[PAT] 02-线性结构2 一元多项式的乘法与加法运算

太过爱你忘了你带给我的痛 2022-09-26 11:59 153阅读 0赞

# \[PAT\] 02-线性结构2 一元多项式的乘法与加法运算 #

## 设计函数分别求两个一元多项式的乘积与和。 ##

### 输入格式说明： ###

输入分2行。每行分别先给出多项式非零项的个数。再以指数递降方式输入一个多项式非零项系数和指数（绝对值均为不超过1000的整数）。数字间以空格分隔。

### 输出格式说明： ###

输出分2行。分别以指数递降方式输出乘积多项式以及和多项式非零项的系数和指数。

数字间以空格分隔，但结尾不能有多余空格。

## 例子输入与输出： ##

## C语言单链表实现 ##

#include <stdio.h>
    #include <stdlib.h>
    
    typedef struct node *PolyNode;
    struct node{
        int coef;
        int expo;
        PolyNode pnode;
    };
    
    PolyNode readPoly()
    {
        PolyNode p,tmp,rear;
        int n,c,e;
        scanf("%d",&n);
        p = (PolyNode)malloc(sizeof(struct node));
        p->coef=p->expo=0;
        p->pnode=NULL;
        rear = p;
        if(n==0){
        return p;
        }
        while(n--){
            scanf("%d %d",&c,&e);
            tmp = (PolyNode)malloc(sizeof(struct node));
            tmp->coef=c;
            tmp->expo=e;
            rear->pnode=tmp;
            tmp->pnode=NULL;
            rear=tmp;
        }
        return p;
    }
    
    int printPoly(PolyNode p)
    {
        int flag=0;
        if(!(p->pnode)){
            printf("0 0\n");
            return 0;
        }else{
            p=p->pnode;
        }
        while(p){
        if(!flag){
            flag+=1;
        }else{
            printf(" ");
        }
        printf("%d %d",p->coef,p->expo);
        p=p->pnode;
        }
        printf("\n");
        return 0;
    }
    
    void attach(int coef, int expo, PolyNode *pRear)
    {
        PolyNode tmp;
        tmp = (PolyNode)malloc(sizeof(struct node));
        tmp->coef=coef;
        tmp->expo=expo;
        tmp->pnode=NULL;
        (*pRear)->pnode=tmp;
        *pRear = tmp;
    }
    
    PolyNode mult(PolyNode p1, PolyNode p2)
    {
        PolyNode p,Rear,t1,t2,t;
        int c, e;
        t1 = p1->pnode;
        t2 = p2->pnode;
        p = (PolyNode)malloc(sizeof(struct node));
        p->coef = p->expo = 0;
        p->pnode = NULL;
        Rear = p;
        if(!t1||!t2)return p;
        while(t2){
            c = t1->coef*t2->coef;
            e = t1->expo+t2->expo;
            attach(c,e,&Rear);
            t2 = t2->pnode;
        }
        t1=t1->pnode;
        while(t1){
            t2=p2->pnode;Rear=p;
            while(t2){
                c = t1->coef*t2->coef;
                e = t1->expo+t2->expo;
                while(Rear->pnode&&Rear->pnode->expo>e){
                    Rear = Rear->pnode;
                }
                if(Rear->pnode&&Rear->pnode->expo==e){
                    if(Rear->pnode->coef+c){
                        Rear->pnode->coef+=c;
                    }else{
                        t = Rear->pnode;
                        Rear->pnode = t->pnode;
                        free(t);
                    }
                }else{
                    t = (PolyNode)malloc(sizeof(struct node));
                    t->coef = c;
                    t->expo = e;
                    t->pnode = Rear->pnode;
                    Rear->pnode = t;
                    Rear=Rear->pnode;
                }
                t2=t2->pnode;
            }
            t1=t1->pnode;
        }
        return p;
    }
    
    int compare(int a,int b)
    {
        if(a>b)return 1;
        if(a==b)return 0;
        return -1;
    }
    
    PolyNode plus(PolyNode p1, PolyNode p2)
    {
        PolyNode p,rear,tmp;
        int sum;
        p = (PolyNode)malloc(sizeof(struct node));
        p->pnode=NULL;
        rear=p;
        p1=p1->pnode;
        p2=p2->pnode;
        while(p1&&p2)
            switch(compare(p1->expo,p2->expo)){
                case 1:
                    attach(p1->coef,p1->expo,&rear);
                    p1=p1->pnode;
                    break;
                case -1:
                    attach(p2->coef,p2->expo,&rear);
                    p2=p2->pnode;
                    break;
                case 0:
                    sum = p1->coef+p2->coef;
                    if(sum)attach(sum,p1->expo,&rear);
                    p1=p1->pnode;
                    p2=p2->pnode;
                    break;
    
            }
    
        for(;p1;p1=p1->pnode)attach(p1->coef,p1->expo,&rear);
        for(;p2;p2=p2->pnode)attach(p2->coef,p2->expo,&rear);
        rear->pnode=NULL;
        return p;
    }
    
    int main()
    {
        PolyNode mul,plu,p1,p2;
        p1 = readPoly();
        p2 = readPoly();
        mul = mult(p1,p2);
        plu = plus(p1,p2);
        printPoly(mul);
        printPoly(plu);
        return 0;
    }