| """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. |
| """ |
| 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. |
| """ |
| |
| 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. |
| """ |
| |
| 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. |
| """ |
| |
| 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: |
| mid = (lo + hi) // 2 |
| if key(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 |
