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.

贪心肯定不对，参考discuss，假设一个结果，然后对结果进行二分逼近。

public double minmaxGasDist(int[] stations, int K) {

int LEN = stations.length;

double left = 0, right = stations[LEN - 1] - stations[0], mid = 0;

while (right >= left + 0.000001) {

mid = right - (right - left) / 2;

int cnt = 0;

for (int i = 0; i < LEN - 1; i++) {

cnt += Math.ceil((stations[i + 1] - stations[i]) / mid) - 1; //重点理解代码，d_i / (cnt_i + 1) <= mid

}

if (cnt > K) {

left = mid;

} else {

right = mid;

}

}

return mid;

}

https://www.cnblogs.com/wxisme/category/672272.html