Large RPS Tournament

AtCoder

IDarc109_c

Time2000ms

Memory256MB

Difficulty—

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 $2^k-1$. ## Constraints * $1 \leq n,k \leq 100$ * $s$ is a string of length $n$ consisting of `R`, `P`, and `S`. ## Input Input is given from Standard Input in the following format: $n$ $k$ $s$ [samples] ## 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` beats `S`; * `P` beats `R`; * `S` beats `P`.

Samples

Input #1

3 2
RPS

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

Input #2

11 1
RPSSPRSPPRS

Output #2

Input #3

1 100
S

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Large RPS Tournament",
    "description": {
      "content": "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 favo",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc109_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "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 favo...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments