875 Koko Eating Bananas.py

#!/usr/bin/python3
"""
Koko loves to eat bananas.  There are N piles of bananas, the i-th 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 won't eat any more bananas
during this hour.

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

Return the minimum integer K such that she can eat all the bananas within H hours.



Example 1:

Input: piles = [3,6,7,11], H = 8
Output: 4
Example 2:

Input: piles = [30,11,23,4,20], H = 5
Output: 30
Example 3:

Input: piles = [30,11,23,4,20], H = 6
Output: 23

Note:

1 <= piles.length <= 10^4
piles.length <= H <= 10^9
1 <= piles[i] <= 10^9
"""
from typing import List
import math


class Solution:
    def minEatingSpeed(self, piles: List[int], H: int) -> int:
        """
        validation:
            each piles  ceil(n/K)

        sum(ceil(piles[i]/K)) <= H
        binary search

        O(log n * n)
        """
        if len(piles) > H:
            return None

        n = len(piles)
        hi = max(piles) + 1
        lo = 1
        while lo < hi:
            mid = (lo + hi) // 2
            if sum(
                math.ceil(piles[i] / mid)
                for i in range(n)
            ) > H:
                lo = mid + 1
            else:
                hi = mid

        return lo


if __name__ == "__main__":
    assert Solution().minEatingSpeed([3,6,7,11], 8) == 4