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March 5, 2022 05:20
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Bisection algorithms
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"""Bisection algorithms.""" | |
def insort_right(a, x, lo=0, hi=None, *, key=None): | |
"""Insert item x in list a, and keep it sorted assuming a is sorted. | |
If x is already in a, insert it to the right of the rightmost x. | |
Optional args lo (default 0) and hi (default len(a)) bound the | |
slice of a to be searched. | |
""" | |
if key is None: | |
lo = bisect_right(a, x, lo, hi) | |
else: | |
lo = bisect_right(a, key(x), lo, hi, key=key) | |
a.insert(lo, x) | |
def bisect_right(a, x, lo=0, hi=None, *, key=None): | |
"""Return the index where to insert item x in list a, assuming a is sorted. | |
The return value i is such that all e in a[:i] have e <= x, and all e in | |
a[i:] have e > x. So if x already appears in the list, a.insert(i, x) will | |
insert just after the rightmost x already there. | |
Optional args lo (default 0) and hi (default len(a)) bound the | |
slice of a to be searched. | |
""" | |
if lo < 0: | |
raise ValueError('lo must be non-negative') | |
if hi is None: | |
hi = len(a) | |
# Note, the comparison uses "<" to match the | |
# __lt__() logic in list.sort() and in heapq. | |
if key is None: | |
while lo < hi: | |
mid = (lo + hi) // 2 | |
if x < a[mid]: | |
hi = mid | |
else: | |
lo = mid + 1 | |
else: | |
while lo < hi: | |
mid = (lo + hi) // 2 | |
if x < key(a[mid]): | |
hi = mid | |
else: | |
lo = mid + 1 | |
return lo | |
def insort_left(a, x, lo=0, hi=None, *, key=None): | |
"""Insert item x in list a, and keep it sorted assuming a is sorted. | |
If x is already in a, insert it to the left of the leftmost x. | |
Optional args lo (default 0) and hi (default len(a)) bound the | |
slice of a to be searched. | |
""" | |
if key is None: | |
lo = bisect_left(a, x, lo, hi) | |
else: | |
lo = bisect_left(a, key(x), lo, hi, key=key) | |
a.insert(lo, x) | |
def bisect_left(a, x, lo=0, hi=None, *, key=None): | |
"""Return the index where to insert item x in list a, assuming a is sorted. | |
The return value i is such that all e in a[:i] have e < x, and all e in | |
a[i:] have e >= x. So if x already appears in the list, a.insert(i, x) will | |
insert just before the leftmost x already there. | |
Optional args lo (default 0) and hi (default len(a)) bound the | |
slice of a to be searched. | |
""" | |
if lo < 0: | |
raise ValueError('lo must be non-negative') | |
if hi is None: | |
hi = len(a) | |
# Note, the comparison uses "<" to match the | |
# __lt__() logic in list.sort() and in heapq. | |
if key is None: | |
while lo < hi: | |
mid = (lo + hi) // 2 | |
if a[mid] < x: | |
lo = mid + 1 | |
else: | |
hi = mid | |
else: | |
while lo < hi: | |
mid = (lo + hi) // 2 | |
if key(a[mid]) < x: | |
lo = mid + 1 | |
else: | |
hi = mid | |
return lo | |
# Overwrite above definitions with a fast C implementation | |
try: | |
from _bisect import * | |
except ImportError: | |
pass | |
# Create aliases | |
bisect = bisect_right | |
insort = insort_right |
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