1002: [FJOI2007]轮状病毒

#include <set>
#include <map>
#include <cstdio>
#include <cstdlib>
#include <cmath>
#include <cstring>
#include <string>
#include <sstream>
#include <algorithm>
#include <vector>
#include <stack>
#include <queue>
#include <iostream>
#include <functional>
using namespace std;
#define ll long long
#define fi first
#define se second
#define re register
#define pb push_back
void read(int &a)
{
    a=0;
    int d=1;
    char ch;
    while(ch=getchar(),ch>‘9‘||ch<‘0‘)
        if(ch==‘-‘)
            d=-1;
    a=ch-‘0‘;
    while(ch=getchar(),ch>=‘0‘&&ch<=‘9‘)
        a=a*10+ch-‘0‘;
    a*=d;
}
void write(int x)
{
    if(x<0)
        putchar(45),x=-x;
    if(x>9)
        write(x/10);
    putchar(x%10+‘0‘);
}
string f[105];
string add(string st1,string st2)
{
    string str;
    int d=0;
    int len1=st1.length();
    int len2=st2.length();
    if(len1>len2)
        for(re int i=0;i<len1-len2;i++)
            st2=‘0‘+st2;
    else
        for(re int i=0;i<len2-len1;i++)
            st1=‘0‘+st1;
    for(re int i=st1.size()-1;i>=0;i--)
    {
        int a,b;
        a=st1[i]-‘0‘;
        b=st2[i]-‘0‘;
        a=a+b+d;
        d=a/10;
        str=char(a%10+‘0‘)+str;
    }
    if(d!=0)  str=char(d+‘0‘)+str;
    return str;
}
string solve(int x)
{
    string s="";
    do
    {
        s.pb(x%10);
        x/=10;
    }while(x);
    reverse(s.begin(),s.end());
    return s;
}
string sub(string st1,string st2)
{
    string tem;
    int d=0;
    bool f=true;
    int len1=st1.length();
    int len2=st2.length();
    if(len1<len2||(len1==len2&&st1<st2))
    {
        string t=st1;
        st1=st2;
        st2=t;
        int tt=len1;
        len1=len2;
        len2=tt;
        f=false;
    }
    else if(len1==len2&&st1==st2)
    {
        tem=‘0‘;
        return tem;
    }
    for(re int i=1;i<=len1-len2;i++)
        st2=‘0‘+st2;
    for(re int i=len1-1;i>=0;i--)
    {
        int t=(st1[i]-‘0‘)-(st2[i]-‘0‘)-d;
        if(t<0)
        {
            t+=10;
            d=1;
        }
        else
            d=0;
        tem=char(t+‘0‘)+tem;
    }
    if(tem.size()==1)
    {
        if(!f)
            tem=‘-‘+tem;
        return tem;
    }
    while(1)
    {
        if(tem[0]==‘0‘)
            tem.erase(0,1);
        else
            break;
    }
    if(!f)
        tem=‘-‘+tem;
    return tem;
}
int main()
{
    int n;read(n);
    string st1,st2;
    f[1]="1",f[2]="5";
    st1=solve(n);st2=solve((n+1)*n);
    for(re int i=3;i<=n;i++)
    {
        for(re int j=1;j<=3;j++) f[i]=add(f[i],f[i-1]);
        f[i]=add(f[i],"2");
        f[i]=sub(f[i],f[i-2]);
    }
    cout<<f[n]<<endl;
    return 0;
}