bit-manipulation

name	bit-manipulation
description	Bit manipulation tricks and techniques for solving problems efficiently using binary operations and XOR properties.
sasmp_version	1.3.0
bonded_agent	07-greedy-advanced
bond_type	PRIMARY_BOND
atomic_responsibility	bit_operation_execution
version	2.0.0
parameter_validation	{"strict":true,"rules":[{"name":"num","type":"integer","required":true},{"name":"bit_index","type":"integer","required":false}]}
retry_logic	{"max_attempts":3,"backoff_ms":[100,200,400],"retryable_errors":["overflow","timeout"]}
logging_hooks	{"on_start":true,"on_complete":true,"on_error":true,"log_format":"[BIT-SKILL] {timestamp} | {operation} | {status}"}
complexity_annotations	{"basic_ops":{"time":"O(1)","space":"O(1)"},"count_bits":{"time":"O(log n) or O(set bits)","space":"O(1)"},"subset_generation":{"time":"O(2^n)","space":"O(1) per subset"}}

Bit Manipulation Skill

Atomic Responsibility: Execute bit-level operations for efficient problem solving.

Essential Bit Operations

def set_bit(num: int, i: int) -> int:
    """Set i-th bit to 1. Time: O(1)"""
    return num | (1 << i)


def clear_bit(num: int, i: int) -> int:
    """Clear i-th bit to 0. Time: O(1)"""
    return num & ~(1 << i)


def toggle_bit(num: int, i: int) -> int:
    """Toggle i-th bit. Time: O(1)"""
    return num ^ (1 << i)


def is_bit_set(num: int, i: int) -> bool:
    """Check if i-th bit is set. Time: O(1)"""
    return (num & (1 << i)) != 0


def is_power_of_two(n: int) -> bool:
    """Check if n is power of 2. Time: O(1)"""
    return n > 0 and (n & (n - 1)) == 0


def () -> :
    
     num & (-num)


 () -> :
    
     num & (num - )