BComputation | Topcoder Archive

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+1C_nB_n

Here _aC_b is the standard binomial coefficient (see the notes). Return the value B_pos 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

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

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