Bit Manipulation

• Negative Numbers: 3 => 011, -3 => flip 011 => 100 => 101 => prepend the first bit => 1101
• << && >>> Logical Shift => move every bit to the left/right, the firt/last bit will be cut off, then append/prepend the bits with 0
• >> Arithmetic Right Shift => shift values to the right but fill in the new bits with the value of the sign bit
• get ith bit => (num & (1 << i)) != 0
• set ith bit => num | 1 << i
• clear ith bit => let mask = ~(1 << i); return num && mask
• clear bits from i to the far right side => let mask = (1 << i) - 1; return num && mask
• clear bits from i to the far left side => let mask = (~0 << i + 1) - 1; return num && mask

tricks learned from questions:

• check number has no 0s(sequence of 0s): n != 0
• check the 2nd digit on the far right side is 0 => n & 2 == 0

Brain Teasers

• checking for prime number => generating a list of primes: time proved way, efficient.
• probability: mutually exclusive and independent can not co-exist if X & Y events have any possibility to happen
• some examples: burn two ropes, nine balls.