Модуль bisect python 3

Bisect Algorithm Functions in Python

The purpose of Bisect algorithm is to find a position in list where an element needs to be inserted to keep the list sorted.

Python in its definition provides the bisect algorithms using the module “bisect” which allows keeping the list in sorted order after the insertion of each element. This is essential as this reduces overhead time required to sort the list again and again after the insertion of each element.

Important Bisection Functions

1. bisect(list, num, beg, end) :- This function returns the position in the sorted list, where the number passed in argument can be placed so as to maintain the resultant list in sorted order. If the element is already present in the list, the rightmost position where element has to be inserted is returned.

This function takes 4 arguments, list which has to be worked with, a number to insert, starting position in list to consider, ending position which has to be considered.

2. bisect_left(list, num, beg, end) :- This function returns the position in the sorted list, where the number passed in argument can be placed so as to maintain the resultant list in sorted order. If the element is already present in the list, the leftmost position where element has to be inserted is returned.

This function takes 4 arguments, list which has to be worked with, number to insert, starting position in list to consider, ending position which has to be considered.

3. bisect_right(list, num, beg, end) :- This function works similar to the “bisect()” and mentioned above.

Python3

Rightmost index to insert, so list remains sorted is : 5 Leftmost index to insert, so list remains sorted is : 2 Rightmost index to insert, so list remains sorted is : 4

Time Complexity: O(log(n)), Bisect method works on the concept of binary search
Auxiliary Space: O(1)

4. insort(list, num, beg, end) :- This function returns the sorted list after inserting number in appropriate position, if the element is already present in the list, the element is inserted at the rightmost possible position.

This function takes 4 arguments, list which has to be worked with, number to insert, starting position in list to consider, ending position which has to be considered.

5. insort_left(list, num, beg, end) :- This function returns the sorted list after inserting number in appropriate position, if the element is already present in the list, the element is inserted at the leftmost possible position.

This function takes 4 arguments, list which has to be worked with, number to insert, starting position in list to consider, ending position which has to be considered.

6. insort_right(list, num, beg, end) :- This function works similar to the “insort()” as mentioned above.

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Модуль bisect — реализация алгоритма бинарного поиска

Модуль bisect — обеспечивает поддержку списка в отсортированном порядке с помощью алгоритма бинарного поиска.

Алгоритм бинарного поиска

Двоичный (бинарный) поиск, известный также как метод деления пополам или дихотомия — классический алгоритм поиска элемента в отсортированном массиве, использующий деление массива на половины. Процесс бинарного поиска состоит из следующих шагов:

1. Определение значения элемента в середине структуры данных. Полученное значение сравнивается с нашим ключом.
2. Если ключ меньше значения середины, то поиск осуществляется в первой половине элементов, иначе — во второй.
3. Затем вновь определяется значение серединного элемента в выбранной половине и сравнивается с ключом.
4. Процесс продолжается до тех пор, пока не будет найден элемент со значением ключа или не станет пустым интервал для поиска.

Сложность алгоритма O(log n), однако вставка в отсортированный список в Python имеет сложность O(n), необходимо это иметь в виду.

Реализация в модуле bisect

bisect.insort(list, elem, lo=0, hi=len(a)), или bisect.insort_right(list, elem, lo=0, hi=len(a)) — вставка элемента в отсортированный список, при этом elem располагается как можно правее (все элементы, равные ему, остаются слева). Параметры lo и hi (здесь и в других функциях) могут быть использованы для указания подмножества списка, которое нужно учитывать; по умолчанию используется весь список.

bisect.insort_left(list, elem, lo=0, hi=len(a)) — вставка элемента в отсортированный список, при этом elem располагается как можно левее (все элементы, равные ему, остаются справа).

bisect.bisect(list, elem, lo=0, hi=len(a)), или bisect.bisect_right(list, elem, lo=0, hi=len(a)) — поиск места для вставки элемента в отсортированный список, таким образом, чтобы elem располагался как можно правее.

bisect.bisect_left(list, elem, lo=0, hi=len(a)) — поиск места для вставки элемента в отсортированный список, таким образом, чтобы elem располагался как можно левее.

Примеры

Функция проверки наличия элемента в списке (аналог elem in l ):

 
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 bisect — Array bisection algorithm¶
 
This module provides support for maintaining a list in sorted order without having to sort the list after each insertion. For long lists of items with expensive comparison operations, this can be an improvement over the more common approach. The module is called bisect because it uses a basic bisection algorithm to do its work. The source code may be most useful as a working example of the algorithm (the boundary conditions are already right!).
 
The following functions are provided:
 
Locate the insertion point for x in a to maintain sorted order. The parameters lo and hi may be used to specify a subset of the list which should be considered; by default the entire list is used. If x is already present in a, the insertion point will be before (to the left of) any existing entries. The return value is suitable for use as the first parameter to list.insert() assuming that a is already sorted.
 
The returned insertion point i partitions the array a into two halves so that all(val < x for val in a[lo : i]) for the left side and all(val >= x for val in a[i : hi]) for the right side.
 
key specifies a key function of one argument that is used to extract a comparison key from each element in the array. To support searching complex records, the key function is not applied to the x value.
 
If key is None , the elements are compared directly with no intervening function call.
 
Changed in version 3.10: Added the key parameter.
 
bisect. bisect_right ( a , x , lo = 0 , hi = len(a) , * , key = None ) ¶ bisect. bisect ( a , x , lo = 0 , hi = len(a) , * , key = None ) ¶
 
Similar to bisect_left() , but returns an insertion point which comes after (to the right of) any existing entries of x in a.
 
The returned insertion point i partitions the array a into two halves so that all(val x for val in a[i : hi]) for the right side.
 
key specifies a key function of one argument that is used to extract a comparison key from each element in the array. To support searching complex records, the key function is not applied to the x value.
 
If key is None , the elements are compared directly with no intervening function call.
 
Changed in version 3.10: Added the key parameter.
 
Insert x in a in sorted order.
 
This function first runs bisect_left() to locate an insertion point. Next, it runs the insert() method on a to insert x at the appropriate position to maintain sort order.
 
To support inserting records in a table, the key function (if any) is applied to x for the search step but not for the insertion step.
 
Keep in mind that the O(log n) search is dominated by the slow O(n) insertion step.
 
Changed in version 3.10: Added the key parameter.
 
bisect. insort_right ( a , x , lo = 0 , hi = len(a) , * , key = None ) ¶ bisect. insort ( a , x , lo = 0 , hi = len(a) , * , key = None ) ¶
 
Similar to insort_left() , but inserting x in a after any existing entries of x.
 
This function first runs bisect_right() to locate an insertion point. Next, it runs the insert() method on a to insert x at the appropriate position to maintain sort order.
 
To support inserting records in a table, the key function (if any) is applied to x for the search step but not for the insertion step.
 
Keep in mind that the O(log n) search is dominated by the slow O(n) insertion step.
 
Changed in version 3.10: Added the key parameter.
 
Performance Notes¶
 
When writing time sensitive code using bisect() and insort(), keep these thoughts in mind:
 
 
Bisection is effective for searching ranges of values. For locating specific values, dictionaries are more performant.
 
The insort() functions are O(n) because the logarithmic search step is dominated by the linear time insertion step.
 
The search functions are stateless and discard key function results after they are used. Consequently, if the search functions are used in a loop, the key function may be called again and again on the same array elements. If the key function isn’t fast, consider wrapping it with functools.cache() to avoid duplicate computations. Alternatively, consider searching an array of precomputed keys to locate the insertion point (as shown in the examples section below).
 
 
 
Sorted Collections is a high performance module that uses bisect to managed sorted collections of data.
 
The SortedCollection recipe uses bisect to build a full-featured collection class with straight-forward search methods and support for a key-function. The keys are precomputed to save unnecessary calls to the key function during searches.
 
 
Searching Sorted Lists¶
 
The above bisect functions are useful for finding insertion points but can be tricky or awkward to use for common searching tasks. The following five functions show how to transform them into the standard lookups for sorted lists:
 
def index(a, x): 'Locate the leftmost value exactly equal to x' i = bisect_left(a, x) if i != len(a) and a[i] == x: return i raise ValueError def find_lt(a, x): 'Find rightmost value less than x' i = bisect_left(a, x) if i: return a[i-1] raise ValueError def find_le(a, x): 'Find rightmost value less than or equal to x' i = bisect_right(a, x) if i: return a[i-1] raise ValueError def find_gt(a, x): 'Find leftmost value greater than x' i = bisect_right(a, x) if i != len(a): return a[i] raise ValueError def find_ge(a, x): 'Find leftmost item greater than or equal to x' i = bisect_left(a, x) if i != len(a): return a[i] raise ValueError 
 
Examples¶
 
The bisect() function can be useful for numeric table lookups. This example uses bisect() to look up a letter grade for an exam score (say) based on a set of ordered numeric breakpoints: 90 and up is an ‘A’, 80 to 89 is a ‘B’, and so on:
 
>>> def grade(score, breakpoints=[60, 70, 80, 90], grades='FDCBA'): . i = bisect(breakpoints, score) . return grades[i] . >>> [grade(score) for score in [33, 99, 77, 70, 89, 90, 100]] ['F', 'A', 'C', 'C', 'B', 'A', 'A'] 
 
The bisect() and insort() functions also work with lists of tuples. The key argument can serve to extract the field used for ordering records in a table:
 
>>> from collections import namedtuple >>> from operator import attrgetter >>> from bisect import bisect, insort >>> from pprint import pprint >>> Movie = namedtuple('Movie', ('name', 'released', 'director')) >>> movies = [ . Movie('Jaws', 1975, 'Spielberg'), . Movie('Titanic', 1997, 'Cameron'), . Movie('The Birds', 1963, 'Hitchcock'), . Movie('Aliens', 1986, 'Cameron') . ] >>> # Find the first movie released after 1960 >>> by_year = attrgetter('released') >>> movies.sort(key=by_year) >>> movies[bisect(movies, 1960, key=by_year)] Movie(name='The Birds', released=1963, director='Hitchcock') >>> # Insert a movie while maintaining sort order >>> romance = Movie('Love Story', 1970, 'Hiller') >>> insort(movies, romance, key=by_year) >>> pprint(movies) [Movie(name='The Birds', released=1963, director='Hitchcock'), Movie(name='Love Story', released=1970, director='Hiller'), Movie(name='Jaws', released=1975, director='Spielberg'), Movie(name='Aliens', released=1986, director='Cameron'), Movie(name='Titanic', released=1997, director='Cameron')] 
 
If the key function is expensive, it is possible to avoid repeated function calls by searching a list of precomputed keys to find the index of a record:
 
>>> data = [('red', 5), ('blue', 1), ('yellow', 8), ('black', 0)] >>> data.sort(key=lambda r: r[1]) # Or use operator.itemgetter(1). >>> keys = [r[1] for r in data] # Precompute a list of keys. >>> data[bisect_left(keys, 0)] ('black', 0) >>> data[bisect_left(keys, 1)] ('blue', 1) >>> data[bisect_left(keys, 5)] ('red', 5) >>> data[bisect_left(keys, 8)] ('yellow', 8) 
 
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