AcWing 1921. Rearranging cows (ring diagram)

【 Title Description 】
Farmer John's $N$ First milk steak in a row , Number $1\sim N$.
They can be sorted by an array $A$ To describe , among $A(i)$ Is in position $i$ The number of your cow .
John wants to rearrange them into a different order .
The new order uses an array $B$ To describe , among $B(i)$ Is in position $i$ The number of your cow .
Suppose the order of cows at the beginning is ：

A = 5 1 4 2 3

And suppose John wants them rearranged to ：

B = 2 5 3 1 4

In order to learn from $A$ Rearrange the order to $B$ The order , The cows did a lot of “ loop ” displacement .
The so-called cyclic shift , It refers to the selection of several cows in the arrangement into a group , The cows in the group were cycled to move their positions , That is, the first cow moves to the position of the second cow , The second cow moves to the position of the third cow , And so on , The last cow moves to the position of the first cow .
The above case, , take $5,1,2$ Cows were divided into a group for cyclic displacement , After moving ,$5$ Cow No. 1 moves to position $2$,$1$ Cow No. 1 moves to position $4$,$2$ Cow No. 1 moves to position $1$; take $4,3$ Cows were divided into another group for cyclic displacement , After moving ,$4$ Cow number one is in position $5$,$3$ Cow number one is in position $3$; Finally complete the rearrangement .
Each cow happens to be involved in a set of cyclic shifts , Unless it is $A,B$ The position in the has not changed .
Please count the cows to complete the rearrangement , How many sets of cyclic shifts are needed , What is the length of the longest set of cyclic shifts .

【 Input format 】
The first line contains integers $N$.
Next $N$ Line inclusion $A(i)$.
Next $N$ Line inclusion $B(i)$.

【 Output format 】
Number of groups of output cyclic shift , And the length of the longest set of cyclic shifts .
If there is no cyclic shift , Then the second number outputs $-1$.

【 Data range 】
$1\le N\le 100$
$1\le A(i),B(i)\le N$

【 sample input 】

5
5
1
4
2
3
2
5
3
1
4

【 sample output 】

2 3

【 analysis 】

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We will first $A$ The position of each element in the new sequence $B$ The position of the middle is connected with a directed edge , For example, for the example , We connect these sides ：$1\to 2,2\to 4,4\to 1,3\to 5,5\to 3$. Then two rings are formed $1,2,4$ and $3,5$. These two rings are the positions of the numbers of the two sets of cyclic shifts we are looking for , That is, there are two sets of numbers that need to be shifted circularly , The length of the longest set of cyclic shifts is $3$.

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【 Code 】

#include <iostream>
#include <cstring>
#include <algorithm>
using namespace std;

const int N = 110;
int a[N], idx[N], st[N];//a Indicates the original order ,idx[i] A cow i Position in the new sequence 
int n, cnt, res;//cnt Indicates the number of rings ,res Indicates the length of the longest ring ( Do not consider self rings )

int main()
{
    
    cin >> n;
    for (int i = 0; i < n; i++) cin >> a[i];
    for (int i = 0; i < n; i++)
    {
    
        int x;
        cin >> x;
        idx[x] = i;
    }
    for (int i = 0; i < n; i++)
    {
    
        int len = 0;
        for (int j = i; !st[j]; j = idx[a[j]])
            st[j] = true, len++;
        if (len > 1) cnt++, res = max(res, len);
    }
    if (!cnt) cout << 0 << ' ' << -1 << endl;
    else cout << cnt << ' ' << res << endl;
    return 0;
}