利用链表实现多项式求值

闲来无事，写了一个多项式之间的加减乘除

// 多项式.cpp : 定义控制台应用程序的入口点。
//

#include "iostream"
#include <stdlib.h>
#include "iostream"
#include "string"
#include "stdafx.h"
using namespace std;

class X{
public :
X();
X* build();
X* auto_build(int n);
X* multiplication(X *x1, X *x2);
X* division(X *x1, X *x2);
X* addition(X *x1, X *x2);
X* subtraction(X *x1, X *x2);
void show();
friend istream & operator >> (istream &, X *);
friend ostream & operator << (ostream &, X *);
friend istream & operator >> (istream &, X *x);
friend ostream & operator << (ostream &output, X *x);
private:
X* next;
X* other;
int exponent;
double coefficient;
int weight;
};

ostream & operator << (ostream &output, X *x){
if (x != NULL){
if (x->coefficient == 0){
return output;
}else if (x->coefficient == 1){
if (x->exponent != 0){
cout << "+";
}else{
cout <<"+"<< 1;
}
}else if (x->coefficient > 1){
cout << "+" << x->coefficient;
}else if (x->coefficient == -1){
cout << "-" ;
}else{
cout << x->coefficient;
}
if (x->exponent == 0){
}else if (x->exponent == 1){
cout << "x";
}else{
cout << "x^" << x->exponent;
}
}
return output;
}

X::X(){
next = NULL;
other = NULL;
exponent = 0;
coefficient = 0;
weight = 0;
}

X* X::build(){ //输入多项式
X *head, *p1,*p2;
p2 = NULL;
head = new X;
head->other = NULL;
head->next = new X;
cout << "请输入该多项式的最高次数" << endl;
cin >> head->weight;
p1 = head->next;
for (int i = 0; i <= head->weight; i++){
p1->exponent = (head->weight) - i;
p1->weight = p1->exponent;
cout << "请输入x^" << (head->weight)-i << "的系数：" ;
cin >> p1->coefficient;
cout << endl;
p1->next = new X;
p2 = p1;
p1 = p1->next;
}
p2->next = NULL;
head->show();
return head;
}

X* X::auto_build(int n){ //自动创建n个结点的空链表
X *head, *p1, *p2;
int i;
p2 = NULL;
head = new X;
head->other = NULL;
head->next = new X;
head->weight = n;
p1 = head->next;
for ( i = 0; i <= head->weight; i++){
p1->exponent = (head->weight) - i;
p1->weight = p1->exponent;
p1->next = new X;
p2 = p1;
p1 = p1->next;
}
if (i == 0){
head->next = NULL;
return head;
}else{
p2->next = NULL;
return head;
}
}

X* X::multiplication(X *x1, X *x2){ // 乘法
X *p1,*p2,*p3,*result;
int n = x1->weight + x2->weight;
result = auto_build(n);
p1 = x1->next;
p2 = x2->next;
p3 = result->next;
while (p2 != NULL){
while (p1 != NULL){
while (p3->exponent != p1->exponent + p2->exponent)
p3 = p3->next;
p3->coefficient = p3->coefficient + p1->coefficient * p2->coefficient;
p1 = p1->next;
}
p1 = x1->next;
p2 = p2->next;
p3 = result->next;
}
cout << "积为" << endl;
result->show();
return result;
}

X* X::division(X *x1, X *x2){ //除法
X *p1, *p2, *p3,*p4,*result;
int i = 0;
int n = x1->weight - x2->weight;
if (n <= 0){
cout << "这是个真分式，咱不能除" << endl;
system("pause");
return NULL;
}
result = auto_build(n);
p1 = x1;
p2 = x2;
p3 = result;
do{
while (p1->next->exponent - p2->next->exponent != n-i) p1 = p1->next;
cout << p3->next->coefficient << "=" << p1->next->coefficient << "/" << p2->next->coefficient << endl;
p3->next->coefficient = p1->next->coefficient / p2->next->coefficient;
p1->show();
cout << "-" << endl;
p3->show();
cout << "*" << endl;
p2->show();
p1 = subtraction(p1, multiplication(p3, p2));
p3 = p3->next;
i++;
} while (p3->next != NULL);
result->other = p1;
result->show();
return result;
}

X* X::addition(X *x1, X *x2){ //加法
X *p[3];
int n = x1->weight > x2->weight ? x1->weight : x2->weight;
X *result = auto_build(n);
p[2] = result->next;
int j = x1->weight > x2->weight ? 0 : 1;//j为大
int k = x1->weight > x2->weight ? 1 : 0;//k为小
p[0] = x1->next;
p[1] = x2->next;
for (int i = 0; i <= n; i++){
if (p[j]->exponent == p[k]->exponent){
p[2]->coefficient = p[j]->coefficient + p[k]->coefficient;
p[j] = p[j]->next;
p[k] = p[k]->next;
p[2] = p[2]->next;
}else{
p[2]->coefficient = p[j]->coefficient;
p[2] = p[2]->next;
p[j] = p[j]->next;
}
}
system("cls");
cout << "和为" << endl;
result->show();
return result;
}

X* X::subtraction(X *x1, X *x2){ //减法
int n = x1->weight > x2->weight ? x1->weight : x2->weight;
X *result = auto_build(n);
X *p1 = x1->next;
X *p2 = x2->next;
X *p3 = result->next;
for (int i = 0; i <= n; i++){
if (p1->exponent == p2->exponent){
p3->coefficient = p1->coefficient - p2->coefficient;
cout << p3 << endl;
p1 = p1->next;
p2 = p2->next;
p3 = p3->next;
}else{
if (p1->exponent > p2->exponent){
p3->coefficient = p1->coefficient;
cout << p3 << endl;
p3 = p3->next;
p1 = p1->next;
}else{
p3->coefficient = 0 - p2->coefficient;
p3 = p3->next;
p2 = p2->next;
}
}
}
cout << 差为" << endl;
result->show();
return result;
}

void X::show(){ //展示多项式
X *p = next;
while (p->coefficient == 0){
p = p->next;
if (p == NULL)
break;
}
if (p==NULL){
cout << "0" << endl;
}else{
if (p->coefficient == 1){
}else if (p->coefficient > 1){
cout << p->coefficient;
}else if (p->coefficient == -1){
cout << "-" ;
}else{
cout << p->coefficient;
}
if (p->exponent == 0){
}else if (p->exponent == 1){
cout << "x";
}else{
cout << "x^" << p->exponent;
}
p = p->next;
while (p != NULL){
cout << p;
p = p->next;
}
}
p = other;
if (p != NULL&&p->coefficient!=0){
cout << "+++++++++++++++++++++++";
while (p != NULL){
cout << p;
p = p->next;
}
}
cout << endl;
}

void menu(){
cout << "****************************************************************" << endl;
cout << "* 1,加法 *" << endl;
cout << "* 2,减法 *" << endl;
cout << "* 3,乘法 *" << endl;
cout << "* 4,除法 *" << endl;
cout << "* 5,退出 *" << endl;
cout << "****************************************************************" << endl;
}

int main(){
int panduan, switch_on;
X *xx = new X;
X *x1, *x2, *X;
X = NULL;
panduan = 1;
cout << "请输入第一个多项式" << endl;
x1 = xx->build();
cout << endl;
cout << "请输入第二个多项式" << endl;
x2 = xx->build();
while (panduan){
system("cls");
cout << endl;
cout << "第一个多项式为：";
x1->show();
cout << endl;
cout << "第二个多项式为：";
x2->show();
cout << endl;
if (X != NULL){
cout << "结果为" << endl;
X->show();
cout << endl;
}
menu();
cin >> switch_on;
switch (switch_on){
case 1:X = xx->addition(x1, x2); break;//加法
case 2:X = xx->subtraction(x1, x2); break;//减法
case 3:X = xx->multiplication(x1, x2); break;//乘法
case 4:X = xx->division(x1, x2); break;//除法
default:panduan = 0; break;
}
}
return 0;
}