LA 4119

https://icpcarchive.ecs.baylor.edu/index.php?option=com_onlinejudge&Itemid=8&page=show_problem&problem=2120

假设式子的最高幂次为k 则只需要测试1到k+1就可以了

原理见 刘汝佳的《算法竞赛入门经典入门指南》 P123

字符串需要自己处理，比较繁琐 一定要细心

代码：

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

#define ll long long
#define lint long long
using namespace std;

const int N=100005;
ll a[N];
ll powerMod(ll x,ll y,ll M)
{//cout<<x<<" "<<y<<" "<<M<<endl;
    ll tmp=1;
    while(y)
    {
        if(y&1)
        tmp=tmp*x%M;
        x=x*x%M;
        y=y>>1;
    }
    //cout<<(tmp%M)<<endl;
    return tmp%M;
}
void func(string s)
{//cout<<s<<endl;
    if(s.size()==0) return;

    int m=s.find('n');
    if(m==-1)
    m=s.size();
    int type=(s[0]=='-')?-1:1;
    ll tmp=0;
    //int l=;cout<<l<<" "<<m<<endl;
    for(int i=(s[0]=='+'||s[0]=='-')?1:0;i<m;++i)
    {//cout<<i<<" "<<tmp<<endl;
        tmp=tmp*10+s[i]-'0';
    }
    if(tmp==0) tmp=1;
    tmp=tmp*type;
    m=s.find('n');//cout<<m<<endl;
    if(m==-1) a[0]=tmp;
    else
    {//cout<<"in1"<<endl;return ;
        int k=s.find('^');
        if(k==-1)
        a[1]=tmp;
        else
        {//cout<<"in2"<<endl;
            int x=0;
            for(int i=k+1;i<s.size();++i)
            {
                x=x*10+s[i]-'0';
            }
            //cout<<x<<" "<<tmp<<endl;
            a[x]=tmp;
        }
    }
    //cout<<"return"<<endl;
}
bool solve(string s)
{
    memset(a,0,sizeof(a));
    int k=s.find('/');
    ll M=0;
    for(int i=k+1;i<s.length();++i)
    M=M*10+s[i]-'0';
    string stmp;
    for(int i=(s[0]=='(')?1:0;i<k&&s[i]!=')';++i)
    {
        if(s[i]=='+'||s[i]=='-')
        {
            func(stmp);
            stmp.clear();
        }
        stmp.push_back(s[i]);
    }
    func(stmp);
    for(ll i=1;i<=101;++i)
    {//cout<<i<<endl;
        ll tmp=0;
        for(ll j=0;j<=100;++j)
        {
            //cout<<j<<" "<<a[j]<<endl;
            tmp=(tmp+a[j]*powerMod(i,j,M))%M;
        }
        if(tmp!=0)
        return false;
    }
    return true;
}
int main()
{
    //freopen("data.in","r",stdin);
    int ca=1;
    string s;
    while(cin>>s)
    {
        if(s==".")break;
        if(solve(s))
        printf("Case %d: Always an integer
",ca++);
        else
        printf("Case %d: Not always an integer
",ca++);
    }
    return 0;
}