TopCoder problem "BComputation" used in TCCC06 Round 2B (Division I Level One)



Problem Statement

    You will be given B0, the first element of our sequence. The following equation must hold for all n > 0: 
        0  =  B0 + n+1C1B1 + n+1C2B2 + ... + n+1CnBn
Here aCb is the standard binomial coefficient (see the notes). Return the value Bpos in the form "p/q" (quotes for clarity) where p and q are integers with no extra leading zeros and no common factors (other than 1). The denominator q must always be positive. If the returned value is 0 then return "0/1".
 

Definition

    
Class:BComputation
Method:getValue
Parameters:int, int
Returns:String
Method signature:String getValue(int B0, int pos)
(be sure your method is public)
    
 

Notes

-aCb has value a!/(b!(a-b)!) where a! = a*(a-1)*...*2*1.
 

Constraints

-B0 will be between -100 and 100, inclusive.
-pos will be between 0 and 15, inclusive.
 

Examples

0)
    
1
0
Returns: "1/1"
Here we simply return B0.
1)
    
1
1
Returns: "-1/2"
Using the given formula, we can compute B1 = -B0/2C1.
2)
    
100
11
Returns: "0/1"
3)
    
92
12
Returns: "-31786/1365"

Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=6777

Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=10112&pm=6777

Writer:

AdminBrett

Testers:

PabloGilberto , Yarin , Olexiy

Problem categories:

Simple Math