Calculate the begin time in Python

I have 3 lists,

First list tells me customer name,

cst=[1,2,3,4,5]

Second list tells me its type,

cst_type=['A', 'B', 'B', 'A', 'B']

Third list tell me its arrival,

 arrived_at=[2,5,7,9,10]

After a customer arrives, it needs to be serviced for 3 minutes.

I want to prioritize customers with A type, that is, if A comes and the person(only 1) serving all of them is free or after becoming free, it will give priority to A, otherwise it will work according to FCFS.

How can I make a python program(simple one) to output a list of at what time they begin to be served?

I know if no priority is there then I can use:

For i in range(1,5):
   Service_begin[i]=max(arrival[i], service_end[i-1])

However how to change the program to add priority.

If you have familiarity with data structures, you may want to try a priority queue. If not, well, then now it's the time

You could build this as a simulation where you progress through the minutes of the day, picking the next customer from two lanes (A and B) based on priorities.

def serviceOrder(names,types,times):
    serviceDuration = 3
    laneA  = [i for i,t in enumerate(types) if t=="A"] # "A" cutomers (indexes)
    laneB  = [i for i,t in enumerate(types) if t=="B"] # "B" cutomers
    minute = 0 # current minute of the day when server is free
    while laneA or laneB:
        # serve all "A" customers currently present/waiting
        while laneA and times[laneA[0]] <= minute:
            index = laneA.pop(0)
            yield minute,names[index],"A"
            minute += serviceDuration
        # when no As to serve, take one B customer
        if laneB and times[laneB[0]] <= minute:
            index  = laneB.pop(0)
            yield minute,names[index],"B"
            minute += serviceDuration
            continue
        # no customers, wait a minute, and check again
        minute += 1 

note: this assumes that times are in increasing order. You'll need to sort the 3 lists if that's not the case.

output:

cst=[1,2,3,4,5]
cst_type=['A', 'B', 'B', 'A', 'B']
arrived_at=[2,5,7,9,10]
for time,name,prio in serviceOrder(cst,cst_type,arrived_at):
    print(time,"...",time+2,"name:",name,prio)

# start...end minute of service, customer name, type
# 2 ... 4 name: 1 A
# 5 ... 7 name: 2 B
# 8 ... 10 name: 3 B
# 11 ... 13 name: 4 A
# 14 ... 16 name: 5 B

Example with an A customer served before a B customer that arrived earlier:

cst=[1,2,3,4,5]
cst_type=['A', 'B', 'A', 'A', 'B']
arrived_at=[2,3,4,9,10]
for time,name,prio in serviceOrder(cst,cst_type,arrived_at):
    print(time,"...",time+2,"name:",name,prio)  

# start...end minutes of service, customer name, type    
# 2 ... 4 name: 1 A
# 5 ... 7 name: 3 A
# 8 ... 10 name: 2 B
# 11 ... 13 name: 4 A
# 14 ... 16 name: 5 B