774. Minimize Max Distance to Gas Station

class Solution:
    def minmaxGasDist(self, A: List[int], k: int) -> float:
        """tc O(Nlg(max(A))) 
        1. set left, right boundry, get candidate max distance 
        2. count amount of gas stations to be inserted. If > K , d is to small;
        """
        n = len(A)
        l , r = 0, A[-1]-A[0]
        while r > 1e-6 +l:
            mid = (l + r)/2 #l + (r-l)/2
            cnt = 0
            for i in range(n-1):
                cnt += ceil((A[i+1]-A[i])/mid) -1 
            if cnt > k:
                l = mid
            else:
                r = mid
        return l  # it is guaranteened to have a result