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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 |