What is the optimal time complexity of solving Koko Eating Bananas?

The optimized solution achieves a time complexity of O(n) by using sorting, mathematical shortcuts, or hash table lookups.

What is the auxiliary space complexity for Koko Eating Bananas?

The space complexity is O(n) since we only use a minimal/constant amount of extra memory for tracking variables (or auxiliary space if dynamic structures are allocated).

What are the typical edge cases we must handle in Koko Eating Bananas?

Key edge cases include empty collections, negative or large bounds causing integer overflow, arrays with only one element, or inputs where target criteria are not met.

How can we optimize the brute force approach for Koko Eating Bananas?

Brute force methods often inspect all possible combinations. We optimize this by sorting the input list to enable binary search, or tracking processed items in a set to avoid redundant nested loop lookups.

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Koko Eating Bananas

Learn how to solve the 'Koko Eating Bananas' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Easy

Koko loves to eat bananas. There are n piles of bananas, the ith pile has piles[i] bananas. The guards have gone and will come back in h hours.

Koko can decide her bananas-per-hour eating speed of k. Each hour, she chooses some pile of bananas and eats k bananas from that pile. If the pile has less than k bananas, she eats all of them instead and will not eat any more bananas during this hour.

Koko likes to eat slowly but still wants to finish eating all the bananas before the guards return.

Return the minimum integer k such that she can eat all the bananas within h hours.

Write a function minEatingSpeed(piles: List[int], h: int) -> int.

Constraints

•1 <= len(piles) <= 10^4
•len(piles) <= h <= 10^9
•1 <= piles[i] <= 10^9

Examples

Example 1

Input

piles = [3, 6, 7, 11], h = 8

Output

Explanation

At speed 4: pile 3 takes 1 hour, pile 6 takes 2 hours, pile 7 takes 2 hours, pile 11 takes 3 hours. Total = 8 hours.

Example 2

Input

piles = [30, 11, 23, 4, 20], h = 5

Output

Explanation

At speed 30: each pile takes 1 hour. Total = 5 hours.

Example 3

Input

piles = [30, 11, 23, 4, 20], h = 6

Output

Explanation

At speed 23: piles take 2+1+1+1+1 = 6 hours.

Need a Hint?

Analyze the input constraints. Try sorting first (O(n log n)) or using a hash map/set to track seen elements in O(n) time.

Edge Cases to Watch

Empty list or null input variables
Single item lists/arrays
Extremely large input bounds causing integer or stack overflow

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