链表完成多项式乘法

多项式乘法是在多项式加法的基础上完成的。

1、多项式加法

#include<iostream>
using namespace std; 
typedef struct lnode{
    int coef;
    int exp;
    lnode *next;
}lnode;
class poly{
    lnode *head;
public:
    void create(int n);//创建n项的多项式
    int comp(int a,int b);//比较函数
    void addpoly(poly &ha,poly hb);
    void print();
};
void poly::create(int n){
    head=new lnode;
    head->next=NULL;
    lnode *p;
    for(int i=0;i<n;i++){
        p=new lnode;
        cin>>p->coef>>p->exp;//升序输入,头插法 
        p->next=head->next;
        head->next=p;
    }
}
int poly::comp(int a,int b){
   if(a>b)return -1;
   else if(a==b)return 0;
   else return 1;
}
//关键
void poly::addpoly(poly &ha,poly hb){
 lnode *q=ha.head,*pa=ha.head->next,  *pb=hb.head->next,*r;
 while(pa&& pb)//pa，pb非空
    switch(comp(pa->exp,pb->exp)){
     case -1: q=pa; pa=pa->next;//pa>pb pa指数更大，链表中pa往右移
              break;
     case 0: pa->coef+=pb->coef;//pa = pb 先将指数相加
             if(pa->coef==0) { //系数为0时
                  q->next=pa->next;
                  delete pa;  //删除pa
                  pa=q;  //后面有整体的pa=pa->next
             }
             else q=pa;
             pa=pa->next;
             pb=pb->next;//不为0时，pa，pb分别正常右移
             break;
     case 1:  r=new lnode;//pa<pb，在表头插入pb
              r->coef=pb->coef;
              r->exp=pb->exp;
              q->next=r;
              r->next=pa;
              q=r;
              pb=pb->next;//勿忘pb右移
              break;
 }
 while(pb!=NULL){//上述执行完pa后pb非空，将剩余pb项插入pa中，类似case 1操作
    r=new lnode;
    r->coef=pb->coef;
    r->exp=pb->exp;
    q->next=r;
    r->next=pa;
    q=r;
    pb=pb->next; 
 }
}
void poly::print(){
    lnode *p=head->next;
    while(p){
        cout<<p->coef<<' '<<p->exp<<' ';
        p=p->next;
    }
    cout<<endl;
}
int main(void){
    poly ha,hb;
    ha.create(5);
    hb.create(4);
    ha.print();
    hb.print();
    ha.addpoly(ha,hb);
    ha.print();
    
    return 0;
}

2、多项式乘法

#include<bits/stdc++.h>
using namespace std;
typedef struct LNode {
    int coef;
    int exp;
    LNode* next;//指针
};
class poly {
    LNode* head;
public:
    poly() { head = new LNode; head->next = NULL; }
    void Create(int n);
    int Comp(int a, int b);
    void AddPoly(poly& ha, poly hb);//两项相加
    void addpnode(poly& ha, LNode* x);//链表ha中添加x结点
    void timespoly(poly& hc, poly ha, poly hb);//ha和hb相乘并将结果放入hc中
    void Print();
};
void poly::Create(int n) {
    head = new LNode;
    head->next = NULL;//建立头结点
    LNode* p;
    for (int i = 0; i < n; i++) {
        p = new LNode;
        cin >> p->coef >> p->exp;//头插法输入
        p->next = head->next;
        head->next = p;

    }

}

int poly::Comp(int a, int b) {
    if (a > b)return -1;
    else if (a == b)return 0;
    else return 1;

}
void poly::AddPoly(poly& ha, poly hb) {
    LNode* q = ha.head, * pa = ha.head->next, * pb = hb.head->next, * r;
    while (pa && pb) {
        switch (Comp(pa->exp, pb->exp)) {
        case -1:q = pa;
            pa = pa->next;
            break;
        //a>b
        case 0://a=b
            pa->coef += pb->coef;
            if (pa->coef == 0) {
                q->next = pa->next;
                delete pa;
                pa = q;
            }
            else q = pa;

            pa = pa->next;
            pb = pb->next;
            break;

        case 1://a<b,将pb插入到pa前面
            r = new LNode;
            r->coef = pb->coef;
            r->exp = pb->exp;
            r->next = pa;
            q->next = r;
            q = r;
            pb = pb->next;
        }
    }
    while (pb) {
        //将hb剩余项复制到ha
        r = new LNode;
        r->coef = pb->coef;
        r->exp = pb->exp;
        q->next = r;
        q = r;
        pb = pb->next;
    }
}
void poly::addpnode(poly& ha, LNode* x) {
    cout<<"enter addpnode"<<endl;
    LNode* q = ha.head, *pa = ha.head->next, * r;
    if (pa == NULL) {
        r = new LNode;
        r->coef = x->coef;
        r->exp = x->exp;
        q->next = r;
        r->next = pa;
        q = r;
        return;
    }//pa为空，直接将x插入
    while (pa) {
        //cout<<"enter pa loop"<<endl;
        switch (Comp(pa->exp, x->exp)) {
        case -1:q = pa; pa=pa->next;//pa系数大于x，因为要找到指数小于等于x->exp的才能进行相加或插入操作，所以q和pa指针继续同步右移
            if (pa == NULL) {
                r = new LNode;
                r->coef = x->coef;
                r->exp = x->exp;
                q->next = r;
                r->next = pa;
                q = r;
                return;
                                //pa为空则直接在链表后面插入x
     
            }break;
        case 1://pa<x,在表头插入
            r = new LNode;
            r->coef = x->coef;
            r->exp = x->exp;
            q->next = r;
            r->next = pa;
            q = r;
            pa=NULL;//这里一定要有pa=NULL否则pa还是指向之前用来比较的结点，循环不会结束，会一直插入r结点
            break;

        case 0://pa=x
            pa->coef += x->coef;
            if (pa->coef == 0) {
                q->next = pa->next;
                delete pa;
                pa = q;
            }//系数为0，删除pa
            else q = pa;
            pa = pa->next;//pa和q正常同步右移
            break;

        }
        
    //    cout<<"exit pa loop"<<endl;
    }

//cout<<"exit addpnode"<<endl;


}
void poly::timespoly(poly& hc, poly ha, poly hb) {
    //cout << "执行timespoly" << endl;
    LNode* pa = ha.head->next, * pb = hb.head->next;
    LNode* r;
    while (pa) {
        while (pb) {
            r = new LNode;
            r->coef = pa->coef * pb->coef;//系数相乘
            r->exp = pa->exp + pb->exp;//指数相加
        //    cout<<"start addpnode"<<endl;
            addpnode(hc, r);将r结点加入到hc链表中
        //    cout<<"end addpnode"<<endl;
            pb = pb->next;

        }
        //cout<<"跳出pb"<<endl; 
        pb = hb.head->next;
        pa = pa->next;
    }
//cout<<"退出timspoly"<<endl;
}
void poly::Print() {
    LNode* p = head->next;
    while (p) {
        cout << p->coef << " " << p->exp << " ";
        p = p->next;
    
    }
    cout << endl;
}
int main() {
    poly ha, hb, hc;
    ha.Create(2);
    hb.Create(2);
    ha.Print();
    hb.Print();
    ha.timespoly(hc, ha, hb);
    hc.Print();

    return 0;
}