1 :mod:`bisect` --- Array bisection algorithm 2 =========================================== 3 4 .. module:: bisect 5 :synopsis: Array bisection algorithms for binary searching. 6 .. sectionauthor:: Fred L. Drake, Jr. <fdrake (a] acm.org> 7 .. sectionauthor:: Raymond Hettinger <python at rcn.com> 8 .. example based on the PyModules FAQ entry by Aaron Watters <arw (a] pythonpros.com> 9 10 **Source code:** :source:`Lib/bisect.py` 11 12 -------------- 13 14 This module provides support for maintaining a list in sorted order without 15 having to sort the list after each insertion. For long lists of items with 16 expensive comparison operations, this can be an improvement over the more common 17 approach. The module is called :mod:`bisect` because it uses a basic bisection 18 algorithm to do its work. The source code may be most useful as a working 19 example of the algorithm (the boundary conditions are already right!). 20 21 The following functions are provided: 22 23 24 .. function:: bisect_left(a, x, lo=0, hi=len(a)) 25 26 Locate the insertion point for *x* in *a* to maintain sorted order. 27 The parameters *lo* and *hi* may be used to specify a subset of the list 28 which should be considered; by default the entire list is used. If *x* is 29 already present in *a*, the insertion point will be before (to the left of) 30 any existing entries. The return value is suitable for use as the first 31 parameter to ``list.insert()`` assuming that *a* is already sorted. 32 33 The returned insertion point *i* partitions the array *a* into two halves so 34 that ``all(val < x for val in a[lo:i])`` for the left side and 35 ``all(val >= x for val in a[i:hi])`` for the right side. 36 37 .. function:: bisect_right(a, x, lo=0, hi=len(a)) 38 bisect(a, x, lo=0, hi=len(a)) 39 40 Similar to :func:`bisect_left`, but returns an insertion point which comes 41 after (to the right of) any existing entries of *x* in *a*. 42 43 The returned insertion point *i* partitions the array *a* into two halves so 44 that ``all(val <= x for val in a[lo:i])`` for the left side and 45 ``all(val > x for val in a[i:hi])`` for the right side. 46 47 .. function:: insort_left(a, x, lo=0, hi=len(a)) 48 49 Insert *x* in *a* in sorted order. This is equivalent to 50 ``a.insert(bisect.bisect_left(a, x, lo, hi), x)`` assuming that *a* is 51 already sorted. Keep in mind that the O(log n) search is dominated by 52 the slow O(n) insertion step. 53 54 .. function:: insort_right(a, x, lo=0, hi=len(a)) 55 insort(a, x, lo=0, hi=len(a)) 56 57 Similar to :func:`insort_left`, but inserting *x* in *a* after any existing 58 entries of *x*. 59 60 .. seealso:: 61 62 `SortedCollection recipe 63 <https://code.activestate.com/recipes/577197-sortedcollection/>`_ that uses 64 bisect to build a full-featured collection class with straight-forward search 65 methods and support for a key-function. The keys are precomputed to save 66 unnecessary calls to the key function during searches. 67 68 69 Searching Sorted Lists 70 ---------------------- 71 72 The above :func:`bisect` functions are useful for finding insertion points but 73 can be tricky or awkward to use for common searching tasks. The following five 74 functions show how to transform them into the standard lookups for sorted 75 lists:: 76 77 def index(a, x): 78 'Locate the leftmost value exactly equal to x' 79 i = bisect_left(a, x) 80 if i != len(a) and a[i] == x: 81 return i 82 raise ValueError 83 84 def find_lt(a, x): 85 'Find rightmost value less than x' 86 i = bisect_left(a, x) 87 if i: 88 return a[i-1] 89 raise ValueError 90 91 def find_le(a, x): 92 'Find rightmost value less than or equal to x' 93 i = bisect_right(a, x) 94 if i: 95 return a[i-1] 96 raise ValueError 97 98 def find_gt(a, x): 99 'Find leftmost value greater than x' 100 i = bisect_right(a, x) 101 if i != len(a): 102 return a[i] 103 raise ValueError 104 105 def find_ge(a, x): 106 'Find leftmost item greater than or equal to x' 107 i = bisect_left(a, x) 108 if i != len(a): 109 return a[i] 110 raise ValueError 111 112 113 Other Examples 114 -------------- 115 116 .. _bisect-example: 117 118 The :func:`bisect` function can be useful for numeric table lookups. This 119 example uses :func:`bisect` to look up a letter grade for an exam score (say) 120 based on a set of ordered numeric breakpoints: 90 and up is an 'A', 80 to 89 is 121 a 'B', and so on:: 122 123 >>> def grade(score, breakpoints=[60, 70, 80, 90], grades='FDCBA'): 124 ... i = bisect(breakpoints, score) 125 ... return grades[i] 126 ... 127 >>> [grade(score) for score in [33, 99, 77, 70, 89, 90, 100]] 128 ['F', 'A', 'C', 'C', 'B', 'A', 'A'] 129 130 Unlike the :func:`sorted` function, it does not make sense for the :func:`bisect` 131 functions to have *key* or *reversed* arguments because that would lead to an 132 inefficient design (successive calls to bisect functions would not "remember" 133 all of the previous key lookups). 134 135 Instead, it is better to search a list of precomputed keys to find the index 136 of the record in question:: 137 138 >>> data = [('red', 5), ('blue', 1), ('yellow', 8), ('black', 0)] 139 >>> data.sort(key=lambda r: r[1]) 140 >>> keys = [r[1] for r in data] # precomputed list of keys 141 >>> data[bisect_left(keys, 0)] 142 ('black', 0) 143 >>> data[bisect_left(keys, 1)] 144 ('blue', 1) 145 >>> data[bisect_left(keys, 5)] 146 ('red', 5) 147 >>> data[bisect_left(keys, 8)] 148 ('yellow', 8) 149 150
