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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
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