# [LeetCode] 774. Minimize Max Distance to Gas Station 最小化去加油站的最大距离

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.

[10, 19, 25, 27, 56, 63, 70, 87, 96, 97]，K = 3

9，6，2，29，7，7，17，9，1

class Solution {
public:
double minmaxGasDist(vector<int>& stations, int K) {
double left = 0, right = 1e8;
while (right - left > 1e-6) {
double mid = left + (right - left) / 2;
if (helper(stations, K, mid)) right = mid;
else left = mid;
}
return left;
}
bool helper(vector<int>& stations, int K, double mid) {
int cnt = 0, n = stations.size();
for (int i = 0; i < n - 1; ++i) {
cnt += (stations[i + 1] - stations[i]) / mid;
}
return cnt <= K;
}
};

class Solution {
public:
double minmaxGasDist(vector<int>& stations, int K) {
double left = 0, right = 1e8;
while (right - left > 1e-6) {
double mid = left + (right - left) / 2;
int cnt = 0, n = stations.size();
for (int i = 0; i < n - 1; ++i) {
cnt += (stations[i + 1] - stations[i]) / mid;
}
if (cnt <= K) right = mid;
else left = mid;
}
return left;
}
};

Github 同步地址：

https://github.com/grandyang/leetcode/issues/774

Find K-th Smallest Pair Distance

Kth Smallest Number in Multiplication Table

Maximum Average Subarray II

Kth Smallest Element in a Sorted Matrix

https://leetcode.com/problems/minimize-max-distance-to-gas-station/solution/

https://leetcode.com/problems/minimize-max-distance-to-gas-station/discuss/113629/Approach-the-problem-using-the-%22trial-and-error%22-algorithm

https://leetcode.com/problems/minimize-max-distance-to-gas-station/discuss/113633/Easy-and-Concise-Solution-using-Binary-Search-C++JavaPython

LeetCode All in One 题目讲解汇总(持续更新中...)

posted @ 2018-04-28 23:59  Grandyang  阅读(7070)  评论(6编辑  收藏  举报