201092: [AtCoder]ARC109 C - Large RPS Tournament
Description
Score : $500$ points
Problem Statement
To decide which is the strongest among Rock, Paper, and Scissors, we will hold an RPS tournament. There are $2^k$ players in this tournament, numbered $0$ through $2^k-1$. Each player has his/her favorite hand, which he/she will use in every match.
A string $s$ of length $n$ consisting of R
, P
, and S
represents the players' favorite hands.
Specifically, the favorite hand of Player $i$ is represented by the $((i\text{ mod } n) + 1)$-th character of $s$; R
, P
, and S
stand for Rock, Paper, and Scissors, respectively.
For $l$ and $r$ such that $r-l$ is a power of $2$, the winner of the tournament held among Players $l$ through $r-1$ will be determined as follows:
- If $r-l=1$ (that is, there is just one player), the winner is Player $l$.
- If $r-l\geq 2$, let $m=(l+r)/2$, and we hold two tournaments, one among Players $l$ through $m-1$ and the other among Players $m$ through $r-1$. Let $a$ and $b$ be the respective winners of these tournaments. $a$ and $b$ then play a match of rock paper scissors, and the winner of this match - or $a$ if the match is drawn - is the winner of the tournament held among Players $l$ through $r-1$.
Find the favorite hand of the winner of the tournament held among Players $0$ through $2^k-1$.
Notes
- $a\text{ mod } b$ denotes the remainder when $a$ is divided by $b$.
- The outcome of a match of rock paper scissors is determined as follows:
- If both players choose the same hand, the match is drawn;
R
beatsS
;P
beatsR
;S
beatsP
.
Constraints
- $1 \leq n,k \leq 100$
- $s$ is a string of length $n$ consisting of
R
,P
, andS
.
Input
Input is given from Standard Input in the following format:
$n$ $k$ $s$
Output
Print the favorite hand of the winner of the tournament held among Players $0$ through $2^k-1$, as R
, P
, or S
.
Sample Input 1
3 2 RPS
Sample Output 1
P
- The favorite hand of the winner of the tournament held among Players $0$ through $1$ is
P
. - The favorite hand of the winner of the tournament held among Players $2$ through $3$ is
R
. - The favorite hand of the winner of the tournament held among Players $0$ through $3$ is
P
.
Thus, the answer is P
.
P ┌─┴─┐ P R ┌┴┐ ┌┴┐ R P S R
Sample Input 2
11 1 RPSSPRSPPRS
Sample Output 2
P
Sample Input 3
1 100 S
Sample Output 3
S