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Benchmarking functions to merge two sorted lists
"""Merging two sorted lists in Python in four ways.
1. The "stupid naive" way of adding them together and sorting the whole thing.
This should be pretty fast as timsort is designed to be fast on partially
sorted lists. However, it uses more memory and might not scale very well?
2. The "picking an algorithm designed for this" way of using heapq.merge. This
provides a generator that walks the two lists without additional use of
3. The "C-way" of indexing our way through two lists. This being Python though,
we will be yielding the values though (wrapping the resulting generator in
list() is actually faster than returning a list.) We'd expect this to be
pretty fast, though it's implementation in Python might not make it as fast
as the sorting. It should beat the heapq.merge though.
4. The Python way of successively iterating over two potentially infinite
iterables. Hopefully Raymond will be proud of us for taking iterators real
serious. We'd expect this to do pretty well, but maybe not quite as fast as
doing it the C-way.
You might be surprised how these compare.
from heapq import merge
from random import sample
import timeit
def merge_naive(left, right):
"""Naive generator for merging two sorted lists."""
i, max_i = 0, len(left)
j, max_j = 0, len(right)
while i < max_i and j < max_j:
if left[i] < right[j]:
yield left[i]
i += 1
yield right[j]
j += 1
yield from left[i:]
yield from right[j:]
def merge_walk(left, right):
"""Yield values from two sorted lists in overall sorted order.
we strive to do the absolute minimum work inside
it, executing checks for exhaustion only when moving the index forward,
rather than checking for exhaustion on each loop cycle.
For good loop performance. this function makes aggressive use of Python's
cheap try/except statement for new array value retrievals. Catching an
exception is expensive, but will only happen once per merge.
The overall time complexity for this function is O(n+m) where n and m are
the sizes of the input lists. These dominate over the startup checks.
if not left or not right:
yield from left
yield from right
i, left_val = 0, left[0]
j, right_val = 0, right[0]
while True:
if left_val < right_val:
yield left_val
i += 1
left_val = left[i]
except IndexError:
yield from right[j:]
yield right_val
j += 1
right_val = right[j]
except IndexError:
yield from left[i:]
def merge_iter(left, right):
"""Yield values from two sorted iterables in overall sorted order.
This operates on a pair of iterables without consuming additional memory
itself, making it safe to use on large or infinite sequences. The hot loop
relies on Python's iter() bookkeeping, which it stands to reason is faster
than manual twiddling of indices.
By wrapping almost the entire function in a single try/except statement we
achieve strong separation of hot and cold code, and maintain reasonable
levels of readability.
Unfortunately, for however hard this code tries, it's still slower than
a simple sorted(la+lb). But this one won't break on infinite lists ;-)
left = iter(left)
right = iter(right)
left_val = next(left)
right_val = next(right)
while True:
if left_val < right_val:
yield left_val
left_val = next(left)
yield right_val
right_val = next(right)
except StopIteration:
if 'left_val' in locals():
if 'right_val' in locals():
yield max(left_val, right_val)
yield left_val
yield from left
yield from right
('combine-and-sort', lambda la, lb: lambda: sorted(la + lb)),
('heap-merge', lambda la, lb: lambda: list(merge(la, lb))),
('merge-naive', lambda la, lb: lambda: list(merge_naive(la, lb))),
('merge-walk', lambda la, lb: lambda: list(merge_walk(la, lb))),
('merge-iter', lambda la, lb: lambda: list(merge_iter(la, lb))),
([1, 2], [3, 4], [1, 2, 3, 4]),
([1, 3], [2, 4], [1, 2, 3, 4]),
([], [1, 3], [1, 3]),
([1, 3], [], [1, 3])]
1: 1000000,
10: 200000,
100: 20000,
1000: 2000,
10000: 400,
100000: 80,
1000000: 16,
10000000: 3}
def main():
for run_a, run_b, expected in TESTS:
for _name, test_func_creator in COMBINERS:
test_func = test_func_creator(run_a, run_b)
assert test_func() == expected
for length, tests in sorted(BENCHMARKS.items()):
run_a = sorted(sample(range(length * 2), round(length * 0.8)))
run_b = sorted(sample(range(length * 2), round(length * 1.2)))
print(f'\nMerging two sorted lists of approximate length {length}')
for name, test_func_creator in COMBINERS:
test_func = test_func_creator(run_a, run_b)
assert test_func() == sorted(run_a + run_b)
best = min(timeit.repeat(test_func, number=tests, repeat=3))
micros = best * 1e6 / tests
if micros > 1000:
print(f' * [{name}]: {micros / 1000:.1f}ms')
print(f' * [{name}]: {micros:.1f}μs')
if __name__ == '__main__':
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