Formatted question description: https://leetcode.ca/all/774.html

# 774. Minimize Max Distance to Gas Station

Hard

## Description

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.

## Solution

Use binary search. Sort stations and initialize low to 0 and high to the difference between the maximum element in stations and the minimum element in stations. While high - low > 1e-6, do binary search. Each time set mid to be the average of low and high and use mid as a candidate of D to calculate the minimum number of gas stations to be added. If the minimum number of gas stations to be added is less than or equal to K, then set high = mid. Otherwise, set low = mid. Finally, return low.

class Solution {
public double minmaxGasDist(int[] stations, int K) {
Arrays.sort(stations);
int length = stations.length;
double low = 0, high = stations[length - 1] - stations[0];
while (high - low > 1e-6) {
double mid = (low + high) / 2;
int minStations = 0;
for (int i = 1; i < length; i++)
minStations += (int) ((stations[i] - stations[i - 1]) / mid);
if (minStations <= K)
high = mid;
else
low = mid;
}
return low;
}
}