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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 * except ImportError: pass