ACPC10A - What’s Next

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According to Wikipedia, an arithmetic progression (AP) is a sequence of numbers such that the difference of any two successive members of the sequence is a constant. For instance, the sequence 3, 5, 7, 9, 11, 13, . . . is an arithmetic progression with common difference 2. For this problem, we will limit ourselves to arithmetic progression whose common difference is a non-zero integer.
On the other hand, a geometric progression (GP) is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed non-zero number called the common ratio. For example, the sequence 2, 6, 18, 54, . . . is a geometric progression with common ratio 3. For this problem, we will limit ourselves to geometric progression whose common ratio is a non-zero integer.
Given three successive members of a sequence, you need to determine the type of the progression and the next successive member.


Your program will be tested on one or more test cases. Each case is specified on a single line with three integers (−10, 000 < a1 , a2 , a3 < 10, 000) where a1 , a2 , and a3 are distinct.
The last case is followed by a line with three zeros.


For each test case, you program must print a single line of the form:
XX v
where XX is either AP or GP depending if the given progression is an Arithmetic or Geometric Progression. v is the next member of the given sequence. All input cases are guaranteed to be either an arithmetic or geometric progressions.


4 7 10
2 6 18
0 0 0

AP 13
GP 54

hide comments
bhaskar_uoh: 2016-12-04 11:53:30

*No need to stress on data type all ints, costed me 4 WAs :(

rv404674: 2016-11-23 00:04:55

625 125 5 can,t be a test case because it,s common ratio is not an integer

esshuvo: 2016-10-23 17:20:45

a,b,c mus be distinct,read the problem :) So,1,1,1 obviously not in the test case .
And corner case may be:
625 125 25
GP 5

goutam1511: 2016-10-03 13:52:11

can anybody give me some corner cases?

harishdatla: 2016-09-29 08:56:50

Why 1 1 1 should be AP while clearly above it stated that difference should be a non zero integer, anyway i guess its not in test case.. :)

Last edit: 2016-09-29 09:04:57
hacker_sk: 2016-09-25 20:04:29

enjoy :)

Last edit: 2016-09-25 20:07:33
devilking: 2016-09-16 16:55:25

common ratio should be integer

narutohokage_1: 2016-08-07 10:28:19

1 1 1 can never be case because all three numbers should be distinct.

mishra_sharad: 2016-08-06 08:04:10

I haven't seen such a stupid question on spoj til date...

sainath123456: 2016-08-03 20:14:00

note 1 1 1 can be both ap and gp

Added by:Omar ElAzazy
Time limit:1.799s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64
Resource:ACPC 2010