BComputation
TCCC06 Round 2B · 2006-08-22 · by AdminBrett
TCCC06 Round 2B · 2006-08-22 · by AdminBrett · Simple Math
Problem Statement
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+1CnBnHere 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".
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)
1 4 Returns: "-1/30"
4)
1 5 Returns: "0/1"
Submissions are judged against all 72 archived test cases, of which 5 are shown here. Case numbers match the judge’s.
Coding Area
Language: C++17 · define a public class BComputation with a public method string getValue(int B0, int pos) · 72 test cases · 2 s / 256 MB per case