Koko Eating Bananas

1. The obvious way

   Try speeds 1, 2, 3, ... and simulate each: too slow when piles are huge.

2. The key insight

   A pile of p bananas needs ceil(p / speed) hours, so the total hours only go down as speed rises. The speeds that work form a range from the answer up to the biggest pile. Binary search the speed between 1 and the biggest pile, checking each guess in one pass over the piles.

3. The algorithm
   1. Speed range: 1 up to the biggest pile.
   2. Guess the middle speed; total hours = sum over piles of ceil(pile / speed).
   3. Within the allowed hours? It works: try slower (keep this speed as a candidate).
   4. Too many hours? Too slow: try faster. Stop when the range is one speed.

Watch it run

speed range 1 to 6

def min_eating_speed(piles, hours):
    slowest, fastest = 1, max(piles)
    while slowest < fastest:
        speed = (slowest + fastest) // 2
        needed = sum((pile + speed - 1) // speed for pile in piles)   # ceil(pile / speed)
        if needed <= hours:
            fastest = speed                  # this speed works: try slower
        else:
            slowest = speed + 1              # too slow: speed up
    return slowest

Now close this and write it again from memory, in the language you will use in the interview. Reattempt after 1 day, 7 days and about 30 days.