+    def leonardo(leonardo_number):
+        """
+        leonardo number represent numbers in pattern where third number is the sum of
+        2 preceding numbers plus 1 also leonardo number used in heap construction
+        every number represent size of tree within the heap
+        they are used in heapify using max heap approach which we will see later
+        """
+        if leonardo_number < 2:
+            return 1
+        return leonardo(leonardo_number - 1) + leonardo(leonardo_number - 2) + 1
+
+    def heapify(start, end):
+        i = start
+        j = 0
+        k = 0
+
+        while k < end - start + 1:
+            if k & 0xAAAAAAAA:
+                j = j + i
+                i = i >> 1
+            else:
+                i = i + j
+                j = j >> 1
+
+            k = k + 1
+
+        while i > 0:
+            j = j >> 1
+            k = i + j
+            while k < end:
+                if unsorted[k] < unsorted[k - i]:
+                    break
+                unsorted[k], unsorted[k - i] = unsorted[k - i], unsorted[k]
+                k = k + i
+
+            i = j
+
+    n = len(unsorted)
+    if n <= 1:
+        return unsorted
+
+    p = n - 1
+    q = p
+    r = 0
+    while p > 0:
+        if (r & 0x03) == 0:
+            heapify(r, q)
+
+        if leonardo(r) == p:
+            r = r + 1
+        else:
+            r = r - 1
+            q = q - leonardo(r)
+            heapify(r, q)
+            q = r - 1
+            r = r + 1
+
+        unsorted[0], unsorted[p] = unsorted[p], unsorted[0]
+        p = p - 1
+
+    for i in range(n - 1):
+        j = i + 1
+        while j > 0 and unsorted[j] < unsorted[j - 1]:
+            unsorted[j], unsorted[j - 1] = unsorted[j - 1], unsorted[j]
+            j = j - 1
+
+    return unsorted
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()
+    try:
+        user_input = input(
+            "Enter numbers separated by a comma (or press Enter to exit):\n"
+        ).strip()
+        if not user_input:
+            print(smooth_sort([]))
+        else:
+            unsorted = [int(item) for item in user_input.split(",")]
+            print(smooth_sort(unsorted))
+    except ValueError:
+        print("Invalid input. Please enter valid integers separated by commas.")