93 lines
2.5 KiB
Python
93 lines
2.5 KiB
Python
|
"""Bisection algorithms."""
|
||
|
|
|
||
|
|
def insort_right(a, x, lo=0, hi=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 lo < 0:
|
||
|
|
raise ValueError('lo must be non-negative')
|
||
|
|
if hi is None:
|
||
|
|
hi = len(a)
|
||
|
|
while lo < hi:
|
||
|
|
mid = (lo+hi)//2
|
||
|
|
if x < a[mid]: hi = mid
|
||
|
|
else: lo = mid+1
|
||
|
|
a.insert(lo, x)
|
||
|
|
|
||
|
|
insort = insort_right # backward compatibility
|
||
|
|
|
||
|
|
def bisect_right(a, x, lo=0, hi=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(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)
|
||
|
|
while lo < hi:
|
||
|
|
mid = (lo+hi)//2
|
||
|
|
if x < a[mid]: hi = mid
|
||
|
|
else: lo = mid+1
|
||
|
|
return lo
|
||
|
|
|
||
|
|
bisect = bisect_right # backward compatibility
|
||
|
|
|
||
|
|
def insort_left(a, x, lo=0, hi=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 lo < 0:
|
||
|
|
raise ValueError('lo must be non-negative')
|
||
|
|
if hi is None:
|
||
|
|
hi = len(a)
|
||
|
|
while lo < hi:
|
||
|
|
mid = (lo+hi)//2
|
||
|
|
if a[mid] < x: lo = mid+1
|
||
|
|
else: hi = mid
|
||
|
|
a.insert(lo, x)
|
||
|
|
|
||
|
|
|
||
|
|
def bisect_left(a, x, lo=0, hi=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(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)
|
||
|
|
while lo < hi:
|
||
|
|
mid = (lo+hi)//2
|
||
|
|
if 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
|