ANARC05H  Chop Ahoy! Revisited!
Given a nonempty string composed of digits only, we may group these digits into subgroups (but maintaining their original order) if, for every subgroup but the last one, the sum of the digits in a subgroup is less than or equal to the sum of the digits in the subgroup immediately on its right. Needless to say, each digit will be in exactly one subgroup.
For example, the string 635 can only be grouped in one subgroup [635] or in two subgroups as follows: [635] (since 6 < 8.) Another example is the string 1117 which can be grouped in one subgroup [1117] or as in the following: [1117], [1117], [1117], [1117], [1117] and [1117] but not any more, hence the total number of possibilities is 7.
Write a program that computes the total number of possibilities of such groupings for a given string of digits.
Input
Your program will be tested on a number of test cases. Each test case is speciﬁed on a separate line. Each line contains a single string no longer than 25, and is made of decimal digits only.
The end of the test cases is identiﬁed by a line made of the word "bye" (without the quotes.) Such line is not part of the test cases.
Output
For each test case, write the result using the following format:
k. n
where k is the test case number (starting at 1,) and n is the result of this test case.
Example
Input: 635 1117 9876 bye Output: 1. 2 2. 7 3. 2
hide comments
ayushpandia:
20201123 19:43:57
Bottomup solution was a challenge for me 

aryan29:
20200330 20:54:12
Easy DP Last edit: 20200330 21:21:08 

dkkv0000:
20200119 17:15:04
easy peasy lemon squeezy AC in one go!!!!!!!!! 

dmorgans:
20190527 12:17:30
it is a backtracking problem with memoization 

zakir068:
20190226 17:39:36
dont need to memorize.


md_meraj1319:
20181229 09:20:09
this is not a dp problem..


manjeet_:
20180718 19:18:46
similar to this: https://www.spoj.com/problems/ROCK/ 

soham_12345:
20180616 10:19:29
Hey can anyone give any corner case? I tried many testcases including string length 25 and even compared it with actual output from spoj toolkit but WA. :(


waqar_ahmad224:
20180317 10:17:30
Nice one , solved using backtracking , AC in 1 go 

Divyam Shah:
20180214 06:49:39
There are no overlapping subproblems , hence it is not a DP problem. The tag is incorrect. 
Added by:  ~!(*(@*!@^& 
Date:  20090705 
Time limit:  1s2s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ERL JSRHINO NODEJS PERL6 VB.NET 
Resource:  ANARC 2005 