Koko Eating Bananas

Problem

Koko loves to eat bananas. There are n piles of bananas. The guards have gone and will come back in h hours. Koko can decide her bananas-per-hour eating speed of k. Return the minimum integer k such that she can eat all the bananas within h hours.

Examples

The brute-force approach

Try every possible speed from 1 to max(piles). For each speed k, compute the total hours needed. Return the first k that finishes within h hours.

def hours_needed(k):
    return sum(ceil(pile / k) for pile in piles)

for k in range(1, max(piles) + 1):
    if hours_needed(k) <= h:
        return k

O(max(piles) × n), you try up to max(piles) speeds and compute hours for each in O(n). For large piles (up to 10^9), this is far too slow. The valid speeds form a monotonic property: if speed k works, every speed k+1, k+2, … also works. That monotonicity is exactly what binary search exploits.

Spotting the pattern

This is a Binary Search problem. The key question to ask yourself:

If I can check whether a given speed works in O(n), how do I find the minimum working speed without trying every possibility?

Answering that is where it clicks, and it's exactly what the guided walkthrough below builds with you: the pattern reasoning, a progressive hint ladder that never spoils the answer, a row-by-row dry run, the optimized solution, and an in-browser editor to run your code against real test cases.