数据结构-多项式相乘

多项式相乘•问题描述此程序解决的是一元多项式相乘的问题。

定义两个一元多项式，然后进行两个一元多项式的相乘。

最后得到一个结果，并按升幂输出最终的多项式。

•设计思路定义一个结构体，里面包含一元多项式的符号、系数、指数。

对多项式进行输入时，先输入多项式的项数，然后从第一项的系数开始输入，然后输入第一项的指数，直至第一项输入完毕。

然后开始输入第二项，输入第二项的方法与输入第一项的方法相同。

在进行相乘时，用第二项的每个元素去乘第一项的每个元素。

最终合并同类项的时候，把后面指数项加到与前面有共同指数的项的上面，然后删除该项。

•数据结构设计将多项式因子的符号、系数、指数封装成一个结构为顺序表类型•功能函数设计void sort(LinkYinzi& Head)排序函数，采用冒泡排序对多项式进行排序void PrintList(const LinkYinzi Head)输出多项式函数void Creat_List(LinkYinzi& Head, int num)创建多项式函数void DelList(LinkYinzi& Head, int n)删除多项式中某一项函数void multip(const LinkYinzi Head1, const LinkYinzi Head2)多项式相乘函数void menu_elect( LinkYinzi Head1, LinkYinzi Head2)功能选择函数•程序代码#include <iostream>using namespace std;typedef struct Yinzi{char sign;float coef;//系数int expn;//指数Yinzi* next;}Yinzi,*LinkYinzi;void sort(LinkYinzi& Head){LinkYinzi Q;//采用冒泡排序对多项式进行排序for(LinkYinzi P1 = NULL; P1 != Head->next->next; P1 = Q)for(LinkYinzi P2 = Head->next; P2->next != P1; P2 = P2->next){if(P2->expn > P2->next->expn){int temp1;double temp2;char temp3; //temp3是交换变量temp2 = P2->coef;P2->coef = P2->next->coef;P2->next->coef = temp2;temp3 = P2->sign;P2->sign = P2->next->sign;P2->next->sign = temp3;temp1 = P2->expn;P2->expn = P2->next->expn;P2->next->expn = temp1;}Q = P2->next;//此处让Q为本次执行后的P2的下一个，以便P1=Q让P1成为P2的下一个，作为下一次循环的结束标志。

}}//冒泡排序（升序）void PrintList(const LinkYinzi Head){LinkYinzi p = Head ->next;if(p != NULL ){if(p->coef != 0){//系数不为0if(p->expn != 0){//指数不为0if(p->expn != 1){if(p->coef == 1)cout << "x^" << p->expn;elsecout << p->coef << "x^" << p->expn;}else{if(p->coef == 1)cout << "x";elsecout << p->coef << "x";}}elsecout << p->coef;}p = p->next;}//输出第一项while(p != NULL){if(p->sign == '+'){if(p->coef != 0){if(p->expn != 0){if(p->expn != 1){if(p->coef == 1)cout << '+' << "x^" << p->expn;elsecout << '+' << p->coef << "x^" << p->expn;}else{if(p->coef == 1)cout << '+' << "x";elsecout << '+' << p->coef << "x";}}elsecout << '+' << p->coef;}else{p = p->next;continue;}}if(p->sign == '-'){if(p->coef != 0){if(p->expn != 0){if(p->expn != 1){if(p->coef == -1)cout << '-' << "x^" << p->expn;elsecout << p->coef << "x^" << p->expn;}else{if(p->coef == -1)cout << '-' << "x";elsecout << p->coef << "x";}}elsecout << p->coef;}else{p = p->next ;continue;}}p = p->next;}}//输出其余的项void Creat_List(LinkYinzi& Head, int num){cout << "请输入你的因式的项数：" << endl;int n;cin >> n;LinkYinzi p = Head;cout << "开始输入因式的系数和指数：" << endl;for(int i = 0; i < n; i++){LinkYinzi Node = new Yinzi;cout<<"请输入第"<<i+1<<"系数：";cin >> Node->coef;if(Node->coef > 0)Node->sign = '+';if(Node->coef < 0)Node->sign = '-';cout<<"请输入第"<<i+1<<"指数：";cin >> Node ->expn;Node->next = p->next;p->next = Node;p = p->next;}p->next = NULL;cout << "多项式创建完毕" << endl<< "此多项式的编号是" << num <<" ";cout << "按升序排列的多项式是：";sort(Head);PrintList(Head);cout << endl;}//创建多项式void DelList(LinkYinzi& Head, int n){LinkYinzi p = Head;for(int i = 0; i < n-1; i++)p = p->next;LinkYinzi Q ;Q = p->next;p->next = Q ->next ;delete Q;}//删除多项式的第n个因式void multip(const LinkYinzi Head1, const LinkYinzi Head2){LinkYinzi Head3 = new Yinzi;Head3->next = NULL;LinkYinzi P1, P2, P3;P3 = Head3;for(P1 = Head1->next ; P1!=NULL; P1 = P1->next)for(P2 = Head2->next ; P2!=NULL;){LinkYinzi Node = new Yinzi;Node->expn = P1->expn + P2->expn;Node->coef = P1->coef * P2->coef;if(Node->coef >= 0)Node->sign = '+';elseNode->sign = '-';P2 = P2->next;Node->next = P3->next;P3->next = Node;P3 = P3->next;}//用P2的元素去乘P1的每个元素sort(Head3);//排序，为合并同类项做基础int i = 1;for(LinkYinzi P = Head3->next; P->next != NULL;){if(P->expn == P->next->expn){P->coef += P->next->coef;DelList(Head3,i+1);//把后面指数项加到与前面相同的指数项上面，然后删除该项}else{P = P->next;i++;}}//end for 为了合并同类项排完序后若有同类项，则一定是位置上相邻的cout << "两多项式相乘的结果是: ";PrintList(Head3);cout << endl;}void menu_elect( LinkYinzi Head1, LinkYinzi Head2){int judge;cout << "按下面的要求输如您的请求:" << endl<< "1: 多项式的相乘" << endl<< "0: 退出程序" <<endl;cin >> judge;switch(judge){case 1: multip(Head1,Head2); break;case 0: exit(0);default : cout <<"输入错误！" << endl; break;}}int main(){int i = 1;LinkYinzi Head1 = new Yinzi;LinkYinzi Head2 = new Yinzi;Head1->next = NULL;Head2->next = NULL;Creat_List(Head1,i);Creat_List(Head2,i+1);while(true){int ju;menu_elect(Head1,Head2);cout << "您是否继续1 = 是，0 = 否" << endl;cin >> ju;if(ju == 0)break;}return 0;}•运行与测试。