Codeforces Gym 100015A Another Rock-Paper-Scissors Problem 找规律

Another Rock-Paper-Scissors Problem

题目连接：

http://codeforces.com/gym/100015/attachments

Description

Sonny uses a very peculiar pattern when it comes to playing rock-paper-scissors. He likes to vary his moves
so that his opponent can’t beat him with his own strategy.

Sonny will play rock (R) on his ﬁrst game, followed by paper (P) and scissors (S) for his second and
third games, respectively. But what if someone else is using the same strategy? To thwart those opponents,
he’ll then play paper to beat rock, scissors to beat paper, and rock to beat scissors, in that order, for his 4th
through 6th games. After that, he’ll play scissors, rock, and paper for games 7–9 to beat anyone copying
his last set of moves. Now we’re back to the original order—rock, paper, scissors—but instead of being
predictable and using the same moves, do you know what would be better? You guessed it! Sonny then
plays the sequence of moves that would beat anyone trying to copy his whole strategy from his ﬁrst move,
and on it goes...

To recap, in symbolic form, Sonny’s rock-paper-scissors moves look like this:
RPSPSRSRPPSRSRPRPSSRPRPSPSRPSRSRPRPSSRPRPSPSRRPSPSRSRP ...

The spaces are present only to help show Sonny’s playing pattern and do not alter what move he’ll play on
a certain game.

Naturally, your job is to beat Sonny at his own game! If you know the number of the game that you’ll
be playing against Sonny, can you ﬁgure out what move you would need to play in order to beat him?

Input

Each line of the input contains a single integer N,1 ! N ! 1012, the number of the game you’ll be playing
against Sonny. An integer N = 1 indicates it would be Sonny’s ﬁrst game, N = 7 indicates it would be the
7th game, and so forth. The input terminates with a line with N = 0. For example:

Warning: N may be large enough to overﬂow a 32-bit integer, so be sure to use a larger data type (i.e.
long in Java or long long in C/C++) in your program.

Output

For each test case, output a single line which contains the letter corresponding to the move you would need
to play to beat Sonny on that game. For example, the correct output for the sample input above would be:

Sample Input

Sample Output

Hint

题意

剪刀石头布

初始串，RPS

每次操作如下：设现在的串为S

1、将之前的串全部击败，得到S'

2、将S'打败，然后得到S''

然后给你第i位，然后输出打败第i位的策略

题解：

找找规律之后会发现，这个串类似于3进制一样的

比如说23，他是23->14->5->2这样过来的

然后我们只用算他是从哪儿过来的，迭代了几次就好了

代码

#include<bits/stdc++.h>
using namespace std;

const long long limit = 1000000000050LL;
vector<long long> three;
string solve(long long n,long long step)
{
    if(n==1)
    {
        if(step%3==0)
            return "P";
        else if(step%3==1)
            return "S";
        else
            return "R";
    }
    if(n==2)
    {
        if(step%3==0)
            return "S";
        else if(step%3==1)
            return "R";
        else
            return "P";
    }
    if(n==3)
    {
        if(step%3==0)
            return "R";
        else if(step%3==1)
            return "P";
        else return "S";
    }
}
int main()
{
    long long k = 3;
    for(int i=0;;i++)
    {
        three.push_back(k);
        k*=3;
        if(k>limit)
            break;
    }
    long long n;
    while(cin>>n)
    {
        if(n==0)break;
        int step = 0;
        while(n>3)
        {
            n-=*--lower_bound(three.begin(),three.end(),n);
            step++;
        }
        cout<<solve(n,step)<<endl;
    }
}