#17 randomized_partition, randomized_quicksort

Author: wojtask

src/book/chapter7/section3.py

@@ -0,0 +1,43 @@
+from book.chapter7.section1 import partition
+from book.data_structures import Array
+from book.data_structures import CT
+from solutions.chapter5.section1.exercise2 import random
+
+
+def randomized_partition(A: Array[CT], p: int, r: int) -> int:
+    """Partitions an array into two subarrays, the low side and the high side, such that each element in the low side of
+    the partition is less than or equal to the pivot value, which is, in turn, less than or equal to each element in the
+    high side. Chooses the pivot element randomly.
+
+    Implements:
+        Randomized-Partition
+
+    Args:
+        A: an Array to partition
+        p: the lower index of the subarray to partition
+        r: the upper index of the subarray to partition
+
+    Returns:
+        The index q, such that each element in A[p:q - 1] is less than or equal to A[q], and that A[q] is less than or
+        equal to each element in A[q + 1:r].
+    """
+    i = random(p, r)
+    A[r], A[i] = A[i], A[r]
+    return partition(A, p, r)
+
+
+def randomized_quicksort(A: Array[CT], p: int, r: int) -> None:
+    """Sorts an array using the randomized version of quicksort.
+
+    Implements:
+        Randomized-Quicksort
+
+    Args:
+        A: an Array containing the values to be sorted
+        p: the lower index of the subarray to sort
+        r: the upper index of the subarray to sort
+    """
+    if p < r:
+        q = randomized_partition(A, p, r)
+        randomized_quicksort(A, p, q - 1)
+        randomized_quicksort(A, q + 1, r)

test/test_book/test_chapter7.py

@@ -4,6 +4,7 @@
 from hypothesis.strategies import lists
 
 from book.chapter7.section1 import quicksort
+from book.chapter7.section3 import randomized_quicksort
 from test_case import ClrsTestCase
 from test_util import create_array
 
@@ -20,3 +21,14 @@ def test_quicksort(self, data):
 
         self.assertArraySorted(A, end=n)
         self.assertArrayPermuted(A, elements, end=n)
+
+    @given(st.data())
+    def test_randomized_quicksort(self, data):
+        elements = data.draw(lists(integers(), min_size=1))
+        A = create_array(elements)
+        n = len(elements)
+
+        randomized_quicksort(A, 1, n)
+
+        self.assertArraySorted(A, end=n)
+        self.assertArrayPermuted(A, elements, end=n)