#75 multiary_parent, multiary_child

Author: wojtask

src/solutions/chapter6/problem2.py

@@ -0,0 +1,34 @@
+from util import ceil_div
+
+
+def multiary_parent(d: int, i: int) -> int:
+    """The index of the parent of a multiary heap node.
+
+    Implements:
+        Multiary-Parent
+
+    Args:
+        d: the arity of the heap, d >= 2
+        i: the index of the node
+
+    Returns:
+        The index of the parent of the node at index i in a d-ary heap.
+    """
+    return ceil_div(i - 1, d)
+
+
+def multiary_child(d: int, i: int, k: int) -> int:
+    """The index of a child of a multiary heap node.
+
+    Implements:
+        Multiary-Child
+
+    Args:
+        d: the arity of the heap, d >= 2
+        i: the index of the node
+        k: the number of a child to get, 1 <= k <= d
+
+    Returns:
+        The index of the k-th child of the node at index i in a d-ary heap.
+    """
+    return d * (i - 1) + k + 1

test/test_solutions/test_chapter6.py

@@ -12,6 +12,8 @@
 from book.data_structures import Heap
 from book.data_structures import KeyObject
 from book.data_structures import PriorityQueue
+from solutions.chapter6.problem2 import multiary_child
+from solutions.chapter6.problem2 import multiary_parent
 from solutions.chapter6.section2.exercise3 import min_heapify
 from solutions.chapter6.section2.exercise6 import iterative_max_heapify
 from solutions.chapter6.section5.exercise3 import min_heap_decrease_key
@@ -272,3 +274,13 @@ def test_max_heap_increase_key__invalid_key(self, data):
             self.assertEqual(A.heap_size, n)
             self.assertArrayPermuted(A, key_objects, end=n)
             self.assertPriorityQueueMappingConsistent(A)
+
+    @given(st.data())
+    def test_multiary_parent_child(self, data):
+        d = data.draw(integers(min_value=2, max_value=20))
+        i = data.draw(integers(min_value=1))
+        k = data.draw(integers(min_value=1, max_value=d))
+
+        actual_node_index = multiary_parent(d, multiary_child(d, i, k))
+
+        self.assertEqual(actual_node_index, i)