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"""Bisection algorithms.""" def insort_right(a, x, lo=0, hi=None, *, key=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. A custom key function can be supplied to customize the sort order. """ if key is None: lo = bisect_right(a, x, lo, hi) else: lo = bisect_right(a, key(x), lo, hi, key=key) a.insert(lo, x) def bisect_right(a, x, lo=0, hi=None, *, key=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(i, 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. A custom key function can be supplied to customize the sort order. """ if lo < 0: raise ValueError('lo must be non-negative') if hi is None: hi = len(a) # Note, the comparison uses "<" to match the # __lt__() logic in list.sort() and in heapq. if key is None: while lo < hi: mid = (lo + hi) // 2 if x < a[mid]: hi = mid else: lo = mid + 1 else: while lo < hi: mid = (lo + hi) // 2 if x < key(a[mid]): hi = mid else: lo = mid + 1 return lo def insort_left(a, x, lo=0, hi=None, *, key=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. A custom key function can be supplied to customize the sort order. """ if key is None: lo = bisect_left(a, x, lo, hi) else: lo = bisect_left(a, key(x), lo, hi, key=key) a.insert(lo, x) def bisect_left(a, x, lo=0, hi=None, *, key=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(i, 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. A custom key function can be supplied to customize the sort order. """ if lo < 0: raise ValueError('lo must be non-negative') if hi is None: hi = len(a) # Note, the comparison uses "<" to match the # __lt__() logic in list.sort() and in heapq. if key is None: while lo < hi: mid = (lo + hi) // 2 if a[mid] < x: lo = mid + 1 else: hi = mid else: while lo < hi: