#include <iostream>
#include <cstring>
#include <iomanip>

struct term{
    float coef;
    int expn;
    term *next;
};
void deletLastOne(term* in){
    auto tmp = in;
    while (tmp->next->next){
        tmp = tmp->next;
    }
    delete tmp->next;
    tmp->next = nullptr;
}
class Polynomial{
public:
    char* name;
    term *termList;
    Polynomial(term*in,char* inName){name=inName;termList=in;}
    ~Polynomial(){
        while(termList){
            auto tmp = termList;
            termList=termList->next;
            delete tmp;
        }
        delete name;
    }
    term* operator+(Polynomial &ri);
    term* operator-(Polynomial &ri);
    term* operator*(Polynomial &ri);
    term* derivative();
    bool operator==(const char* in);
    float operator()(float in);
    float fPower(float m, int n){   //m^n
        if(n==1) return m;
        if(n==0) return 1;
        float temp=fPower(m,n/2);
        return (n%2==0 ? 1 : m)*temp*temp;
    }
};
term* Polynomial::operator+(Polynomial &ri) {
    auto* head = new term{0,0, nullptr};
    auto end = head;
    auto this_head = this->termList;
    auto that_head = ri.termList;
    while (this_head || that_head){
        if(!that_head || (this_head && this_head->expn < that_head->expn)){
            end->coef = this_head->coef;
            end->expn = this_head->expn;
            end->next = new term{0,0, nullptr};
            end = end->next;
            this_head = this_head->next;
            continue;
        }
        if(!this_head || this_head->expn > that_head->expn){
            end->coef = that_head->coef;
            end->expn = that_head->expn;
            end->next = new term{0,0, nullptr};
            end = end->next;
            that_head = that_head->next;
            continue;
        }
        if(this_head->expn == that_head->expn){
            end->coef = this_head->coef+that_head->coef;
            end->expn = that_head->expn;
            end->next = new term{0,0, nullptr};
            end = end->next;
            that_head = that_head->next;
            this_head = this_head->next;
            continue;
        }
    }
    deletLastOne(head);
    return head;
}
term* Polynomial::operator-(Polynomial &ri) {
    auto* head = new term{0,0, nullptr};
    auto end = head;
    auto this_head = this->termList;
    auto that_head = ri.termList;
    while (this_head||that_head){
        if(!that_head || (this_head && this_head->expn < that_head->expn)){
            end->coef = this_head->coef;
            end->expn = this_head->expn;
            end->next = new term{0,0, nullptr};
            end = end->next;
            this_head = this_head->next;
            continue;
        }
        if(!this_head || this_head->expn > that_head->expn){
            end->coef = 0-that_head->coef;
            end->expn = that_head->expn;
            end->next = new term{0,0, nullptr};
            end = end->next;
            that_head = that_head->next;
            continue;
        }
        if(this_head->expn == that_head->expn){
            end->coef = this_head->coef - that_head->coef;
            end->expn = that_head->expn;
            end->next = new term{0,0, nullptr};
            end = end->next;
            that_head = that_head->next;
            this_head = this_head->next;
            continue;
        }
    }
    deletLastOne(head);
    return head;
}
term* Polynomial::operator*(Polynomial &ri) {
    int numa = 0,numb=0;
    term* tmp = this->termList;
    while (tmp->next)tmp=tmp->next;
    numa = tmp->expn;
    tmp = ri.termList;
    while (tmp->next)tmp=tmp->next;
    numb = tmp->expn;
    auto *coList = new float[numa+numb+1]{0};
    term* la = this->termList ,*lb;
    while (la){
        lb = ri.termList;
        while (lb){
            coList[la->expn+lb->expn]=la->coef*lb->coef;
            lb = lb->next;
        }
        la=la->next;
    }
    auto* head = new term{0,0, nullptr};
    auto end = head;
    for(int i = 0;i<=numa+numb;i++){
        if(coList[i] == 0) continue;
        end->coef = coList[i];
        end->expn = i;
        end->next = new term{0,0, nullptr};
        end = end->next;
    }
    deletLastOne(head);
    return head;
}
term* Polynomial::derivative() {
    auto* head = new term{0,0, nullptr};
    auto end = head;
    auto tmp = this->termList;
    while (tmp){
        if(tmp->expn != 0) {
            end->coef = tmp->coef * tmp->expn;
            end->expn = tmp->expn - 1;
            end->next = new term{0, 0, nullptr};
            end = end->next;
        }
        tmp = tmp->next;
    }
    deletLastOne(head);
    return head;
}
bool Polynomial::operator==(const char *in) {
    return strcmp(this->name, in) == 0;
}
float Polynomial::operator()(float in) {
    auto tmp = this->termList;
    float  out = 0;
    while (tmp){
        out += tmp->coef* fPower(in,tmp->expn);
        tmp = tmp->next;
    }
    return out;
}
std::ostream & operator<<(std::ostream &out,const Polynomial &obj){
    out << obj.name << "(x)=";
    auto tmp = obj.termList;
    while (tmp){
        out << ' '<<(tmp->coef>0?"+":"")<<std::setprecision(2)<<std::fixed<< tmp->coef;
        if(tmp->expn != 0) {
            out << "x^" << tmp->expn;
        }
        tmp = tmp->next;
    }
    return out;
}

#include <list>
#include <algorithm>
using namespace std;
int main(){
    list<Polynomial> a;
    while (true){
        cout << "当前暂存的函数有:" <<endl;
        for(const auto &item : a){
            cout << item <<endl;
        }
        cout << "请选择下面的操作:"<<endl;
        cout << "1. 创建新的多项式" <<endl;
        cout << "2. 多项式加法" << endl;
        cout << "3. 多项式减法" <<endl;
        cout << "4. 多项式乘法" <<endl;
        cout << "5. 多项式求导" << endl;
        cout << "6. 多项式带入求值" << endl;
        cout << "0. 退出程序" <<endl;
        int check;
        cin >> check;
        auto* name = new char[20];
        int ex,num;float co;
        auto * head = new term{0,0,nullptr};
        auto end = head;
        char c[20],b[20];
        list<Polynomial>::iterator itb,itc;
        switch (check){
            case 1:
                cout << "多项式名称:";
                cin >> name;
                cout << "请输入项数:";
                cin >> num;
                cout << "请按照次数从小到大的顺序输入 指数 和 系数"<< endl;
                for(int i = 0;i<num;i++){
                    cin >> ex >> co;
                    end->expn = ex;
                    end->coef = co;
                    end->next = new term{0,0, nullptr};
                    end = end->next;
                }
                deletLastOne(head);
                a.emplace_back(head,name);
                cout << endl << "输入结束,您输入的表达式为:"<<endl;
                cout << a.back() << endl;
                break;
            case 2:
            case 3:
            case 4:
                cout << "请输入结果多项式的名称:";
                cin >> name;
                cout << "请输入两个运算多项式的名称 空格分隔:";
                cin >> c >> b;
                itc = find(a.begin(),a.end(),c);
                itb = find(a.begin(),a.end(),b);
                if(itc == a.end() || itb == a.end()){
                    cout << "输入的名字有误";
                }else{
                    switch (check){
                        case 2:
                            a.emplace_back(*itc+*itb,name);
                            break;
                        case 3:
                            a.emplace_back(*itc-*itb,name);
                            break;
                        case 4:
                            a.emplace_back(*itc**itb,name);
                            break;
                        default:break;
                    }
                    cout << "输入结束,得到的表达式为:"<<endl;
                    cout << a.back() << endl;
                }
                break;
            case 5:
                cout << "请输入结果多项式的名称:";
                cin >> name;
                cout << "请输入需要计算的多项式名称:";
                cin >> b;
                itb = find(a.begin(),a.end(),b);
                if(itb == a.end()){
                    cout << "输入的名字有误";
                } else{
                    a.emplace_back((*itb).derivative(),name);
                    cout <<"输入结束,得到的表达式为:"<<endl;
                    cout << a.back() << endl;
                }
                break;
            case 6:
                cout << "请输入多项式的名称:";
                cin >> name;
                itb = find(a.begin(),a.end(),name);
                if(itb == a.end()){
                    cout << "输入的名字有误";
                } else{
                    cout << "请输入参数:";
                    cin >> co;
                    cout << "计算结果:";
                    cout << (*itb)(co) << endl;
                }
                break;
            case 0:
                return 0;
            default:
                break;
        }
    }
}