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
Anubhav Gupta:
20151002 05:25:28
Awesome question!!! 

Harsh Vardhan Ladha:
20150909 09:28:14
My 100th :D


Apoorv Dwivedi:
20150828 01:00:20
why is recursion better than dp for this question?


Rishabh Joshi:
20150614 20:39:28
Nice Problem.


Rishit Sanmukhani:
20150611 11:31:48
1. Simple recursion works.


coderforcoding:
20150601 07:53:18
. Last edit: 20150601 07:53:56 

Shubham Jadhav:
20150510 21:01:33
simple recursion without memoization works.. 

GAURAV CHANDEL:
20150428 15:01:46
dp needs practice... 

Mauro Persano:
20141224 02:26:55
Very nice problem, but had to filter out nondigit characters from input before my Scheme solution was accepted. Careful with garbage at the end of input lines. :( 

Infinity:
20141029 08:36:37
DP would be a bad choice here if you want the best :P

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 