ACPC10A  What’s Next
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 nonzero 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 nonzero 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 nonzero integer.
Given three successive members of a sequence, you need to determine the type of the progression and the next successive member.
Input
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.
Output
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.
Example
Input:
4 7 10
2 6 18
0 0 0
Output:
AP 13
GP 54
hide comments
Dushyant Singh:
20151202 16:15:13
@jinesl  Use if ( b == ( a + c ) / 2.0 ) instead of if ( b == ( a + c ) / 2 ) 

jinesl:
20151201 15:15:57
This thing is blowing me up... I can't understand why I'm getting wrong answer... 

rameshkonatala:
20151117 07:52:04
Should I convert next no. in GP into fraction and display it? 

Sid:
20151116 23:15:44
Do take a note of this line above "three integers (−10, 000 < a1 , a2 , a3 < 10, 000) where a1 , a2 , and a3 are distinct." This proves 1, 1, 1 will never be a test case.


HEMANTH SAVASERE:
20151116 13:40:37
hey guys according to definition of AP common difference can be any constant 0 or any negative number


suresh007:
20151028 14:50:27
i think there is no need to check for 1,1,1 sequence as number are distinct(input section). 

sarthak_8:
20151017 13:56:31
should I put a condition to satisfy the constraints? Last edit: 20151017 13:58:02 

cqui:
20151016 10:46:12
a1 , a2 , and a3 are distinct 1 1 1 should not be input.


johnnycash:
20151007 22:25:49
check for silly mistake......its a simple one but costed me many WA because of that reason...


harshmmodi:
20151001 19:56:38
@ nonushikhar... 111 is a GP and not an AP since the given condition says that c.d. and c.ratio both are nonzero integer. Hence c.d. of AP cannot be Zero but c.ratio can be 1 Last edit: 20151001 19:58:30 
Added by:  Omar ElAzazy 
Date:  20101130 
Time limit:  1.799s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ASM64 
Resource:  ACPC 2010 