Codeforces Round #485 (Div. 2) E. Petr and Permutations

题目连接：

http://codeforces.com/contest/987/problem/E

Description

Petr likes to come up with problems about randomly generated data. This time problem is about random permutation. He decided to generate a random permutation this way: he takes identity permutation of numbers from $1$ to $n$ and then $3n$ times takes a random pair of different elements and swaps them. Alex envies Petr and tries to imitate him in all kind of things. Alex has also come up with a problem about random permutation. He generates a random permutation just like Petr but swaps elements $7n+1$ times instead of $3n$ times. Because it is more random, OK?!

You somehow get a test from one of these problems and now you want to know from which one.

Sample Input

5

2 4 5 1 3

Sample Output

Petr

题意

给定一个排列，问它是从$1, 2, 3,...,n$变换$3n$次而来，还是$7n+1$

Give a random permutation, it maybe transform $3n$ times or $7n+1$ times from the permutation of numbers from $1$ to n. Judging it is $3n$ or $7n+1$ ?

题解：

考虑n是奇数的情况，$3n$为奇数，$7n+1$为偶数；n是偶数时，$3n$为偶数，$7n+1$为奇数。

考虑最小交换次数，假定为k，$k+2*t$次交换都可以变成目标串，但奇偶性相同。所以只需判断最小交换次数的奇偶性即可。

When n is a odd number, $3n$ is odd，$7n+1$ is even.When n is a even number, $3n$ is even，$7n+1$ is odd.

Consider about the swap times, assume k is the mininum swap times to the final permutation , $k+2*t$ will reach the final result , $k$ and $k+2*t$ have the same parity. So we need to know the parity of the mininum swap times.

如果我们不把stdio的同步关闭，将会读入超时

If we dont close the sync with stdio , time limit exceeded.

代码

#include <bits/stdc++.h>

using namespace std;

int n;

map<int,int> m;

int a[1000010];

int c[1000010];

int ans;

inline int lowbit(int k) {

    return (k&(-k));

}

void update(int t) {

    while (t<n) {

        c[t]++;

        t+=lowbit(t);

    }

}

int sum(int t) {

    int ret=0;

    while (t>0) {

        ret+=c[t];

        t-=lowbit(t);

    }

    return ret;

}

int main() {

    ios_base::sync_with_stdio(false);

    cin.tie(nullptr);

    cout.tie(nullptr);

    cerr.tie(nullptr);

    cin>>n;

    for (int i=1;i<=n;i++) {

        cin>>a[i];

        m[a[i]]=i;

    }

    for (int i=n;i;i--) {

        ans += i-(m[i]-sum(m[i]-1));

        update(m[i]);

    }

    if ((n&1)^(ans&1)==0) cout << "Petr" <<endl;

    else cout << "Um_nik" <<endl;

}