"""

Insert Bit

Insert one or more bits into an integer at a specific bit position.

Reference: https://en.wikipedia.org/wiki/Bit_manipulation

Complexity:

Time: O(1)

Space: O(1)

"""

from __future__ import annotations

def insert_one_bit(number: int, bit: int, position: int) -> int:

"""Insert a single bit at a specific position in an integer.

Splits the number at *position*, shifts the upper part left by one

to make room, inserts *bit*, and merges with the lower part.

Args:

number: The integer to modify.

bit: The bit value to insert (0 or 1).

position: Zero-based index at which to insert the bit.

Returns:

The resulting integer after insertion.

Examples:

>>> insert_one_bit(21, 1, 2)

45

>>> insert_one_bit(21, 0, 2)

41

"""

upper = number >> position

upper = (upper << 1) | bit

upper = upper << position

lower = ((1 << position) - 1) & number

return lower | upper

def insert_mult_bits(number: int, bits: int, length: int, position: int) -> int:

"""Insert multiple bits at a specific position in an integer.

Splits the number at *position*, shifts the upper part left by

*length* positions, inserts the *bits* value, and merges with the

lower part.

Args:

number: The integer to modify.

bits: The bit pattern to insert.

length: The number of bits in the pattern.

position: Zero-based index at which to insert.

Returns:

The resulting integer after insertion.

Examples:

>>> insert_mult_bits(5, 7, 3, 1)

47

>>> insert_mult_bits(5, 7, 3, 3)

61

"""

upper = number >> position

upper = (upper << length) | bits

upper = upper << position

lower = ((1 << position) - 1) & number

return lower | upper