Add hilbert sort

DIRECTORY.md

@@ -1063,6 +1063,7 @@
   * [External Sort](sorts/external_sort.py)
   * [Gnome Sort](sorts/gnome_sort.py)
   * [Heap Sort](sorts/heap_sort.py)
+  * [Hilbert Sort](sorts/hilbert_sort.py)
   * [Insertion Sort](sorts/insertion_sort.py)
   * [Intro Sort](sorts/intro_sort.py)
   * [Iterative Merge Sort](sorts/iterative_merge_sort.py)

sorts/hilbert_sort.py

@@ -0,0 +1,44 @@
+import numpy as np
+
+
+def hilbert_sort(data: list) -> list:
+    """
+    Imagine you have a bunch of balls, each with a different number on it. To sort the balls, you first throw them up in the air. As each ball falls back down, it follows a unique path based on its number.
+    As the balls fall back down and land, they come to rest at a location in 2D space.
+    To sort the balls based on their 2D coordinates, you can imagine lining up the balls along a winding road (Hilbert curve) based on their location. The balls that are close together along the road are also close together in 2D space.
+    Finally, you can read off the sorted order of the balls by simply following the order in which they appear along the winding road. This is similar to reading a book by following the order of the words on the page.
+    In this analogy the balls would start in 1D space and be transposed into 2D space, the 3rd dimension is mostly analogy.
+    """
+    data = np.array(data)
+
+    # Map each number in the input array to a point in 2D space using the Hilbert curve
+    # Step 1: Convert each number to binary using zfill to ensure each binary string is 16 bits long
+    binary_array = np.array([list(bin(n)[2:].zfill(16)) for n in data], dtype=int)
+
+    # Step 2: Generate the coordinates for each binary string using the Hilbert curve
+    coords_array = np.zeros((len(data), 32))
+
+    # Step 2a: Compute the odd-indexed coordinates using the cumulative sum of the product of the binary values and powers of 2
+    coords_array[:, 1::2] = np.cumsum(
+        (-1) ** binary_array[:, ::-1] * 2 ** np.arange(16), axis=1
+    )[:, ::-1]
+
+    # Step 2b: Compute the even-indexed coordinates using a cumulative product of the binary values, reversed and shifted by 1
+    # We reverse the binary values so that the most significant bit is at the end of the array, making it easier to compute the cumulative product
+    # We shift the array by 1 so that we don't include the value for the current index in the product
+    # We use np.cumprod to compute the cumulative product of the binary values, which are either -1 or 1
+    # We reverse the result again and concatenate a column of zeros to obtain the even-indexed coordinates
+    coords_array[:, ::2] = np.concatenate(
+        (
+            np.zeros((len(data), 1)),
+            np.cumprod((-1) ** binary_array[:, ::-1][:, :-1], axis=1)[:, ::-1],
+        ),
+        axis=1,
+    )
+
+    # Step 2c: Compute the cumulative sum of the coordinates to obtain the final Hilbert curve coordinates
+    np.add.accumulate(coords_array, axis=1, out=coords_array)
+
+    # Step 3: Sort the data array based on the Hilbert curve coordinates
+    sorted_indices = np.lexsort(coords_array.T)
+    return data[sorted_indices].tolist()[::-1]