Game of Connections

Posted 2020-08-21 勿忘初心0924

Game of Connections

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)

Total Submission(s): 856 Accepted Submission(s): 565

Problem Description This is a small but ancient game. You are supposed to write down the numbers 1, 2, 3, ... , 2n - 1, 2n consecutively in clockwise order on the ground to form a circle, and then, to draw some straight line segments to connect them into number pairs. Every number must be connected to exactly one another. And, no two segments are allowed to intersect. It‘s still a simple game, isn‘t it? But after you‘ve written down the 2n numbers, can you tell me in how many different ways can you connect the numbers into pairs? Life is harder, right?

Input Each line of the input file will be a single positive number n, except the last line, which is a number -1. You may assume that 1 <= n <= 100.

Output For each n, print in a single line the number of ways to connect the 2n numbers into pairs.

Sample Input 2 3 -1

Sample Output 2 5

Source Asia 2004, Shanghai (Mainland China), Preliminary

Recommend Eddy

/*
卡特兰数邝斌模板水过........

*/
#include <iostream>
#include <stdio.h>
#include <algorithm>
#include <string.h>
using namespace std;
/*
* 完全大数模板
* 输出cin>>a
* 输出a.print();
* 注意这个输入不能自动去掉前导0的，可以先读入到char数组，去掉前导0，再用构造函数。
*/
#define MAXN 9999
#define MAXSIZE 1010
#define DLEN 4

class BigNum {
    private:
        int a[500];  //可以控制大数的位数
        int len;
    public:
        BigNum()
        {
            len=1;memset(a,0,sizeof(a));
        }  //构造函数
        BigNum(const int);     //将一个int类型的变量转化成大数
        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)
{
    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--)
    {
        printf("%04d",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;
    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
{
    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
{
    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;
    printf("%d",a[len-1]);
    for(i=len-2;i>=0;i--)
        printf("%04d",a[i]);
    printf("\n");
}

BigNum f[110];//卡特兰数
int main()
{
    f[0]=1;
    for(int i=1;i<=100;i++)
        f[i]=f[i-1]*(4*i-2)/(i+1);//卡特兰数递推式
    int n;
    while(scanf("%d",&n)==1)
    {
        if(n==-1)
            break;
        f[n].print();
    }
    return 0;
}