# Python Bisect Module

The `bisect` 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.

## Importing the Module

```python
import bisect
```

## Finding Insertion Points

### `bisect.bisect()` (or `bisect_right`)

Locates the insertion point for `x` in `a` to maintain sorted order. If `x` is already present in `a`, the insertion point will be after (to the right of) any existing entries.

```python
import bisect

a = [1, 2, 4, 5]
x = 3

# Find position to insert 3
pos = bisect.bisect(a, x)
print(pos) # Output: 2
```

### `bisect.bisect_left()`

Locates the insertion point for `x` in `a` to maintain sorted order. If `x` is already present in `a`, the insertion point will be before (to the left of) any existing entries.

```python
import bisect

a = [1, 2, 4, 5]
x = 2

# Find position to insert 2 (left)
pos_left = bisect.bisect_left(a, x)
print(pos_left) # Output: 1

# Find position to insert 2 (right/default)
pos_right = bisect.bisect(a, x)
print(pos_right) # Output: 2
```

## Inserting Elements

### `bisect.insort()` (or `bisect.insort_right`)

Inserts `x` in `a` in sorted order. This is equivalent to `a.insert(bisect.bisect(a, x), x)`.

```python
import bisect

a = [1, 2, 4, 5]
bisect.insort(a, 3)
print(a) # Output: [1, 2, 3, 4, 5]
```

### `bisect.insort_left()`

Inserts `x` in `a` in sorted order. This is equivalent to `a.insert(bisect.bisect_left(a, x), x)`.

```python
import bisect

a = [1, 2, 4, 5]
bisect.insort_left(a, 2)
print(a) # Output: [1, 2, 2, 4, 5] (Inserted at index 1)
```

## Examples

### Numeric Grades to Letter Grades

The `bisect()` function can be useful for numeric table lookups.

```python
import bisect

def grade(score, breakpoints=[60, 70, 80, 90], grades='FDCBA'):
    i = bisect.bisect(breakpoints, score)
    return grades[i]

print([grade(score) for score in [33, 99, 77, 70, 89, 90, 100]])
# Output: ['F', 'A', 'C', 'C', 'B', 'A', 'A']
```

[[programming/python/python]]