Leetcode 774. Minimize Max Distance to Gas Station

LWC 69: 774. Minimize Max Distance to Gas Station

传送门：774. Minimize Max Distance to Gas Station

Problem:

On a horizontal number line, we have gas stations at positions stations[0], stations1, …, 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:

stations.length will be an integer in range [10, 2000].

stations[i] will be an integer in range [0, 10^8].

K will be an integer in range [1, 10^6].

Answers within 10^-6 of the true value will be accepted as correct.

思路：
首先求出每个station之间的距离，考虑如下问题：两个station为[1, 9]，gap为8。要插入一个station使得最大的最小，显然插入后应该为[1, 5, 9]，最大间隔为4。举个反例，如果插入后为[1, 6, 9], [1, 3, 9]，它们的最大间隔分别为5， 6，明显不是最小。从这里可以看出，对于插入k个station使得最大的最小的唯一办法是均分。

一种贪心的做法是，找到最大的gap，插入1个station，依此类推，但很遗憾，这种贪心策略是错误的。问题的难点在于我们无法确定到底哪两个station之间需要插入station，插入几个station也无法得知。

换个思路，如果我们假设知道了答案会怎么样？因为知道了最大间隔，所以如果目前的两个station之间的gap没有符合最大间隔的约束，那么我们就必须添加新的station来让它们符合最大间隔的约束，这样一来，对于每个gap我们是能够求得需要添加station的个数。如果需求数<=K，说明我们还可以进一步减小最大间隔，直到需求数>K。

Python版本：

class Solution(object):def minmaxGasDist(self, st, K):""":type stations: List[int]:type K: int:rtype: float"""lf = 1e-6rt = st[-1] - st[0]eps = 1e-7while rt - lf > eps:mid = (rt + lf) / 2cnt = 0for a, b in zip(st, st[1:]):cnt += (int)((b - a) / mid)if cnt <= K: rt = midelse: lf = midreturn rt

Leetcode 774. Minimize Max Distance to Gas Station相关推荐

[Leetcode] 774. Minimize Max Distance to Gas Station 解题报告
题目: On a horizontal number line, we have gas stations at positions stations[0], stations[1], ..., st ...
LWC 69: 774. Minimize Max Distance to Gas Station
LWC 69: 774. Minimize Max Distance to Gas Station 传送门:774. Minimize Max Distance to Gas Station Prob ...
加油python_力扣——gas station （加油站） python实现
题目描述: 中文: 在一条环路上有 N 个加油站,其中第 i 个加油站有汽油 gas[i] 升. 你有一辆油箱容量无限的的汽车,从第 i 个加油站开往第 i+1 个加油站需要消耗汽油 cost[i] ...
LeetCode 134 Gas Station
LeetCode 134 Gas Station 水题,暴力一下就ok class Solution { public:int tag[100005];int sum[100005];int canC ...
LeetCode 134. Gas Station
LeetCode 134. Gas Station Solution1:我的答案,无数次试错得到的,不成系统,没有思路.. 时间复杂度O(n2)O(n2)O(n^2) class Solution { ...
LeetCode 134.Gas Station 解题分析
题目来源: https://leetcode.com/problems/gas-station/description/ 题目描述: There are N gas stations along a ...
[leetcode] Gas Station
题目描述: There are N gas stations along a circular route, where the amount of gas at stationi is gas[i] ...
pat 甲级 1072. Gas Station (30)
1072. Gas Station (30) 时间限制 200 ms 内存限制 65536 kB 代码长度限制 16000 B 判题程序 Standard 作者 CHEN, Yue A gas sta ...
【LeetCode】849. Maximize Distance to Closest Person
[LeetCode]849. Maximize Distance to Closest Person 849. Maximize Distance to Closest Person Easy In ...

Leetcode 774. Minimize Max Distance to Gas Station

LWC 69: 774. Minimize Max Distance to Gas Station

Leetcode 774. Minimize Max Distance to Gas Station相关推荐

最新文章

热门文章