Minimum Time to Repair Cars Python Solution

lcpy gen -n 2594   # by problem number
lcpy gen -s minimum_time_to_repair_cars   # by problem name

Input: ranks = [4,2,3,1], cars = 10
Output: 16
Explanation:
- The first mechanic will repair two cars. The time required is 4 * 2 * 2 = 16 minutes.
- The second mechanic will repair two cars. The time required is 2 * 2 * 2 = 8 minutes.
- The third mechanic will repair two cars. The time required is 3 * 2 * 2 = 12 minutes.
- The fourth mechanic will repair four cars. The time required is 1 * 4 * 4 = 16 minutes.
It can be proved that the cars cannot be repaired in less than 16 minutes.

Input: ranks = [5,1,8], cars = 6
Output: 16
Explanation:
- The first mechanic will repair one car. The time required is 5 * 1 * 1 = 5 minutes.
- The second mechanic will repair four cars. The time required is 1 * 4 * 4 = 16 minutes.
- The third mechanic will repair one car. The time required is 8 * 1 * 1 = 8 minutes.
It can be proved that the cars cannot be repaired in less than 16 minutes.

from math import isqrt


class Solution:
    # Time: O(m * log(min(ranks) * cars^2)) where m = len(ranks)
    # Space: O(1)
    def repair_cars(self, ranks: list[int], cars: int) -> int:
        lo, hi = 1, min(ranks) * cars * cars
        while lo < hi:
            mid = (lo + hi) // 2
            if sum(isqrt(mid // r) for r in ranks) >= cars:
                hi = mid
            else:
                lo = mid + 1
        return lo