PTA一元多项式的乘法与加法运算 另一种算法

设计函数分别求两个一元多项式的乘积与和。

输入格式:

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:

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。零多项式应输出0 0。

输入样例:

4 3 4 -5 2  6 1  -2 0
3 5 20  -7 4  3 1

 

输出样例:

15 24 -25 22 30 21 -10 20 -21 8 35 6 -33 5 14 4 -15 3 18 2 -6 1
5 20 -4 4 -5 2 9 1 -2 0

#include <stdio.h>
#include <stdlib.h>

typedef struct PolyNode *Polynomial;
struct PolyNode{
    int coef;
    int expon;
    Polynomial link;
};

Polynomial ReadPoly(void); // 采用带头节点插入的方法建立多项式链表 先建立带头节点的链表读入多项式数据 最后删除头节点
Polynomial Mult(Polynomial P1,Polynomial P2);
Polynomial Add(Polynomial P1,Polynomial P2);
void PrintPoly(Polynomial P);
void Attach(int coef,int expon, Polynomial *pRear); //增加新节点到多项式链表后 pRear 指向链表最后节点地址的指针
void DeletePoly(Polynomial p); // 删除一个多项式链表

int main(){
    Polynomial P1,P2,PP,PS;
    
    P1 = ReadPoly();
 //   PrintPoly(P1);
    P2 = ReadPoly();
    PP = Mult(P1,P2);
    PrintPoly(PP);
    PS = Add(P1,P2);
    PrintPoly(PS);

    return 0;
}

void Attach(int coef,int expon, Polynomial *pRear){
    Polynomial p;
    p = (Polynomial)malloc(sizeof(struct PolyNode));
    p->coef = coef;
    p->expon = expon;
    p->link = NULL;
    (*pRear)->link = p;
    *pRear = p;
}

Polynomial ReadPoly(void){
    Polynomial P,Rear,t;
    int n;
    int coef,expon;
    scanf("%d",&n);
    P = (Polynomial)malloc(sizeof(struct PolyNode)); // 建立链表空的头节点
    P->link = NULL;
    Rear = P;
    while (n--) {
        scanf("%d %d",&coef,&expon);
        Attach(coef,expon,&Rear);
    }
    t = P;
    P = P->link;
    free(t);
    return P;
}

void PrintPoly(Polynomial P){
    int flag = 0;
    if(P == NULL){
        printf("0 0\n");
        return;
    }
// 最后一个没有空格 相当于除了开始，后面%d %d输出中间都有空格
    while (P) {
        if(!flag)
            flag = 1;
        else
            printf(" ");
        printf("%d %d",P->coef,P->expon);
        P = P->link;
    }
    printf("\n");
}

Polynomial Add(Polynomial P1,Polynomial P2){
    Polynomial t1 = P1,t2 = P2,t;
    Polynomial p,rear;
    p = (Polynomial)malloc(sizeof(struct PolyNode));
    rear = p;
    while (t1 && t2) {
        if(t1->expon == t2->expon){
            if(t1->coef + t2->coef){
                Attach(t1->coef+t2->coef, t1->expon, &rear);
                t1 = t1->link;
                t2 = t2->link;
            }else{
                t1 = t1->link;
                t2 = t2->link;
            }
        }else if (t1->expon > t2->expon){
            Attach(t1->coef, t1->expon, &rear);
            t1 = t1->link;
        }else{
            Attach(t2->coef, t2->expon, &rear);
            t2 = t2->link;
        }
    }
    while (t1) {
        Attach(t1->coef, t1->expon, &rear);
        t1 = t1->link;
    }
    while (t2) {
        Attach(t2->coef, t2->expon, &rear);
        t2 = t2->link;
    }
    t = p;
    p = p->link;
    free(t);
    return p;
}

// 多项式相乘算法：
// 第一个多项式第一项和第二个多项式所有项相乘得到结果多项式P
// 遍历第一个多项式其他元素和第二个多项式相乘一个一个元素插入到结果多项式P中
Polynomial Mult(Polynomial P1,Polynomial P2){
    Polynomial P,Rear,t1,t2,t;
    int coef,expon;
    
    if(!P1 || !P2)  // 多项式为NULL 多项式输出 ceof expon为0
        return NULL;
    
    t1 = P1;
    t2 = P2;
    P = (Polynomial)malloc(sizeof(struct PolyNode));
    Rear = P;
    while (t2) {
        Attach(t1->coef*t2->coef, t1->expon+t2->expon, &Rear);
        t2 = t2->link;
    }
    t1 = t1->link;
    while (t1) {
        t2 = P2;
        Rear = P;
        while (t2) {
            expon = t1->expon + t2->expon;
            coef = t1->coef * t2->coef;
            while (Rear->link && Rear->link->expon > expon) {
                Rear = Rear->link;
            }
            if(Rear->link && Rear->link->expon == expon){
                if(Rear->link->coef + coef){
                    Rear->link->coef = Rear->link->coef + coef;
                }else{
                    t = Rear->link;
                    Rear->link = t->link;
                    free(t);
                }
            }else{
                t = (Polynomial)malloc(sizeof(struct PolyNode));
                t->expon = expon;
                t->coef = coef;
                t->link = Rear->link;
                Rear->link = t;
                Rear = Rear->link;
            }
            t2 = t2->link;
        }
        t1 = t1->link;
    }
    t = P;
    P = P->link;
    free(t);
    return P;
}