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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.
- """
-
- 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 bisect_right, bisect_left, insort_left, insort_right, insort, bisect
- except ImportError:
- pass
-