# 9.5. 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:

bisect.bisect_left(list, item[, lo[, hi]])

Locate the proper insertion point for item in list 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 item is already present in list, 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(). This assumes that list is already sorted.

New in version 2.1.

bisect.bisect_right(list, item[, lo[, hi]])

Similar to bisect_left(), but returns an insertion point which comes after (to the right of) any existing entries of item in list.

New in version 2.1.

bisect.bisect(...)
Alias for bisect_right().
bisect.insort_left(list, item[, lo[, hi]])

Insert item in list in sorted order. This is equivalent to list.insert(bisect.bisect_left(list, item, lo, hi), item). This assumes that list is already sorted.

New in version 2.1.

bisect.insort_right(list, item[, lo[, hi]])

Similar to insort_left(), but inserting item in list after any existing entries of item.

New in version 2.1.

bisect.insort(...)
Alias for insort_right().

## 9.5.1. Examples¶

The bisect() function is generally useful for categorizing numeric data. This example uses bisect() to look up a letter grade for an exam total (say) based on a set of ordered numeric breakpoints: 85 and up is an ‘A’, 75..84 is a ‘B’, etc.

```>>> grades = "FEDCBA"
>>> breakpoints = [30, 44, 66, 75, 85]
>>> from bisect import bisect
...
'C'
>>> map(grade, [33, 99, 77, 44, 12, 88])
['E', 'A', 'B', 'D', 'F', 'A']
```

Unlike the sorted() function, it does not make sense for the bisect() functions to have key or reversed arguments because that would lead to an inefficent design (successive calls to bisect functions would not “remember” all of the previous key lookups).

Instead, it is better to search a list of precomputed keys to find the index of the record in question:

```>>> data = [('red', 5), ('blue', 1), ('yellow', 8), ('black', 0)]
>>> data.sort(key=lambda r: r[1])
>>> keys = [r[1] for r in data]         # precomputed 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)
```