题目描述：

LeetCode 774. Minimize Max Distance to Gas Station

On a horizontal number line, we have gas stations at positions stations[0], stations[1], ..., stations[N-1], where N = stations.length.

Now, we add K more gas stations so that D, the maximum distance between adjacent gas stations, is minimized.

Return the smallest possible value of D.

Example:

Input: stations = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], K = 9
Output: 0.500000

Note:

1. stations.length will be an integer in range [10, 2000].
2. stations[i] will be an integer in range [0, 10^8].
3. K will be an integer in range [1, 10^6].
4. Answers within 10^-6 of the true value will be accepted as correct.

题目大意：

给定一组加油站的位置stations，在这些加油站中新增K个加油站，使得相邻加油站之间的最大距离最小化。

求最小化的最大距离。

解题思路：

二分枚举答案（Binary Search）

Python代码：

class Solution(object):
    def minmaxGasDist(self, stations, K):
        """
        :type stations: List[int]
        :type K: int
        :rtype: float
        """
        stations.sort()
        step = 1e-9
        left, right = 0, 1e9
        while left <= right:
            mid = (left + right) / 2
            if self.isValid(mid, stations, K):
                right = mid - step
            else:
                left = mid + step
        return mid
    def isValid(self, gap, stations, K):
        for x in range(len(stations) - 1):
            dist = stations[x + 1] - stations[x]
            K -= int(math.ceil(dist / gap)) - 1
        return K >= 0

 

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