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"""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.
"""
lo = bisect_right(a, x, lo, hi)
a.insert(lo, x)
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
# Use __lt__ to match the logic in list.sort() and in heapq
if x < a[mid]: hi = mid
else: lo = mid+1
return lo
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.
"""
lo = bisect_left(a, x, lo, hi)
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
# Use __lt__ to match the logic in list.sort() and in heapq
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
# Create aliases
bisect = bisect_right
insort = insort_right