| Olivier Deprez | f4ef2d0 | 2021-04-20 13:36:24 +0200 | [diff] [blame^] | 1 | """Bisection algorithms.""" |
| 2 | |
| 3 | def insort_right(a, x, lo=0, hi=None): |
| 4 | """Insert item x in list a, and keep it sorted assuming a is sorted. |
| 5 | |
| 6 | If x is already in a, insert it to the right of the rightmost x. |
| 7 | |
| 8 | Optional args lo (default 0) and hi (default len(a)) bound the |
| 9 | slice of a to be searched. |
| 10 | """ |
| 11 | |
| 12 | lo = bisect_right(a, x, lo, hi) |
| 13 | a.insert(lo, x) |
| 14 | |
| 15 | def bisect_right(a, x, lo=0, hi=None): |
| 16 | """Return the index where to insert item x in list a, assuming a is sorted. |
| 17 | |
| 18 | The return value i is such that all e in a[:i] have e <= x, and all e in |
| 19 | a[i:] have e > x. So if x already appears in the list, a.insert(x) will |
| 20 | insert just after the rightmost x already there. |
| 21 | |
| 22 | Optional args lo (default 0) and hi (default len(a)) bound the |
| 23 | slice of a to be searched. |
| 24 | """ |
| 25 | |
| 26 | if lo < 0: |
| 27 | raise ValueError('lo must be non-negative') |
| 28 | if hi is None: |
| 29 | hi = len(a) |
| 30 | while lo < hi: |
| 31 | mid = (lo+hi)//2 |
| 32 | # Use __lt__ to match the logic in list.sort() and in heapq |
| 33 | if x < a[mid]: hi = mid |
| 34 | else: lo = mid+1 |
| 35 | return lo |
| 36 | |
| 37 | def insort_left(a, x, lo=0, hi=None): |
| 38 | """Insert item x in list a, and keep it sorted assuming a is sorted. |
| 39 | |
| 40 | If x is already in a, insert it to the left of the leftmost x. |
| 41 | |
| 42 | Optional args lo (default 0) and hi (default len(a)) bound the |
| 43 | slice of a to be searched. |
| 44 | """ |
| 45 | |
| 46 | lo = bisect_left(a, x, lo, hi) |
| 47 | a.insert(lo, x) |
| 48 | |
| 49 | |
| 50 | def bisect_left(a, x, lo=0, hi=None): |
| 51 | """Return the index where to insert item x in list a, assuming a is sorted. |
| 52 | |
| 53 | The return value i is such that all e in a[:i] have e < x, and all e in |
| 54 | a[i:] have e >= x. So if x already appears in the list, a.insert(x) will |
| 55 | insert just before the leftmost x already there. |
| 56 | |
| 57 | Optional args lo (default 0) and hi (default len(a)) bound the |
| 58 | slice of a to be searched. |
| 59 | """ |
| 60 | |
| 61 | if lo < 0: |
| 62 | raise ValueError('lo must be non-negative') |
| 63 | if hi is None: |
| 64 | hi = len(a) |
| 65 | while lo < hi: |
| 66 | mid = (lo+hi)//2 |
| 67 | # Use __lt__ to match the logic in list.sort() and in heapq |
| 68 | if a[mid] < x: lo = mid+1 |
| 69 | else: hi = mid |
| 70 | return lo |
| 71 | |
| 72 | # Overwrite above definitions with a fast C implementation |
| 73 | try: |
| 74 | from _bisect import * |
| 75 | except ImportError: |
| 76 | pass |
| 77 | |
| 78 | # Create aliases |
| 79 | bisect = bisect_right |
| 80 | insort = insort_right |