#17 hoare_partition

Author: wojtask

src/book/chapter7/problem1.py

@@ -0,0 +1,36 @@
+from book.data_structures import Array
+from book.data_structures import CT
+
+
+def hoare_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 each element in the high side. Uses the original algorithm invented by
+    C. A. R. Hoare.
+
+    Implements:
+        Hoare-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 j such that each element in A[p:j] is less than or equal to each element in A[j + 1:r].
+    """
+    x = A[p]
+    i = p - 1
+    j = r + 1
+    while True:
+        while True:
+            j -= 1
+            if A[j] <= x:
+                break
+        while True:
+            i += 1
+            if A[i] >= x:
+                break
+        if i < j:
+            A[i], A[j] = A[j], A[i]
+        else:
+            return j

test/test_book/test_chapter7.py

@@ -1,8 +1,11 @@
+import math
+
 from hypothesis import given
 from hypothesis import strategies as st
 from hypothesis.strategies import integers
 from hypothesis.strategies import lists
 
+from book.chapter7.problem1 import hoare_partition
 from book.chapter7.problem4 import stooge_sort
 from book.chapter7.problem5 import tre_quicksort
 from book.chapter7.section1 import quicksort
@@ -64,6 +67,23 @@ def test_median_of_3_partition(self, data):
             self.assertGreaterEqual(A[i], A[actual_pivot_index])
         self.assertArrayPermuted(A, elements, end=n)
 
+    @given(st.data())
+    def test_hoare_partition(self, data):
+        elements = data.draw(lists(integers(), min_size=1))
+        A = create_array(elements)
+        n = len(elements)
+
+        actual_split_index = hoare_partition(A, 1, n)
+
+        left_max = -math.inf
+        right_min = math.inf
+        for i in range_of(1, to=actual_split_index):
+            left_max = max(left_max, A[i])
+        for i in range_of(actual_split_index + 1, to=n):
+            right_min = min(right_min, A[i])
+        self.assertLessEqual(left_max, right_min)
+        self.assertArrayPermuted(A, elements, end=n)
+
     @given(st.data())
     def test_stooge_sort(self, data):
         elements = data.draw(lists(integers(), min_size=1))