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Minor clean-ups for heapq.

This commit is contained in:
Raymond Hettinger 2014-05-26 00:58:56 -07:00
parent 79cae680a3
commit 41331e8193
1 changed files with 11 additions and 11 deletions
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22
Lib/heapq.py
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@ -127,8 +127,6 @@ From all times, sorting has always been a Great Art! :-)
__all__ = ['heappush', 'heappop', 'heapify', 'heapreplace', 'merge',
'nlargest', 'nsmallest', 'heappushpop']
from itertools import islice, count
def heappush(heap, item):
"""Push item onto heap, maintaining the heap invariant."""
heap.append(item)
@ -378,8 +376,10 @@ def merge(*iterables):
# 2 n - k compare remaining elements to top of heap
# 3 k * (1 + lg2(k)) * ln(n/k) replace the topmost value on the heap
# 4 k * lg2(k) - (k/2) final sort of the k most extreme values
#
# Combining and simplifying for a rough estimate gives:
# comparisons = n + k * (1 + log(n/k)) * (1 + log(k, 2))
#
# comparisons = n + k * (log(k, 2) * log(n/k)) + log(k, 2) + log(n/k))
#
# Computing the number of comparisons for step 3:
# -----------------------------------------------
@ -391,12 +391,12 @@ def merge(*iterables):
# * The probabilty times the cost gives:
# (k/i) * (1 + log(k, 2))
# * Summing across the remaining n-k elements gives:
# sum((k/i) * (1 + log(k, 2)) for xrange(k+1, n+1))
# sum((k/i) * (1 + log(k, 2)) for i in range(k+1, n+1))
# * This reduces to:
# (H(n) - H(k)) * k * (1 + log(k, 2))
# * Where H(n) is the n-th harmonic number estimated by:
# gamma = 0.5772156649
# H(n) = log(n, e) + gamma + 1.0 / (2.0 * n)
# H(n) = log(n, e) + gamma + 1 / (2 * n)
# http://en.wikipedia.org/wiki/Harmonic_series_(mathematics)#Rate_of_divergence
# * Substituting the H(n) formula:
# comparisons = k * (1 + log(k, 2)) * (log(n/k, e) + (1/n - 1/k) / 2)
@ -445,12 +445,12 @@ def nsmallest(n, iterable, key=None):
# When key is none, use simpler decoration
if key is None:
it = iter(iterable)
result = list(islice(zip(it, count()), n))
result = [(elem, i) for i, elem in zip(range(n), it)]
if not result:
return result
_heapify_max(result)
order = n
top = result[0][0]
order = n
_heapreplace = _heapreplace_max
for elem in it:
if elem < top:
@ -466,8 +466,8 @@ def nsmallest(n, iterable, key=None):
if not result:
return result
_heapify_max(result)
order = n
top = result[0][0]
order = n
_heapreplace = _heapreplace_max
for elem in it:
k = key(elem)
@ -506,12 +506,12 @@ def nlargest(n, iterable, key=None):
# When key is none, use simpler decoration
if key is None:
it = iter(iterable)
result = list(islice(zip(it, count(0, -1)), n))
result = [(elem, i) for i, elem in zip(range(0, -n, -1), it)]
if not result:
return result
heapify(result)
order = -n
top = result[0][0]
order = -n
_heapreplace = heapreplace
for elem in it:
if top < elem:
@ -527,8 +527,8 @@ def nlargest(n, iterable, key=None):
if not result:
return result
heapify(result)
order = -n
top = result[0][0]
order = -n
_heapreplace = heapreplace
for elem in it:
k = key(elem)