PAT 1017. Queueing at Bank (25)

本文探讨了在银行排队场景中,如何通过合理安排顾客等待时间来减少整体等待时间,提出了一个基于优先级排序和时间分配的算法。该算法考虑了顾客到达时间和处理时间,通过排序和动态调整等待时间,实现了排队效率的提升。
//
//1017. Queueing at Bank (25)
//	accept
#include <iostream>
#include <algorithm>
	using namespace std;

typedef struct 
{
	int second;
	int time;
}Record;


bool cmp(Record r1, Record r2)
{
	if (r1.second == r2.second)
	{
		return r1.time < r2.time;
	}
	return r1.second < r2.second;
}
int main()
{
	int n;
	int k;
	Record r[10005];
	cin >> n >> k;

	int waitingtime = 0;
	int curr[105];


	int len = n;

	int i;

	int h, m, s;

	int index = 0;
	for (i = 0;i<n;i++)
	{
		scanf("%d:%d:%d %d", &h, &m, &s, &r[index].time);
		r[index].second = h * 60 * 60  + m * 60 + s;


		if (r[index].second > 61200)
		{
			index--;
			len--;
		}
		index++;
	}


	fill(curr, curr+k, 8*60*60);
	sort(r, r+len, cmp);

	int start = 0;

	for (i = start; i< start + k && i< len; i++ )
	{
		if (r[i].second < curr[i - start])
		{
			waitingtime += curr[ i- start ] - r[i].second;
			curr[i - start] = curr[i-start] + (r[i].time * 60) ;
		}
		else
		{
			curr[i-start] = r[i].second + (r[i].time * 60);
		}
	}

	i+=start;

	sort(curr, curr+k);
	while( i < len)
	{
		if (r[i].second < curr[0])
		{
			waitingtime += curr[0] - r[i].second;
			curr[0] = curr[0] + (r[i].time * 60) ;
		}
		else
		{
			curr[0] = r[i].second + (r[i].time * 60);
		}
		sort(curr, curr+k);
		i++;
	}
	printf("%.1f", waitingtime / len / 60.0);
	return 0;
}

### 银行排队问题的Python实现 银行排队问题是典型的并行处理和任务分配场景,可以通过ZeroMQ框架中的Ventilator-Worker-Sink模型来解决[^1]。以下是基于该模型的一个简单Python实现: #### ZeroMQ Ventilator 实现 Ventilator负责生成任务并将它们发送给Workers。 ```python import zmq import time context = zmq.Context() # Socket to send tasks to workers sender = context.socket(zmq.PUSH) sender.bind("tcp://*:5557") print("Press Enter when the workers are ready...") _ = input() print("Sending tasks to workers...") # Send out tasks total_msec = 0 for task_nbr in range(100): workload = int((task_nbr * task_nbr) % 100 + 1) # Some random work load total_msec += workload sender.send_string(str(workload)) print(f"Total expected cost: {total_msec} msec") time.sleep(1) # Give 0MQ time to deliver ``` #### ZeroMQ Worker 实现 Worker接收来自Ventilator的任务并执行计算后将结果返回给Sink。 ```python import zmq import sys import time context = zmq.Context() # Socket to receive messages on receiver = context.socket(zmq.PULL) receiver.connect("tcp://localhost:5557") # Socket to send messages to sender = context.socket(zmq.PUSH) sender.connect("tcp://localhost:5558") while True: s = receiver.recv_string() print(f"Received request: {s}") # Do some 'work' time.sleep(int(s) / 10) # Send results to sink sender.send(b'') ``` #### ZeroMQ Sink 实现 Sink收集所有Worker的结果,并统计完成时间。 ```python import zmq import time context = zmq.Context() # Socket to collect worker responses receiver = context.socket(zmq.PULL) receiver.bind("tcp://*:5558") # Wait for start of batch s = receiver.recv() # Start our clock now tstart = time.time() # Process 100 confirmations for task_nbr in range(100): s = receiver.recv() if task_nbr % 10 == 0: sys.stdout.write(':') else: sys.stdout.write('.') sys.stdout.flush() # Calculate and report duration of batch tend = time.time() print(f"\nTotal elapsed time: {(tend-tstart)*1000} msec") ``` 上述代码展示了如何通过ZeroMQ构建一个简单的分布式任务管理系统[^2]。对于银行排队问题,可以将其视为多个客户作为任务被分配到不同的柜员(即Worker),而最终的结果由Sink汇总。 此外,在高并发环境下,还需要注意内存管理和I/O性能优化[^3]。建议使用缓存机制减少磁盘操作频率,并利用消息队列实现各模块间的异步通信。
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