牛客多校(2020第五场) E Bogo Sort

题目链接： https://ac.nowcoder.com/acm/contest/5670/E

题意：给出一个置换P，问1~n这n个数有多少种排列，能经过若干次p的置换变为有序序列？答案对10^N取模

题解：找出数组中，每一个环得长度，求所有环的长度的最小公倍数

难点：大数模板，取环长度

计算环长度模板

for(int i=1; i<=n; i++)
{
    if(!vis[i])
    {
        num.clear();
        int tmp=i;
        while(!vis[tmp])
        {
            vis[tmp]=1;
            num.push_back(tmp);
            tmp=a[tmp];
        }
        f();
    }
}

大数模板

#define MAXN 9999
#define MAXSIZE 500   //最大长度
#define DLEN 4
class BigNum {
private:
    int a[21000];    //控制大数的位数
    int len;       //长度
public:
    BigNum() { len = 1; memset(a, 0, sizeof(a)); }   //构造函数
    void XD();
    BigNum(const int);
    BigNum(const long long int);
    BigNum(const char*);
    BigNum(const string&);
    BigNum(const BigNum&);  //拷贝构造函数
    BigNum& operator = (const BigNum&);   //重载赋值运算符
    BigNum& operator = (const int&);
    BigNum& operator = (const long long int&);

    friend istream& operator >> (istream&, BigNum&);   //重载输入运算符
    friend ostream& operator << (ostream&, BigNum&);   //重载输出运算符

    template<typename T> BigNum operator << (const T&) const;
    template<typename T> BigNum operator >> (const T&) const;

    BigNum operator + (const BigNum&) const;   //重载加法运算符，大数加大数
    BigNum operator - (const BigNum&) const;   //重载减法运算符，大数减大数
    BigNum operator * (const BigNum&) const;   //重载乘法运算符，大数乘大数
    bool   operator > (const BigNum& b)const;   //重载大于
    bool   operator < (const BigNum& b) const;   //重载小于
    bool   operator == (const BigNum& b) const;  //重载等于符号
    template<typename T> BigNum operator / (const T&) const;    //重载除法运算符，大数除整数
    template<typename T> BigNum operator ^ (const T&) const;    //大数的n次方
    template<typename T> T    operator % (const T&) const;    //大数对int取模

    template<typename T> BigNum operator + (const T& b) const { BigNum t = b; t = *this + t; return t; }
    template<typename T> BigNum operator - (const T& b) const { BigNum t = b; t = *this - t; return t; }
    template<typename T> BigNum operator * (const T& b) const { BigNum t = b; t = (*this) * t; return t; }
    template<typename T> bool   operator < (const T& b) const { BigNum t = b; return ((*this) < t); }
    template<typename T> bool   operator > (const T& b) const { BigNum t = b; return ((*this) > t); }
    template<typename T> bool   operator == (const T& b) const { BigNum t = b; return ((*this) == t); }

    bool   operator <= (const BigNum& b) const { return (*this) < b || (*this) == b; }
    bool   operator >= (const BigNum& b) const { return (*this) > b || (*this) == b; }
    bool   operator != (const BigNum& b) const { return !((*this) == b); }

    template<typename T> bool   operator >= (const T& b) const { BigNum t = b; return !((*this) < t); }
    template<typename T> bool   operator <= (const T& b) const { BigNum t = b; return !((*this) > t); }
    template<typename T> bool   operator != (const T& b) const { BigNum t = b; return !((*this) == t); }

    BigNum& operator += (const BigNum& b) { *this = *this + b; return *this; }
    BigNum& operator -= (const BigNum& b) { *this = *this - b; return *this; }
    BigNum& operator *= (const BigNum& b) { *this = *this * b; return *this; }
    template<typename T> BigNum& operator /= (const T& b) { *this = *this / b; return *this; }
    template<typename T> BigNum& operator %= (const T& b) { *this = *this % b; return *this; }
    template<typename T> BigNum& operator += (const T& b) { *this = *this + b; return *this; }
    template<typename T> BigNum& operator -= (const T& b) { *this = *this - b; return *this; }
    template<typename T> BigNum& operator *= (const T& b) { *this = *this * b; return *this; }
    template<typename T> BigNum& operator ^= (const T& b) { *this = *this ^ b; return *this; }

    BigNum operator ++ (int) { BigNum t = *this; *this += 1; return t; }
    BigNum operator -- (int) { BigNum t = *this; *this -= 1; return t; }
    BigNum& operator -- () { *this -= 1; return *this; }
    BigNum& operator ++ () { *this += 1; return *this; }

    template<typename T> BigNum& operator <<= (const T& b) { *this = *this << b; return *this; }
    template<typename T> BigNum& operator >>= (const T& b) { *this = *this >> b; return *this; }

    template<typename T> BigNum friend operator + (const T& a, const BigNum& b) { BigNum t = a; t = t + a; return t; }
    template<typename T> BigNum friend operator - (const T& a, const BigNum& b) { BigNum t = a; t = t - b; return t; }
    template<typename T> BigNum friend operator * (const T& a, const BigNum& b) { BigNum t = a; t = t * b; return t; }
    template<typename T> friend bool operator < (const T& a, const BigNum& b) { return b > a; }
    template<typename T> friend bool operator > (const T& a, const BigNum& b) { return b < a; }
    template<typename T> friend bool operator <= (const T& a, const BigNum& b) { return b >= a; }
    template<typename T> friend bool operator >= (const T& a, const BigNum& b) { return b <= a; }
    template<typename T> friend bool operator == (const T& a, const BigNum& b) { return b == a; }
    template<typename T> friend bool operator != (const T& a, const BigNum& b) { return b != a; }

    void print();       //输出大数
    int Size();            //返回大数长度
    int the_first();    //返回第一个数字
    int the_last();        //返回最后一位数字
    int to_int();       //转化为整数
    long long int to_long();
    string to_String();        //转化为string类型
    //char* to_char();
};

BigNum::BigNum(const int b)     //将一个int类型的变量转化为大数
{
    int c, d = b;
    len = 0;
    memset(a, 0, sizeof(a));
    while (d > MAXN) {
        c = d - (d / (MAXN + 1)) * (MAXN + 1);
        d = d / (MAXN + 1);
        a[len++] = c;
    }
    a[len++] = d;
}
BigNum::BigNum(const long long int b)
{
    long long int c, d = b;
    len = 0;
    memset(a, 0, sizeof(a));
    while (d > MAXN) {
        c = d - (d / (MAXN + 1)) * (MAXN + 1);
        d = d / (MAXN + 1);
        a[len++] = c;
    }
    a[len++] = d;
}
BigNum::BigNum(const string& s)
{
    int t, k, index, l, i;
    memset(a, 0, sizeof(a));
    l = s.size();
    len = l / DLEN;
    if (l % DLEN)
        len++;
    index = 0;
    for (i = l - 1; i >= 0; i -= DLEN) {
        t = 0;
        k = i - DLEN + 1;
        if (k < 0) k = 0;
        for (int j = k; j <= i; j++)
            t = t * 10 + s[j] - '0';
        a[index++] = t;
    }
}
BigNum::BigNum(const char* s)     //将一个字符串类型的变量转化为大数
{
    int t, k, index, l, i;
    memset(a, 0, sizeof(a));
    l = strlen(s);
    len = l / DLEN;
    if (l % DLEN)
        len++;
    index = 0;
    for (i = l - 1; i >= 0; i -= DLEN) {
        t = 0;
        k = i - DLEN + 1;
        if (k < 0) k = 0;
        for (int j = k; j <= i; j++)
            t = t * 10 + s[j] - '0';
        a[index++] = t;
    }
}
BigNum::BigNum(const BigNum& b) : len(b.len)  //拷贝构造函数
{
    memset(a, 0, sizeof(a));
    for (int i = 0; i < len; i++)
        a[i] = b.a[i];
}
BigNum& BigNum::operator = (const BigNum& n)   //重载赋值运算符，大数之间进行赋值运算
{
    len = n.len;
    memset(a, 0, sizeof(a));
    for (int i = 0; i < len; i++)
        a[i] = n.a[i];
    return *this;
}
BigNum& BigNum::operator = (const int& num)
{
    BigNum t(num);
    *this = t;
    return *this;
}
BigNum& BigNum::operator = (const long long int& num)
{
    BigNum t(num);
    *this = t;
    return *this;
}
void XD()
{
    cout << "A hidden egg! Good luck for u!" << endl;
}

template<typename T> BigNum BigNum::operator << (const T& b) const
{
    T temp = 1;
    for (int i = 0; i < b; i++)
        temp *= 2;
    BigNum t = (*this) * temp;
    return t;
}
template<typename T> BigNum BigNum::operator >> (const T& b) const
{
    T temp = 1;
    for (int i = 0; i < b; i++)
        temp *= 2;
    BigNum t = (*this) / temp;
    return t;
}

BigNum BigNum::operator + (const BigNum& b) const   //两个大数之间的相加运算
{
    BigNum t(*this);
    int i, big;
    big = b.len > len ? b.len : len;
    for (i = 0; i < big; i++) {
        t.a[i] += b.a[i];
        if (t.a[i] > MAXN) {
            t.a[i + 1]++;
            t.a[i] -= MAXN + 1;
        }
    }
    if (t.a[big] != 0)
        t.len = big + 1;
    else
        t.len = big;
    return t;
}
BigNum BigNum::operator - (const BigNum& b) const   //两个大数之间的相减运算
{
    int i, j, big;
    bool flag;
    BigNum t1, t2;
    if (*this > b) {
        t1 = *this;
        t2 = b;
        flag = 0;
    }
    else {
        t1 = b;
        t2 = *this;
        flag = 1;
    }
    big = t1.len;
    for (i = 0; i < big; i++) {
        if (t1.a[i] < t2.a[i]) {
            j = i + 1;
            while (t1.a[j] == 0)
                j++;
            t1.a[j--]--;
            while (j > i)
                t1.a[j--] += MAXN;
            t1.a[i] += MAXN + 1 - t2.a[i];
        }
        else
            t1.a[i] -= t2.a[i];
    }
    t1.len = big;
    while (t1.a[t1.len - 1] == 0 && t1.len > 1) {
        t1.len--;
        big--;
    }
    if (flag)
        t1.a[big - 1] = 0 - t1.a[big - 1];
    return t1;
}

BigNum BigNum::operator * (const BigNum& b) const   //两个大数之间的相乘运算
{
    BigNum ret;
    int i, j, up;
    int temp, temp1;
    for (i = 0; i < len; i++) {
        up = 0;
        for (j = 0; j < b.len; j++) {
            temp = a[i] * b.a[j] + ret.a[i + j] + up;
            if (temp > MAXN) {
                temp1 = temp - temp / (MAXN + 1) * (MAXN + 1);
                up = temp / (MAXN + 1);
                ret.a[i + j] = temp1;
            }
            else {
                up = 0;
                ret.a[i + j] = temp;
            }
        }
        if (up != 0) ret.a[i + j] = up;
    }
    ret.len = i + j;
    while (ret.a[ret.len - 1] == 0 && ret.len > 1)
        ret.len--;
    return ret;
}
template<typename T> BigNum BigNum::operator / (const T& b) const
{
    BigNum ret;
    T i, down = 0;
    for (i = len - 1; i >= 0; i--) {
        ret.a[i] = (a[i] + down * (MAXN + 1)) / b;
        down = a[i] + down * (MAXN + 1) - ret.a[i] * b;
    }
    ret.len = len;
    while (ret.a[ret.len - 1] == 0 && ret.len > 1)
        ret.len--;
    return ret;
}
template<typename T> T BigNum::operator % (const T& b) const
{
    T i, d = 0;
    for (i = len - 1; i >= 0; i--) {
        d = ((d * (MAXN + 1)) % b + a[i]) % b;
    }
    return d;
}


template<typename T> BigNum BigNum::operator^(const T& n) const    //大数的n次方运算
{
    BigNum t, ret(1);
    int i;
    if (n < 0) return 0;
    if (n == 0)
        return 1;
    if (n == 1)
        return *this;
    int m = n;
    while (m > 1) {
        t = *this;
        for (i = 1; (i << 1) <= m; i <<= 1)
            t = t * t;
        m -= i;
        ret = ret * t;
        if (m == 1) ret = ret * (*this);
    }
    return ret;
}

bool BigNum::operator > (const BigNum& b) const   //大数和另一个大数的大小比较
{
    int tot;
    if (len > b.len)
        return true;
    else if (len == b.len) {
        tot = len - 1;
        while (a[tot] == b.a[tot] && tot >= 0)
            tot--;
        if (tot >= 0 && a[tot] > b.a[tot])
            return true;
        else
            return false;
    }
    else
        return false;
}

bool BigNum::operator < (const BigNum& b) const
{
    int tot;
    if (len > b.len)
        return false;
    else if (len == b.len) {
        tot = len - 1;
        while (a[tot] == b.a[tot] && tot >= 0)
            tot--;
        if (tot >= 0 && a[tot] > b.a[tot])
            return false;
        else
            return false;
    }
    else
        return true;
}

bool BigNum::operator == (const BigNum& b) const
{
    int tot = len - 1;
    if (len != b.len)
        return false;
    while (a[tot] == b.a[tot] && tot >= 0)
        tot--;
    if (tot < 0)
        return true;
    return false;
}

void BigNum::print()    //输出大数
{ 
    int i;   
    cout << a[len - 1]; 
    for(i = len - 2 ; i >= 0 ; i--)
    { 
        cout.width(DLEN); 
        cout.fill('0'); 
        cout << a[i]; 
    } 
    cout << endl;
}

int BigNum::Size()
{
    int t = a[len - 1], cnt = 0;
    while (t) { t /= 10; cnt++; }
    cnt += (len - 1) * 4;
    return cnt;
}
int BigNum::the_first()
{
    int t = a[len - 1];
    while (t > 10) { t /= 10; }
    return t;
}
int BigNum::the_last()
{
    int t = a[0];
    return t % 10;
}
int BigNum::to_int()
{
    int i, num;
    num = a[len - 1];
    for (i = len - 2; i >= 0; i--)
        num = num * (MAXN + 1) + a[i];
    return num;
}
long long int BigNum::to_long()
{
    int i;
    long long int num;
    num = a[len - 1];
    for (i = len - 2; i >= 0; i--)
        num = num * (MAXN + 1) + a[i];
    return num;
}
string BigNum::to_String()
{
    int i;
    string s = "", tp = "";
    s += to_string(a[len - 1]);
    for (i = len - 2; i >= 0; i--) {
        tp = to_string(a[i]);
        int tot = tp.size();
        tp.insert(tp.begin(), 4 - tot, '0');
        s = s + tp;
    }
    return s;
}

#include<iostream> 
#include<string> 
#include<iomanip> 
#include<algorithm> 
using namespace std; 

#define MAXN 9999
#define MAXSIZE 10
#define DLEN 4

class BigNum
{ 
private: 
    int a[500];    //可以控制大数的位数 
    int len;       //大数长度
public: 
    BigNum(){ len = 1;memset(a,0,sizeof(a)); }   //构造函数
    BigNum(const int);       //将一个int类型的变量转化为大数
    BigNum(const char*);     //将一个字符串类型的变量转化为大数
    BigNum(const BigNum &);  //拷贝构造函数
    BigNum &operator=(const BigNum &);   //重载赋值运算符，大数之间进行赋值运算

    friend istream& operator>>(istream&,  BigNum&);   //重载输入运算符
    friend ostream& operator<<(ostream&,  BigNum&);   //重载输出运算符

    BigNum operator+(const BigNum &) const;   //重载加法运算符，两个大数之间的相加运算 
    BigNum operator-(const BigNum &) const;   //重载减法运算符，两个大数之间的相减运算 
    BigNum operator*(const BigNum &) const;   //重载乘法运算符，两个大数之间的相乘运算 
    BigNum operator/(const int   &) const;    //重载除法运算符，大数对一个整数进行相除运算

    BigNum operator^(const int  &) const;    //大数的n次方运算
    int    operator%(const int  &) const;    //大数对一个int类型的变量进行取模运算    
    bool   operator>(const BigNum & T)const;   //大数和另一个大数的大小比较
    bool   operator>(const int & t)const;      //大数和一个int类型的变量的大小比较

    void print();       //输出大数
}; 
BigNum::BigNum(const int b)     //将一个int类型的变量转化为大数
{ 
    int c,d = b;
    len = 0;
    memset(a,0,sizeof(a));
    while(d > MAXN)
    {
        c = d - (d / (MAXN + 1)) * (MAXN + 1); 
        d = d / (MAXN + 1);
        a[len++] = c;
    }
    a[len++] = d;
}
BigNum::BigNum(const char*s)     //将一个字符串类型的变量转化为大数
{
    int t,k,index,l,i;
    memset(a,0,sizeof(a));
    l=strlen(s);   
    len=l/DLEN;
    if(l%DLEN)
        len++;
    index=0;
    for(i=l-1;i>=0;i-=DLEN)
    {
        t=0;
        k=i-DLEN+1;
        if(k<0)
            k=0;
        for(int j=k;j<=i;j++)
            t=t*10+s[j]-'0';
        a[index++]=t;
    }
}
BigNum::BigNum(const BigNum & T) : len(T.len)  //拷贝构造函数
{ 
    int i; 
    memset(a,0,sizeof(a)); 
    for(i = 0 ; i < len ; i++)
        a[i] = T.a[i]; 
} 
BigNum & BigNum::operator=(const BigNum & n)   //重载赋值运算符，大数之间进行赋值运算
{
    int i;
    len = n.len;
    memset(a,0,sizeof(a)); 
    for(i = 0 ; i < len ; i++) 
        a[i] = n.a[i]; 
    return *this; 
}
istream& operator>>(istream & in,  BigNum & b)   //重载输入运算符
{
    char ch[MAXSIZE*4];
    int i = -1;
    in>>ch;
    int l=strlen(ch);
    int count=0,sum=0;
    for(i=l-1;i>=0;)
    {
        sum = 0;
        int t=1;
        for(int j=0;j<4&&i>=0;j++,i--,t*=10)
        {
            sum+=(ch[i]-'0')*t;
        }
        b.a[count]=sum;
        count++;
    }
    b.len =count++;
    return in;

}
ostream& operator<<(ostream& out,  BigNum& b)   //重载输出运算符
{
    int i;  
    cout << b.a[b.len - 1]; 
    for(i = b.len - 2 ; i >= 0 ; i--)
    { 
        cout.width(DLEN); 
        cout.fill('0'); 
        cout << b.a[i]; 
    } 
    return out;
}

BigNum BigNum::operator+(const BigNum & T) const   //两个大数之间的相加运算
{
    BigNum t(*this);
    int i,big;      //位数   
    big = T.len > len ? T.len : len; 
    for(i = 0 ; i < big ; i++) 
    { 
        t.a[i] +=T.a[i]; 
        if(t.a[i] > MAXN) 
        { 
            t.a[i + 1]++; 
            t.a[i] -=MAXN+1; 
        } 
    } 
    if(t.a[big] != 0)
        t.len = big + 1; 
    else
        t.len = big;   
    return t;
}
BigNum BigNum::operator-(const BigNum & T) const   //两个大数之间的相减运算 
{  
    int i,j,big;
    bool flag;
    BigNum t1,t2;
    if(*this>T)
    {
        t1=*this;
        t2=T;
        flag=0;
    }
    else
    {
        t1=T;
        t2=*this;
        flag=1;
    }
    big=t1.len;
    for(i = 0 ; i < big ; i++)
    {
        if(t1.a[i] < t2.a[i])
        { 
            j = i + 1; 
            while(t1.a[j] == 0)
                j++; 
            t1.a[j--]--; 
            while(j > i)
                t1.a[j--] += MAXN;
            t1.a[i] += MAXN + 1 - t2.a[i]; 
        } 
        else
            t1.a[i] -= t2.a[i];
    }
    t1.len = big;
    while(t1.a[len - 1] == 0 && t1.len > 1)
    {
        t1.len--; 
        big--;
    }
    if(flag)
        t1.a[big-1]=0-t1.a[big-1];
    return t1; 
} 

BigNum BigNum::operator*(const BigNum & T) const   //两个大数之间的相乘运算 
{ 
    BigNum ret; 
    int i,j,up; 
    int temp,temp1;   
    for(i = 0 ; i < len ; i++)
    { 
        up = 0; 
        for(j = 0 ; j < T.len ; j++)
        { 
            temp = a[i] * T.a[j] + ret.a[i + j] + up; 
            if(temp > MAXN)
            { 
                temp1 = temp - temp / (MAXN + 1) * (MAXN + 1); 
                up = temp / (MAXN + 1); 
                ret.a[i + j] = temp1; 
            } 
            else
            { 
                up = 0; 
                ret.a[i + j] = temp; 
            } 
        } 
        if(up != 0) 
            ret.a[i + j] = up; 
    } 
    ret.len = i + j; 
    while(ret.a[ret.len - 1] == 0 && ret.len > 1)
        ret.len--; 
    return ret; 
} 
BigNum BigNum::operator/(const int & b) const   //大数对一个整数进行相除运算
{ 
    BigNum ret; 
    int i,down = 0;   
    for(i = len - 1 ; i >= 0 ; i--)
    { 
        ret.a[i] = (a[i] + down * (MAXN + 1)) / b; 
        down = a[i] + down * (MAXN + 1) - ret.a[i] * b; 
    } 
    ret.len = len; 
    while(ret.a[ret.len - 1] == 0 && ret.len > 1)
        ret.len--; 
    return ret; 
}
int BigNum::operator %(const int & b) const    //大数对一个int类型的变量进行取模运算    
{
    int i,d=0;
    for (i = len-1; i>=0; i--)
    {
        d = ((d * (MAXN+1))% b + a[i])% b;  
    }
    return d;
}
BigNum BigNum::operator^(const int & n) const    //大数的n次方运算
{
    BigNum t,ret(1);
    int i;
    if(n<0)
        exit(-1);
    if(n==0)
        return 1;
    if(n==1)
        return *this;
    int m=n;
    while(m>1)
    {
        t=*this;
        for( i=1;i<<1<=m;i<<=1)
        {
            t=t*t;
        }
        m-=i;
        ret=ret*t;
        if(m==1)
            ret=ret*(*this);
    }
    return ret;
}
bool BigNum::operator>(const BigNum & T) const   //大数和另一个大数的大小比较
{ 
    int ln; 
    if(len > T.len)
        return true; 
    else if(len == T.len)
    { 
        ln = len - 1; 
        while(a[ln] == T.a[ln] && ln >= 0)
            ln--; 
        if(ln >= 0 && a[ln] > T.a[ln])
            return true; 
        else
            return false; 
    } 
    else
        return false; 
}
bool BigNum::operator >(const int & t) const    //大数和一个int类型的变量的大小比较
{
    BigNum b(t);
    return *this>b;
}

void BigNum::print()    //输出大数
{ 
    int i;   
    cout << a[len - 1]; 
    for(i = len - 2 ; i >= 0 ; i--)
    { 
        cout.width(DLEN); 
        cout.fill('0'); 
        cout << a[i]; 
    } 
    cout << endl;
}
int main(void)
{
    int i,n;
    BigNum x[101];      //定义大数的对象数组
    x[0]=1;
    for(i=1;i<101;i++)
        x[i]=x[i-1]*(4*i-2)/(i+1);
    while(scanf("%d",&n)==1 && n!=-1)
    {
        x[n].print();
    }
}

ac代码

#include<iostream>
#include<cstring>
#include<string>
#include<cstdio>
#include<algorithm>

using namespace std;
#define maxn 100100
#define MAXN 9999
#define MAXSIZE 500   //最大长度
#define DLEN 4

class BigNum {
private:
    int a[21000];    //控制大数的位数
    int len;       //长度
public:
    BigNum() { len = 1; memset(a, 0, sizeof(a)); }   //构造函数
    void XD();
    BigNum(const int);
    BigNum(const long long int);
    BigNum(const char*);
    BigNum(const string&);
    BigNum(const BigNum&);  //拷贝构造函数
    BigNum& operator = (const BigNum&);   //重载赋值运算符
    BigNum& operator = (const int&);
    BigNum& operator = (const long long int&);
 
    friend istream& operator >> (istream&, BigNum&);   //重载输入运算符
    friend ostream& operator << (ostream&, BigNum&);   //重载输出运算符
 
    template<typename T> BigNum operator << (const T&) const;
    template<typename T> BigNum operator >> (const T&) const;
 
    BigNum operator + (const BigNum&) const;   //重载加法运算符，大数加大数
    BigNum operator - (const BigNum&) const;   //重载减法运算符，大数减大数
    BigNum operator * (const BigNum&) const;   //重载乘法运算符，大数乘大数
    bool   operator > (const BigNum& b)const;   //重载大于
    bool   operator < (const BigNum& b) const;   //重载小于
    bool   operator == (const BigNum& b) const;  //重载等于符号
    template<typename T> BigNum operator / (const T&) const;    //重载除法运算符，大数除整数
    template<typename T> BigNum operator ^ (const T&) const;    //大数的n次方
    template<typename T> T    operator % (const T&) const;    //大数对int取模
 
    template<typename T> BigNum operator + (const T& b) const { BigNum t = b; t = *this + t; return t; }
    template<typename T> BigNum operator - (const T& b) const { BigNum t = b; t = *this - t; return t; }
    template<typename T> BigNum operator * (const T& b) const { BigNum t = b; t = (*this) * t; return t; }
    template<typename T> bool   operator < (const T& b) const { BigNum t = b; return ((*this) < t); }
    template<typename T> bool   operator > (const T& b) const { BigNum t = b; return ((*this) > t); }
    template<typename T> bool   operator == (const T& b) const { BigNum t = b; return ((*this) == t); }
 
    bool   operator <= (const BigNum& b) const { return (*this) < b || (*this) == b; }
    bool   operator >= (const BigNum& b) const { return (*this) > b || (*this) == b; }
    bool   operator != (const BigNum& b) const { return !((*this) == b); }
 
    template<typename T> bool   operator >= (const T& b) const { BigNum t = b; return !((*this) < t); }
    template<typename T> bool   operator <= (const T& b) const { BigNum t = b; return !((*this) > t); }
    template<typename T> bool   operator != (const T& b) const { BigNum t = b; return !((*this) == t); }
 
    BigNum& operator += (const BigNum& b) { *this = *this + b; return *this; }
    BigNum& operator -= (const BigNum& b) { *this = *this - b; return *this; }
    BigNum& operator *= (const BigNum& b) { *this = *this * b; return *this; }
    template<typename T> BigNum& operator /= (const T& b) { *this = *this / b; return *this; }
    template<typename T> BigNum& operator %= (const T& b) { *this = *this % b; return *this; }
    template<typename T> BigNum& operator += (const T& b) { *this = *this + b; return *this; }
    template<typename T> BigNum& operator -= (const T& b) { *this = *this - b; return *this; }
    template<typename T> BigNum& operator *= (const T& b) { *this = *this * b; return *this; }
    template<typename T> BigNum& operator ^= (const T& b) { *this = *this ^ b; return *this; }
 
    BigNum operator ++ (int) { BigNum t = *this; *this += 1; return t; }
    BigNum operator -- (int) { BigNum t = *this; *this -= 1; return t; }
    BigNum& operator -- () { *this -= 1; return *this; }
    BigNum& operator ++ () { *this += 1; return *this; }
 
    template<typename T> BigNum& operator <<= (const T& b) { *this = *this << b; return *this; }
    template<typename T> BigNum& operator >>= (const T& b) { *this = *this >> b; return *this; }
 
    template<typename T> BigNum friend operator + (const T& a, const BigNum& b) { BigNum t = a; t = t + a; return t; }
    template<typename T> BigNum friend operator - (const T& a, const BigNum& b) { BigNum t = a; t = t - b; return t; }
    template<typename T> BigNum friend operator * (const T& a, const BigNum& b) { BigNum t = a; t = t * b; return t; }
    template<typename T> friend bool operator < (const T& a, const BigNum& b) { return b > a; }
    template<typename T> friend bool operator > (const T& a, const BigNum& b) { return b < a; }
    template<typename T> friend bool operator <= (const T& a, const BigNum& b) { return b >= a; }
    template<typename T> friend bool operator >= (const T& a, const BigNum& b) { return b <= a; }
    template<typename T> friend bool operator == (const T& a, const BigNum& b) { return b == a; }
    template<typename T> friend bool operator != (const T& a, const BigNum& b) { return b != a; }
 
    void print();       //输出大数
    int Size();            //返回大数长度
    int the_first();    //返回第一个数字
    int the_last();        //返回最后一位数字
    int to_int();       //转化为整数
    long long int to_long();
    string to_String();        //转化为string类型
    //char* to_char();
};
 
BigNum::BigNum(const int b)     //将一个int类型的变量转化为大数
{
    int c, d = b;
    len = 0;
    memset(a, 0, sizeof(a));
    while (d > MAXN) {
        c = d - (d / (MAXN + 1)) * (MAXN + 1);
        d = d / (MAXN + 1);
        a[len++] = c;
    }
    a[len++] = d;
}
BigNum::BigNum(const long long int b)
{
    long long int c, d = b;
    len = 0;
    memset(a, 0, sizeof(a));
    while (d > MAXN) {
        c = d - (d / (MAXN + 1)) * (MAXN + 1);
        d = d / (MAXN + 1);
        a[len++] = c;
    }
    a[len++] = d;
}
BigNum::BigNum(const string& s)
{
    int t, k, index, l, i;
    memset(a, 0, sizeof(a));
    l = s.size();
    len = l / DLEN;
    if (l % DLEN)
        len++;
    index = 0;
    for (i = l - 1; i >= 0; i -= DLEN) {
        t = 0;
        k = i - DLEN + 1;
        if (k < 0) k = 0;
        for (int j = k; j <= i; j++)
            t = t * 10 + s[j] - '0';
        a[index++] = t;
    }
}
BigNum::BigNum(const char* s)     //将一个字符串类型的变量转化为大数
{
    int t, k, index, l, i;
    memset(a, 0, sizeof(a));
    l = strlen(s);
    len = l / DLEN;
    if (l % DLEN)
        len++;
    index = 0;
    for (i = l - 1; i >= 0; i -= DLEN) {
        t = 0;
        k = i - DLEN + 1;
        if (k < 0) k = 0;
        for (int j = k; j <= i; j++)
            t = t * 10 + s[j] - '0';
        a[index++] = t;
    }
}
BigNum::BigNum(const BigNum& b) : len(b.len)  //拷贝构造函数
{
    memset(a, 0, sizeof(a));
    for (int i = 0; i < len; i++)
        a[i] = b.a[i];
}
BigNum& BigNum::operator = (const BigNum& n)   //重载赋值运算符，大数之间进行赋值运算
{
    len = n.len;
    memset(a, 0, sizeof(a));
    for (int i = 0; i < len; i++)
        a[i] = n.a[i];
    return *this;
}
BigNum& BigNum::operator = (const int& num)
{
    BigNum t(num);
    *this = t;
    return *this;
}
BigNum& BigNum::operator = (const long long int& num)
{
    BigNum t(num);
    *this = t;
    return *this;
}
void XD()
{
    cout << "A hidden egg! Good luck for u!" << endl;
}
 
template<typename T> BigNum BigNum::operator << (const T& b) const
{
    T temp = 1;
    for (int i = 0; i < b; i++)
        temp *= 2;
    BigNum t = (*this) * temp;
    return t;
}
template<typename T> BigNum BigNum::operator >> (const T& b) const
{
    T temp = 1;
    for (int i = 0; i < b; i++)
        temp *= 2;
    BigNum t = (*this) / temp;
    return t;
}
 
BigNum BigNum::operator + (const BigNum& b) const   //两个大数之间的相加运算
{
    BigNum t(*this);
    int i, big;
    big = b.len > len ? b.len : len;
    for (i = 0; i < big; i++) {
        t.a[i] += b.a[i];
        if (t.a[i] > MAXN) {
            t.a[i + 1]++;
            t.a[i] -= MAXN + 1;
        }
    }
    if (t.a[big] != 0)
        t.len = big + 1;
    else
        t.len = big;
    return t;
}
BigNum BigNum::operator - (const BigNum& b) const   //两个大数之间的相减运算
{
    int i, j, big;
    bool flag;
    BigNum t1, t2;
    if (*this > b) {
        t1 = *this;
        t2 = b;
        flag = 0;
    }
    else {
        t1 = b;
        t2 = *this;
        flag = 1;
    }
    big = t1.len;
    for (i = 0; i < big; i++) {
        if (t1.a[i] < t2.a[i]) {
            j = i + 1;
            while (t1.a[j] == 0)
                j++;
            t1.a[j--]--;
            while (j > i)
                t1.a[j--] += MAXN;
            t1.a[i] += MAXN + 1 - t2.a[i];
        }
        else
            t1.a[i] -= t2.a[i];
    }
    t1.len = big;
    while (t1.a[t1.len - 1] == 0 && t1.len > 1) {
        t1.len--;
        big--;
    }
    if (flag)
        t1.a[big - 1] = 0 - t1.a[big - 1];
    return t1;
}
 
BigNum BigNum::operator * (const BigNum& b) const   //两个大数之间的相乘运算
{
    BigNum ret;
    int i, j, up;
    int temp, temp1;
    for (i = 0; i < len; i++) {
        up = 0;
        for (j = 0; j < b.len; j++) {
            temp = a[i] * b.a[j] + ret.a[i + j] + up;
            if (temp > MAXN) {
                temp1 = temp - temp / (MAXN + 1) * (MAXN + 1);
                up = temp / (MAXN + 1);
                ret.a[i + j] = temp1;
            }
            else {
                up = 0;
                ret.a[i + j] = temp;
            }
        }
        if (up != 0) ret.a[i + j] = up;
    }
    ret.len = i + j;
    while (ret.a[ret.len - 1] == 0 && ret.len > 1)
        ret.len--;
    return ret;
}
template<typename T> BigNum BigNum::operator / (const T& b) const
{
    BigNum ret;
    T i, down = 0;
    for (i = len - 1; i >= 0; i--) {
        ret.a[i] = (a[i] + down * (MAXN + 1)) / b;
        down = a[i] + down * (MAXN + 1) - ret.a[i] * b;
    }
    ret.len = len;
    while (ret.a[ret.len - 1] == 0 && ret.len > 1)
        ret.len--;
    return ret;
}
template<typename T> T BigNum::operator % (const T& b) const
{
    T i, d = 0;
    for (i = len - 1; i >= 0; i--) {
        d = ((d * (MAXN + 1)) % b + a[i]) % b;
    }
    return d;
}
 
 
template<typename T> BigNum BigNum::operator^(const T& n) const    //大数的n次方运算
{
    BigNum t, ret(1);
    int i;
    if (n < 0) return 0;
    if (n == 0)
        return 1;
    if (n == 1)
        return *this;
    int m = n;
    while (m > 1) {
        t = *this;
        for (i = 1; (i << 1) <= m; i <<= 1)
            t = t * t;
        m -= i;
        ret = ret * t;
        if (m == 1) ret = ret * (*this);
    }
    return ret;
}
 
bool BigNum::operator > (const BigNum& b) const   //大数和另一个大数的大小比较
{
    int tot;
    if (len > b.len)
        return true;
    else if (len == b.len) {
        tot = len - 1;
        while (a[tot] == b.a[tot] && tot >= 0)
            tot--;
        if (tot >= 0 && a[tot] > b.a[tot])
            return true;
        else
            return false;
    }
    else
        return false;
}
 
bool BigNum::operator < (const BigNum& b) const
{
    int tot;
    if (len > b.len)
        return false;
    else if (len == b.len) {
        tot = len - 1;
        while (a[tot] == b.a[tot] && tot >= 0)
            tot--;
        if (tot >= 0 && a[tot] > b.a[tot])
            return false;
        else
            return false;
    }
    else
        return true;
}
 
bool BigNum::operator == (const BigNum& b) const
{
    int tot = len - 1;
    if (len != b.len)
        return false;
    while (a[tot] == b.a[tot] && tot >= 0)
        tot--;
    if (tot < 0)
        return true;
    return false;
}

int n; //定义n

void BigNum::print()    //输出大数
{
    int i;
    if (len >= n) {
        cout << a[len - 1];
        for (i = len - 2; i >= len - n; i--) {
            cout.width(DLEN);
            cout.fill('0');
            cout << a[i];
        }
        cout << endl;
    }
    else {
        cout << a[len - 1];
        for (i = len - 2; i >= 0; i--) {
            cout.width(DLEN);
            cout.fill('0');
            cout << a[i];
        }
        cout << endl;
    }
}
int BigNum::Size()
{
    int t = a[len - 1], cnt = 0;
    while (t) { t /= 10; cnt++; }
    cnt += (len - 1) * 4;
    return cnt;
}
int BigNum::the_first()
{
    int t = a[len - 1];
    while (t > 10) { t /= 10; }
    return t;
}
int BigNum::the_last()
{
    int t = a[0];
    return t % 10;
}
int BigNum::to_int()
{
    int i, num;
    num = a[len - 1];
    for (i = len - 2; i >= 0; i--)
        num = num * (MAXN + 1) + a[i];
    return num;
}
long long int BigNum::to_long()
{
    int i;
    long long int num;
    num = a[len - 1];
    for (i = len - 2; i >= 0; i--)
        num = num * (MAXN + 1) + a[i];
    return num;
}
string BigNum::to_String()
{
    int i;
    string s = "", tp = "";
    s += to_string(a[len - 1]);
    for (i = len - 2; i >= 0; i--) {
        tp = to_string(a[i]);
        int tot = tp.size();
        tp.insert(tp.begin(), 4 - tot, '0');
        s = s + tp;
    }
    return s;
}

int p[maxn];
int to[maxn];
int vis[maxn];

int gcd1(int x, int y) {
    return y ? gcd1(y, x % y) : x;
}
int gcd(BigNum x, int y) {
    return gcd1(y, x % y);
}

BigNum lcm(BigNum ans, int res) {
    return ans / gcd(ans, res) * res;
}

int main() {
    cin >> n; 
    for (int i = 1; i <= n; i++) {
        scanf("%d", &p[i]);
        to[i] = p[i];
    }

    BigNum ans = BigNum(1);
    for (int i = 1; i <= n; i++) { //找环的长度
        if (vis[i]) continue;
        int tmp = i;
        int res = 0; //环的长度
        while (to[tmp] != i) {
            vis[tmp] = 1;
            tmp = to[tmp];
            res++;
        }
        res++;
        ans = lcm(ans, res);
    }
    ans.print();
    return 0;
} 

参考链接：https://www.cnblogs.com/kangkang-/p/13387908.html