No.2516 Credit Creation
タグ : / 解いたユーザー数 169
作問者 :
MasKoaTS
/ テスター :
Shirotsume
fky_
Problem Statement
The Uribo Kingdom has $N$ banks numbered $1,2,\dots,N$.
In the Uribo Kingdom, the "beef" is used as the unit of currency, and amounts of it are represented by non-negative real values.
Initially, the deposit of bank $1$ is $100$ beef, and the deposits of all other banks are $0$ beef.
For these banks, the following operation is performed in the order $i=1,2,\dots,N$.
Let $x$ beef be the deposit of bank $i$. First, bank $i$ writes $x$ in its ledger. Next, if bank $i + 1$ exists, bank $i$ keeps $Rx$ beef on hand and deposits $(1 - R)x$ beef in bank $i+1$.
After this operation, the deposit of bank $i+1$ is $(1-R)x$ beef.
The total deposit of the Uribo Kingdom is defined as the sum of the real numbers written in the ledgers during this process. Find this value.
Constraints
$2 \leq N \leq 100$
$N$ is an integer
$0 < R < 1$
$R$ is a real number with at most $2$ digits in its fractional part
Input
The input is given in the following format.
$N$ $R$
Line $1$ contains $N$
Line $2$ contains $R$
Output
Print the answer on $1$ line, followed by a newline.
The output is judged as correct if its absolute or relative error from the expected answer is at most $10^{−9}$.
It is guaranteed that the expected answer of this problem is always equal to the true value.
Sample
Sample 1
Input
3 0.05
Output
285.25
Initially, the deposit of bank $1$ is $100$ beef, and the deposits of banks $2, 3$ are both $0$ beef.
Bank $1$ writes the real number $100$ in its ledger, then deposits $100 \times (1 - 0.05) = 95$ beef in bank $2$.
As a result, the deposit of bank $2$ becomes $95$ beef.
Next, bank $2$ writes the real number $95$ in its ledger, then deposits $95 \times (1 - 0.05) = 90.25$ beef in bank $3$.
As a result, the deposit of bank $3$ becomes $90.25$ beef.
Finally, bank $3$ writes the real number $90.25$ in its ledger. Since bank $4$ does not exist, the operation ends here.
Therefore, the total deposit is $100 + 95 + 90.25 = 285.25$ beef.
Sample 2
Input
30 0.3
Output
333.325820219903102580637378917
It is guaranteed that the expected answer of this problem is always equal to the true value, but even if the printed value does not exactly match the expected answer,
it is judged as correct if its absolute or relative error from the expected answer is at most $10^{−9}$.
When using std::cout in C++, be careful about the number of digits displayed in the output value.
Sample 3
Input
100 0.99
Output
101.0101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101
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