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parallel_intersect.py
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parallel_intersect.py
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import random # Do NOT seed the random generator
import unittest
from typing import Tuple, Iterator
def get_value(array, idx):
# If index is out of right boundary, assume +INF
# If index is out of left boundary, assume -INF
if idx < 0:
return -float('inf')
elif idx >= len(array):
return float("inf")
return array[idx]
def create_disjoint_sublist(
A: list, B: list, i: int, p: int) -> Tuple[int, int]:
if len(B) > len(A):
i, j = create_disjoint_sublist(B, A, i, p)
return j, i
length = (len(A) + len(B)) // p
diag = i * length
if diag > len(A):
a_top = len(A)
b_top = diag - len(A)
else:
a_top = diag
b_top = 0
a_btm = b_top
while True:
ai = (a_top + a_btm) // 2
bi = diag - ai
a_val = get_value(A, ai)
b_val = get_value(B, bi - 1)
if a_val > b_val:
a_val = get_value(A, ai - 1)
b_val = get_value(B, bi)
if a_val < b_val:
return ai, bi
# Since the adjacency list has not duplicates, this branch can only occur
# at most once per function call.
elif a_val == b_val:
diag += 1
else:
a_top = ai - 1
else:
a_btm = ai + 1
def partition(A: list, B: list, p: int) -> Iterator[list]:
"""Partition array A and B into p disjointed sets.
A = {A0, A1, ... Ap-1}, B = {B0, B1, ... Bp-1},
where max(A0, B0) < min (A1, B1), max(A1, B1) < min(A2, B2) ...
max(Ap-2, Bp-2) < min(Ap-1, Bp-1)
Such partitioning guarantees that the intersection on A and B can be
parallelized to intersect(A1, B1) union intersect(A2, B2) ...
union intersect(Ap-1, Bp-1).
"""
a_start, b_start = 0, 0
for i in range(1, p):
a_start_now, b_start_now = create_disjoint_sublist(A, B, i, p)
yield A[a_start: a_start_now], B[b_start: b_start_now]
a_start, b_start = a_start_now, b_start_now
yield A[a_start:], B[b_start:]
_TEST_CASE = {
# all unique elements
"unique1": {"p": 2,
"arr1": [1, 2, 3, 5, 8, 9],
"arr2": [4, 6, 7, 11, 13],
"expected": [([1, 2, 3, 5], [4]),
([8, 9], [6, 7, 11, 13])]},
"unique2": {"p": 3,
"arr1": [1, 2, 3, 5, 8, 9],
"arr2": [4, 6, 7, 11, 13],
"expected": [([1, 2, 3], []),
([5], [4, 6]),
([8, 9], [7, 11, 13])]},
"unique3": {"p": 4,
"arr1": [1, 2, 3, 5, 8, 9],
"arr2": [4, 6, 7, 11, 13],
"expected": [([1, 2], []),
([3], [4]),
([5], [6]),
([8, 9], [7, 11, 13])]},
"unique4": {"p": 5,
"arr1": [1, 2, 3, 5, 8, 9],
"arr2": [4, 6, 7, 11, 13],
"expected": [([1, 2], []),
([3], [4]),
([5], [6]),
([8], [7]),
([9], [11, 13])]},
# one partition
"one_partition": {"p": 1,
"arr1": [1, 2, 3, 5, 8, 9],
"arr2": [4, 6, 7, 11, 13],
"expected": [([1, 2, 3, 5, 8, 9], [4, 6, 7, 11, 13])]},
# A is longer than B
"long_short1": {"p": 2,
"arr1": [1, 2, 3, 5, 8, 9],
"arr2": [4],
"expected": [([1, 2, 3], []),
([5, 8, 9], [4])]},
"long_short2": {"p": 4,
"arr1": [1, 2, 3, 5, 8, 9],
"arr2": [4],
"expected": [([1], []),
([2], []),
([3], []),
([5, 8, 9], [4])]},
# B is longer than A
"short_long1": {"p": 2,
"arr1": [8],
"arr2": [4, 6, 7, 11, 13],
"expected": [([], [4, 6, 7]),
([8], [11, 13])]},
"short_long2": {"p": 3,
"arr1": [8],
"arr2": [4, 6, 7, 11, 13],
"expected": [([], [4, 6]),
([8], [7]),
([], [11, 13])]},
# The equal element must be placed within the same partition.
"equal_ele1": {"p": 2,
"arr1": [1, 2, 3, 7, 8, 9],
"arr2": [4, 6, 7, 11, 13],
"expected": [([1, 2, 3], [4, 6]),
([7, 8, 9], [7, 11, 13])]},
"equal_ele2": {"p": 3,
"arr1": [1, 2, 3, 7, 8, 9],
"arr2": [4, 6, 7, 11, 13],
"expected": [([1, 2, 3], []),
([7], [4, 6, 7]),
([8, 9], [11, 13])]},
"equal_ele3": {"p": 4,
"arr1": [1, 2, 3, 7, 8, 9],
"arr2": [4, 6, 7, 11, 13],
"expected": [([1, 2], []),
([3], [4]),
([7], [6, 7]),
([8, 9], [11, 13])]},
# The equal element is at the beginning of list B
"equal_ele_4": {"p": 2,
"arr1": [1, 2, 3, 7, 8, 9],
"arr2": [7, 10, 11, 13],
"expected": [([1, 2, 3, 7], [7]),
([8, 9], [10, 11, 13])]},
"equal_ele_5": {"p": 4,
"arr1": [1, 2, 3, 7, 8, 9],
"arr2": [7, 10, 11, 13],
"expected": [([1, 2], []),
([3, 7], [7]),
([8], []),
([9], [10, 11, 13])]},
# The equal element is at the end of list A
"equal_ele_6": {"p": 2,
"arr1": [1, 2, 3, 7, 8, 9],
"arr2": [4, 5, 6, 9, 10, 11, 13],
"expected": [([1, 2, 3], [4, 5, 6]),
([7, 8, 9], [9, 10, 11, 13])]},
"equal_ele_7": {"p": 4,
"arr1": [1, 2, 3, 7, 8, 9],
"arr2": [4, 5, 6, 9, 10, 11, 13],
"expected": [([1, 2, 3], []),
([], [4, 5, 6]),
([7, 8, 9], [9]),
([], [10, 11, 13])]},
# Multiple equal elements
"equal_ele_8": {"p": 2,
"arr1": [1, 2, 3, 7, 8, 9, 11],
"arr2": [2, 4, 6, 9, 10, 11, 13],
"expected": [([1, 2, 3, 7], [2, 4, 6]),
([8, 9, 11], [9, 10, 11, 13])]},
"equal_ele_9": {"p": 3,
"arr1": [1, 2, 3, 7, 8, 9, 11],
"arr2": [2, 4, 6, 9, 10, 11, 13],
"expected": [([1, 2, 3], [2]),
([7, 8], [4, 6]),
([9, 11], [9, 10, 11, 13])]},
"equal_ele_10": {"p": 4,
"arr1": [1, 2, 3, 7, 8, 9, 11],
"arr2": [2, 4, 6, 9, 10, 11, 13],
"expected": [([1, 2], [2]),
([3], [4, 6]),
([7, 8, 9], [9]),
([11], [10, 11, 13])]},
"equal_ele_11": {"p": 5,
"arr1": [1, 2, 3, 7, 8, 9, 11],
"arr2": [2, 4, 6, 9, 10, 11, 13],
"expected": [([1, 2], [2]),
([3], []),
([], [4, 6]),
([7, 8], []),
([9, 11], [9, 10, 11, 13])]},
}
class TestParallelIntersect(unittest.TestCase):
def test_handwritten_cases(self):
for case_label, data in _TEST_CASE.items():
self.assertEqual(data["expected"],
list(partition(data["arr1"], data["arr2"], data["p"])))
def test_random_cases(self):
for i in range(1000):
# Create two sorted lists. Since the algorithm is designed for adjacency
# list, we use |random.sample| to ensure the list itself does not contain
# duplicated values.
la = sorted(random.sample(range(0, 2000), 1000))
lb = sorted(random.sample(range(0, 2000), 600))
# Intersection using Python set
expected = sorted(set(la).intersection(set(lb)))
actual = list()
# Iterate through the disjoint sub-lists and intersect the two sub-lists
for sub_la, sub_lb in partition(la, lb, 10):
actual.extend(sorted(set(sub_la).intersection(set(sub_lb))))
self.assertEqual(expected, sorted(list(actual)))
if __name__ == '__main__':
unittest.main()