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Solution: Koko Eating Bananas

Explore how to apply modified binary search to determine the minimum eating speed Koko needs to finish all banana piles within a given time frame. Learn to leverage monotonic properties of the problem to optimize your solution and understand its time and space complexity trade-offs.

Statement

Koko has nn piles of bananas in front of her, where the ithi^{th} pile has piles[i] bananas. The guards have left and will return in h hours, and Koko must finish all the bananas before they come back.

Before eating, Koko chooses an integer as an eating speed kk (bananas per hour). She keeps this speed constant throughout.

In each hour, Koko selects one pile of bananas and eats from it according to the following rules:

  • If the pile contains at least kk bananas, she eats exactly kk bananas from it.

  • If the pile contains fewer than kk bananas, she eats all the bananas from that pile and does not eat from any other pile during that hour.

Your task is to return the minimum eating speed k ...