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 [【技术文档】]多项式计算 |
在学习了链栈和链队列以后,试着完成了多项式计算的问题,除法的计算有些问题,还望高人指点.
以下是源代码:
link.h//链栈及链队列,扩展链队列模板类定义
enum Error_code{success,fail,overflow,underflow};#define NULL 0//节点定义开始template <class Node_entry>struct Node{ Node_entry entry; Node *next; Node(); Node(Node_entry item,Node *add_on=NULL);};template <class Node_entry>Node<Node_entry>::Node(){ next=NULL;}template <class Node_entry>Node<Node_entry>::Node(Node_entry item,Node *add_on){ entry=item; next=add_on;}//节点定义结束
//链栈模板定义开始template <class Stack_entry>class Stack{public: Stack(); bool empty()const; Error_code push(const Stack_entry &item); Error_code pop(); Error_code top(Stack_entry &item)const; ~Stack(); Stack(const Stack &original); void operator=(const Stack &original);protected: Node<Stack_entry> *top_node;};template <class Stack_entry>Stack<Stack_entry>::Stack(){ top_node=NULL; }template <class Stack_entry>bool Stack<Stack_entry>::empty()const{ if (top_node==NULL) return true; else return false;}template <class Stack_entry>Error_code Stack<Stack_entry>::push(const Stack_entry &item){ Node<Stack_entry> *new_top=new Node<Stack_entry>(item,top_node); if(new_top==NULL)return overflow; top_node =new_top; return success;}template <class Stack_entry>Error_code Stack<Stack_entry>::pop(){ Node<Stack_entry> *old_top=top_node; if (top_node==NULL)return underflow; top_node=old_top->next; delete old_top; return success;}template <class Stack_entry>Error_code Stack<Stack_entry>::top(Stack_entry &item)const{ if (top_node==NULL)return fail; item=top_node->entry; return success;
}template <class Stack_entry>Stack<Stack_entry>::~Stack(){ while(pop()==success);}template <class Stack_entry>Stack<Stack_entry>::Stack(const Stack &original){ Node<Stack_entry> *new_copy,*original_node=original.top_node; if (original_node==NULL)top_node=NULL; else{ top_node=new_copy=new Node<Stack_entry>(original_node->entry); while (original_node->next!=NULL) { original_node=original_node->next; new_copy->next=new Node<Stack_entry>(original_node->entry); new_copy=new_copy->next; } }
}template <class Stack_entry>void Stack<Stack_entry>::operator=(const Stack &original){ Node<Stack_entry> *new_top,*new_copy,*original_node=original.top_node; if (original_node==NULL)new_top=NULL; else { new_copy=new_top=new Node<Stack_entry>(original_node->entry); while (original_node->next!=NULL) { original_node=original_node->next; new_copy->next=new Node<Stack_entry>(original_node->entry); new_copy=new_copy->next;
}
} while (pop()==success); top_node=new_top;
}//链栈定义结束.
//链队列定义开始template <class Queue_entry>class Queue{public: Queue(); bool empty()const; Error_code append(const Queue_entry &item); Error_code serve(); Error_code retrieve(Queue_entry &item)const; ~Queue(); Queue(const Queue &original); void operator=(const Queue &original);protected: Node<Queue_entry> *front,*rear;};template <class Queue_entry>Queue<Queue_entry>::Queue(){ front=rear=NULL;}template <class Queue_entry>bool Queue<Queue_entry>::empty()const{ if (front==NULL) return true; else return false;}template <class Queue_entry>Error_code Queue<Queue_entry>::append(const Queue_entry &item){ Node<Queue_entry> *new_rear=new Node<Queue_entry>(item); if (new_rear==NULL)return overflow; if (rear==NULL)front=rear=new_rear; else { rear->next=new_rear; rear=new_rear; } return success;}template <class Queue_entry>Error_code Queue<Queue_entry>::serve(){ if (front==NULL)return underflow; Node<Queue_entry> *old_front=front; front=old_front->next; if (front==NULL)rear=NULL; delete old_front; return success;}template <class Queue_entry>Error_code Queue<Queue_entry>::retrieve(Queue_entry &item)const{ if (front==NULL)return fail; item=front->entry; return success;}
template <class Queue_entry>Queue<Queue_entry>::~Queue(){ while (serve()==success);}template <class Queue_entry>Queue<Queue_entry>::Queue(const Queue &original){ Node<Queue_entry> *new_copy,*original_node=original.front; if (original_node== NULL) front=NULL; else { front=new_copy=new Node<Queue_entry>(original_node->entry); while (original_node->next!=NULL) { original_node=original_node->next; new_copy->next=new Node<Queue_entry>(original_node->entry); new_copy=new_copy->next;
}
} rear=new_copy;}template <class Queue_entry>void Queue<Queue_entry>::operator =(const Queue &original){ Node<Queue_entry> *new_front,*new_copy,*original_node=original.front; if (original_node==NULL)new_front=NULL; else { new_copy=new Node<Queue_entry>(original_node->entry); new_front=new_copy; while (original_node->next!=NULL) { original_node=original_node->next; new_copy->next=new Node<Queue_entry>(original_node->entry); new_copy=new_copy->next;
}
} while (serve()==success); front=new_front; rear=new_copy;}//链队列定义结束.
//扩展链队列定义开始.template <class Queue_entry>class Extened_queue:public Queue<Queue_entry>{public: int size()const; void clear(); Error_code serve_and_retrieve(Queue_entry &item);};template <class Queue_entry>int Extened_queue<Queue_entry>::size()const{ Node<Queue_entry> *window=front; int count=0; while (window!=NULL) { window=window->next; count++; } return count;
}template <class Queue_entry>void Extened_queue<Queue_entry>::clear(){ while (serve()==success);
}template <class Queue_entry>Error_code Extened_queue<Queue_entry>::serve_and_retrieve(Queue_entry &item){ if (front==NULL)return fail;
retrieve(item); serve(); return success;}
Polynomial.h//多项式类的定义.
#include "link.h"#include <iostream.h>#include <cctype>#include <stdio.h>
struct Term{ int degree; double coefficient; Term(int exponent=0,double scalar=0);};Term::Term(int exponent,double scalar){ degree=exponent; coefficient=scalar;}//template <class Queue_entry>class Polynomial:private Extened_queue<Term>{public: void read(); void print()const; void equals_sum(Polynomial p,Polynomial q); void equals_difference(Polynomial p,Polynomial q); void equals_product(Polynomial p,Polynomial q); Error_code equals_quotient(Polynomial p,Polynomial q,Polynomial &y); int degree()const; bool isempty()const; void quyu();private: void mult_term(Polynomial p,Term t); };//template <class Queue_entry>bool Polynomial::isempty()const//不空返回假，空返回真{ if (!empty()) return false; else return true;}
void Polynomial::mult_term(Polynomial p,Term t){ Term p_term; clear(); while (!p.empty()) { p.serve_and_retrieve(p_term); Term answer(p_term.degree+t.degree,p_term.coefficient*t.coefficient); append(answer);
}}
void Polynomial::read(){ clear(); double coefficient; int last_exponent,exponent; bool first_term=true; cout<<"请输入多项式的系数和X的指数," <<"依次输入每一项,并且按指数递减输入."<<endl <<"输入系数0或指数0来完成一个多项式的输入"<<endl; do { cout<<"请输入系数:"<<flush; cin>>coefficient; if (coefficient!=0.0) { cout<<"请输入指数:"<<flush; cin>>exponent; if ((!first_term&&exponent>=last_exponent)||exponent<0) { exponent=0; cout<<"错误的指数输入,将丢失最近输入的一项." <<endl; } else { Term new_term(exponent,coefficient); append(new_term); first_term=false;
} last_exponent=exponent; } }while (coefficient!=0.0&&exponent!=0);}//template <class Queue_entry>void Polynomial::print()const{ Node<Term> *print_node=front; bool first_term=true; while (print_node!=NULL) { Term &print_term=print_node->entry; if (first_term) { first_term=false; if (print_term.coefficient<0)cout<<"-"; } else if (print_term.coefficient<0)cout<<"-"; else cout<<"+"; //if (print_term.coefficient=0.0)break; double r=(print_term.coefficient>0) ?print_term.coefficient:-(print_term.coefficient); if (r!=1)cout<<r; if (print_term.degree>1||print_term.degree<0)cout<<"X^"<<print_term.degree; if (print_term.degree==1)cout<<"X"; if (r==1&&print_term.degree==0)cout<<"1"; print_node=print_node->next; } if (first_term) cout<<"0"; cout<<endl;}//template <class Queue_entry>//加法void Polynomial::equals_sum(Polynomial p,Polynomial q){ clear(); while (!p.empty()||!q.empty()) { Term p_term,q_term; if (p.degree()>q.degree()) { p.serve_and_retrieve(p_term); append(p_term); } else if (q.degree()>p.degree()) { q.serve_and_retrieve(q_term); append(q_term); } else { p.serve_and_retrieve(p_term); q.serve_and_retrieve(q_term); if (p_term.coefficient+q_term.coefficient!=0) { Term answer_term(p_term.degree,p_term.coefficient+q_term.coefficient); append(answer_term); } } }}
void Polynomial::equals_difference(Polynomial p,Polynomial q)//减法{ Term p_term,q_term; clear(); while (!p.empty()||!q.empty()) { if (p.degree()>q.degree()) { p.serve_and_retrieve(p_term); append(p_term); } else if (q.degree()>p.degree()) { q.serve_and_retrieve(q_term); append(q_term); } else { p.serve_and_retrieve(p_term); q.serve_and_retrieve(q_term); if (p_term.coefficient-q_term.coefficient!=0) { Term answer_term(p_term.degree,p_term.coefficient-q_term.coefficient); append(answer_term); }
}}}void Polynomial::equals_product(Polynomial p,Polynomial q)//乘法{ Term p_term,q_term; clear(); Polynomial y; y=q; //Node<Term> *old_front=front; while (!p.empty()) { p.retrieve(p_term); while (!q.empty()) { q.retrieve(q_term); Term answer_term(p_term.degree+q_term.degree,p_term.coefficient*q_term.coefficient); append(answer_term); q.serve(); } q=y; p.serve(); } q.clear();
Node<Term> *f=front; Node<Term> *r; Node<Term> *del_r,*front_f,*front_r; while (f->next!=NULL) { r=f->next; front_r=f; while (r!=NULL) { if (r->entry.degree==f->entry.degree) { del_r=r; f->entry.coefficient=f->entry.coefficient+r->entry.coefficient;
front_r->next=r->next; r=r->next; front_r=r; delete del_r; } else { front_r=r; r=r->next; } } if (f->entry.coefficient==0) { front_f->next=f->next; delete f; f=front_f; r=front->next; } front_f=f; f=f->next; } }
Error_code Polynomial::equals_quotient(Polynomial p,Polynomial q,Polynomial &y){ clear(); y.clear(); Term p_term,q_term,k_term; Polynomial temp; p.retrieve(p_term);//bei q.retrieve(q_term);
while (!p.empty()) { if (p_term.degree>=q_term.degree) { k_term.degree=p_term.degree-q_term.degree; k_term.coefficient=p_term.coefficient/q_term.coefficient; if (k_term.degree!=0) append (k_term); temp.mult_term(q,k_term); p.equals_difference(p,temp); if (p.size()==0) {append(k_term);break;} else { y=p; break; } p.retrieve(p_term); } else { k_term.degree=p_term.degree-q_term.degree; k_term.coefficient=p_term.coefficient/q_term.coefficient; append(k_term); temp.mult_term(q,k_term); p.equals_difference(p,temp); //p.serve_and_retrieve(p_term); y=p; break;
} } //y.print(); return success;}
//template <class Queue_entry>int Polynomial::degree()const{ if (empty())return -1; Term lead; retrieve(lead); return lead.degree;}
fun.h功能函数的实现,如输入命令啊,提示啊,等等
#include "Polynomial.h"
Polynomial p,q,r,y;void introduction(){ cout<<"多项式计算器[版本：1.0.0426]"<<endl; cout<<"(C) 版权所有 2005-2007 Lthsoft Corp. 作者:李庭弘 "<<endl<<endl;}void instructions(){ cout<<"帮助"<<endl; cout<<"请先输入命令,然后按提示操作."<<endl <<"命令说明:"<<endl <<"?:输入多项式."<<endl <<"=:输出结果."<<endl <<"+:做加法运算."<<endl <<"-:做减法运算."<<endl <<"*:做乘法运算."<<endl <<"/:做除法运算."<<endl <<"q:退出程序."<<endl <<endl<<"祝您使用愉快!"<<endl<<endl;}char get_command(){ char command; bool waiting=true; cout<<"请输入命令,并按<Eenter>键:"<<endl; while (waiting) { cin>>command; while (cin.get()!='\n') continue; command=tolower(command); if (command=='?'||command=='+'||command=='-'||command=='*'||command=='/'||command=='q'||command=='=')waiting=false; else { cout<<"您输入的命令不正确,请输入一个正确的命令:"<<endl <<"?:输入多项式. " <<"=:输出结果."<<endl <<"+:做加法运算. " <<"-:做减法运算."<<endl <<"*:做乘法运算. " <<"/:做除法运算. "<<"q:退出程序."<<endl<<endl;
} } return command;}bool do_command(char command,Stack<Polynomial> &stored_polynomials){ //Polynomial p,q,r,y; switch (command) { case '?': p.read(); if (stored_polynomials.push(p)==overflow) cout<<"警告:系统内存空间不够,将丢失你刚才输入的数据."<<endl<<endl; break; case '=': if (stored_polynomials.empty()) cout<<"无数据"<<endl<<endl; else { stored_polynomials.top(p); p.print(); if (!y.isempty()){cout<<"余项是："<<endl;y.print();}
} break; case '+': if (stored_polynomials.empty()) cout<<"无数据,无法计算"<<endl<<endl; else { stored_polynomials.top(p); stored_polynomials.pop(); if (stored_polynomials.empty()) {cout<<"只有一个多项式,无法计算."<<endl<<endl;stored_polynomials.push(p);} else { stored_polynomials.top(q); stored_polynomials.pop(); r.equals_sum(q,p); if (stored_polynomials.push(r)==overflow) cout<<"警告:系统内存空间不够,将丢失结果."<<endl<<endl; } } break; case '-': if (stored_polynomials.empty()) cout<<"无数据,无法计算"<<endl<<endl; else { stored_polynomials.top(p); stored_polynomials.pop(); if (stored_polynomials.empty()) {cout<<"只有一个多项式,无法计算."<<endl<<endl;stored_polynomials.push(p);} else { stored_polynomials.top(q); stored_polynomials.pop(); r.equals_difference(q,p); if (stored_polynomials.push(r)==overflow) cout<<"警告:系统内存空间不够,将丢失结果."<<endl<<endl; } } break; case '*': if (stored_polynomials.empty()) cout<<"无数据,无法计算"<<endl<<endl; else { stored_polynomials.top(p); stored_polynomials.pop(); if (stored_polynomials.empty()) {cout<<"只有一个多项式,无法计算."<<endl<<endl;stored_polynomials.push(p);} else { stored_polynomials.top(q); stored_polynomials.pop(); r.equals_product(q,p); if (stored_polynomials.push(r)==overflow) cout<<"警告:系统内存空间不够,将丢失结果."<<endl<<endl; } } break; case '/': if (stored_polynomials.empty()) cout<<"无数据,无法计算"<<endl<<endl; else { stored_polynomials.top(p); stored_polynomials.pop(); if (stored_polynomials.empty()) {cout<<"只有一个多项式,无法计算."<<endl<<endl;stored_polynomials.push(p);} else { stored_polynomials.top(q); stored_polynomials.pop(); r.equals_quotient(q,p,y); // y.print(); if (stored_polynomials.push(r)==overflow) cout<<"警告:系统内存空间不够,将丢失结果."<<endl<<endl; } } break; case 'q': cout<<"感谢使用Lthsoft软件."<<endl; return false;
} return true;}
polynomial.cpp文件,主函数,很简单,只有几行
#include "fun.h"
void main(){ Stack<Polynomial> stored_polynomials; introduction(); instructions(); while (do_command(get_command(),stored_polynomials));}
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| 回复:多项式计算 |
一个运行实例：
请输入命令,并按<Enter>键:?请输入多项式的系数和X的指数,依次输入每一项,并且按指数递减输入.输入系数0或指数0来完成一个多项式的输入请输入系数:1请输入指数:4请输入系数:5请输入指数:3请输入系数:6请输入指数:2请输入系数:7请输入指数:1请输入系数:13请输入指数:0请输入命令,并按<Enter>键:?请输入多项式的系数和X的指数,依次输入每一项,并且按指数递减输入.输入系数0或指数0来完成一个多项式的输入请输入系数:1请输入指数:2请输入系数:3请输入指数:1请输入系数:6请输入指数:0请输入命令,并按<Enter>键:/请输入命令,并按<Enter>键:=X^2余项是：2X^3+7X+13请输入命令,并按<Enter>键:
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请作者登陆邮箱:njucs2001@hotmail.com.cn,
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