PAT甲级真题 1014 Waiting in Line (30分) C++实现(题意有坑,测试点2、4、5会报错)

该博客详细介绍了PAT甲级竞赛中的1014题——银行排队模拟问题。作者通过C++实现了模拟算法,利用队列数据结构解决顾客在多个窗口按规则排队等待的问题。博客内容包括题目描述、解题思路、代码实现以及需要注意的陷阱,如正确处理17:00的截止时间。

题目

Suppose a bank has N windows open for service. There is a yellow line in front of the windows which devides the waiting area into two parts. The rules for the customers to wait in line are:
The space inside the yellow line in front of each window is enough to contain a line with M customers. Hence when all the N lines are full, all the customers after (and including) the (NM+1)st one will have to wait in a line behind the yellow line.
Each customer will choose the shortest line to wait in when crossing the yellow line. If there are two or more lines with the same length, the customer will always choose the window with the smallest number.
Customer[i] will take T[i] minutes to have his/her transaction processed.
The first N customers are assumed to be served at 8:00am.
Now given the processing time of each customer, you are supposed to tell the exact time at which a customer has his/her business done.
For example, suppose that a bank has 2 windows and each window may have 2 custmers waiting inside the yellow line. There are 5 customers waiting with transactions taking 1, 2, 6, 4 and 3 minutes, respectively. At 08:00 in the morning, customer1 is served at window1 while customer2 is served at window2. Customer3 will wait in front of window1 and customer4 will wait in front of window2. Customer5 will wait behind the yellow line.
At 08:01, customer1 is done and customer5 enters the line in front of window1 since that line seems shorter now. Customer2 will leave at 08:02, customer4 at 08:06, customer3 at 08:07, and finally customer5 at 08:10.
Input
Each input file contains one test case. Each case starts with a line containing 4 positive integers: N (<=20, number of windows), M (<=10, the maximum capacity of each line inside the yellow line), K (<=1000, number of customers), and Q (<=1000, number of customer queries).
The next line contains K positive integers, which are the processing time of the K customers.
The last line contains Q positive integers, which represent the customers who are asking about the time they can have their transactions done. The customers are numbered from 1 to K.
Output
For each of the Q customers, print in one line the time at which his/her transaction is finished, in the format HH:MM where HH is in [08, 17] and MM is in [00, 59]. Note that since the bank is closed everyday after 17:00, for those customers who cannot be served before 17:00, you must output “Sorry” instead.
Sample Input
2 2 7 5
1 2 6 4 3 534 2
3 4 5 6 7
Sample Output
08:07
08:06
08:10
17:00
Sorry

思路

用队列queue模拟排队情况。

使用数据结构如下:

  1. 用结构体C存储顾客编号和所需时间:struct C{id; t};
  2. 用队列数组表示所有窗口排队情况:vector<queue<C> > window(n);
  3. 用队列存储等待区域顾客信息:queue<C> wait;
  4. 用数组time记录顾客完成时间:vector<int> time(k+1);

步骤如下:

  1. 读入顾客信息,将顾客尽可能排到各个窗口;剩下的加入等待队列当中;
  2. 遍历各窗口队头,找出当前最短时间;各队头均减去该最短时间;对所有时间为0队头,将其出队,记录其结束时间到time[]中,并将等待区顾客(如果有的话)入队;
  3. 若当前最快的顾客结束时间已达17:00,把当前所有窗口正在进行的服务处理完即结束(此处易错)
  4. 最后对于查询的人,若在time[]有记录则直接输出;若无记录, 则输出“sorry”。

注意坑

17:00截止指的是开始时间而不是结束时间,若17:00前已经开始,无论时间多久都要服务完(题目中给的输出时间范围,最大可以是17:59)。否则测试点2、4、5会报错。

例如测试用例:

2 1 3 3
1 540 540
1 2 3

应输出:

08:01
17:00
17:01

代码

#include <iostream>
#include <vector>
#include <queue>
#
### PAT 甲级 1034 测试点 4 的解析 PAT 甲级 1034 题目名为 **"Elevator"**,主要涉及电梯运行过程中的时间计算以及路径规划问题。对于测试点 4 的注意事项和可能的陷阱如下: #### 输入数据范围 测试点 4 可能会包含大量的输入数据或者极端情况下的边界条件。例如,可能存在非常大的楼层差值或较多的人数请求。因此,在实现算法时需特别关注变量的数据类型选择,建议使用 `long` 或者更大的整型来存储中间结果以防止溢出[^1]。 #### 边界条件处理 该测试点可能会考察一些特殊的边界场景,比如所有人都在同一层楼等待的情况、目标楼层为负数或者是零等情况。程序应该能够正确识别并合理处理这些特殊情况而不应报错或返回错误的结果。 #### 时间复杂度优化 由于此题涉及到多次循环迭代来进行模拟运算,如果效率不够高,则容易超时。针对这一点,可以考虑采用更高效的数据结构如优先队列 (priority queue) 来管理乘客请求顺序,从而减少不必要的比较操作次数,提高整体性能表现。 以下是基于上述析的一个 Python 实现方案: ```python def elevator(): n = int(input()) floors = list(map(int, input().split())) total_time = abs(floors[0]) * 6 current_floor = floors[0] for i in range(1, len(floors)): diff_floors = abs(current_floor - floors[i]) if floors[i] > current_floor: total_time += diff_floors * 6 + 5 elif floors[i] < current_floor: total_time += diff_floors * 4 + 5 else: continue current_floor = floors[i] print(total_time) elevator() ``` 以上代码片段展示了如何通过遍历每一对相邻的目标楼层之间的距离,并根据不同方向调整所需的时间增量完成整个行程耗时统计的任务逻辑。
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