线性结构习题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:

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

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题目解读：

以输入样例为例，首先输入4表示有四个非零项，其次输入四组非零项的系数和指数，即样例中输入的多项式为：

f₁(x)=3x⁴-5x²+6x-2;    f₂(x)=5x²⁰-7x⁴+3x

输出样例中，

第一行为积：f3(x)=15x²⁴-25x²²+30x²¹-10x²⁰-21x⁸+35x⁶-33x⁵+14x⁴-15x³+18x²-6x

第二行为和：f4(x)=5x²⁰-4x⁴-5x²+9x-2

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 参考一些别人的博客，对于链表中指针操作需要进一步熟练才行。具体的实现过程可以在草稿纸上走一下，加深理解。

程序实现【vs2015】：

关于结构体

#include <stdio.h>
#include <stdlib.h>
typedef struct node{//定义结构体类型的结点
    int coefficient;//系数
    int exponent;   //指数
    struct node * next;//下一个结点
}PolyNode, *Polynomial;
//声明结构体变量PolyNode,以及一个指向它的指针polynomial

Polynomial ReadPoly();//获取多项式的函数
void Attach(int c, int e, Polynomial * Rear);
Polynomial MultPoly(Polynomial P1, Polynomial P2);
Polynomial AddPoly(Polynomial P1, Polynomial P2);
void PrintPoly(Polynomial P);

int main(int argc, char const *argv[]){
    Polynomial Poly1, Poly2, PolySum, PolyMul;
    Poly1 = ReadPoly();
    Poly2 = ReadPoly();
    PolyMul = MultPoly(Poly1, Poly2);
    PrintPoly(PolyMul);
    PolySum = AddPoly(Poly1, Poly2);
    PrintPoly(PolySum);
    system("pause");
    return 0;
}

Polynomial ReadPoly(){
    Polynomial P, Rear, temp;
    P = (PolyNode*)malloc(sizeof(PolyNode));//开辟一个新结点空间，将其
    P->next = NULL;//指向链表的第一个结点
    Rear = P;
    int N, c, e;
    scanf_s("%d", &N);
    while(N--){
        scanf_s("%d %d", &c, &e);
        Attach(c, e, &Rear);
    }
    temp = P;
    P = P->next; 
    free(temp);
    return P;
}

void Attach(int c, int e, Polynomial * pRear){
    Polynomial P;
    P = (PolyNode*)malloc(sizeof(PolyNode));
    P->coefficient = c;
    P->exponent = e;
    P->next = NULL;
    (*pRear)->next = P;
    *pRear = P;
}

Polynomial MultPoly(Polynomial P1, Polynomial P2){
    Polynomial P, temp1, temp2, Rear, temp;
    int c, e;
    if(!P1 || !P2)
        return NULL;
    temp1 = P1;
    temp2 = P2;
    P = (PolyNode*)malloc(sizeof(PolyNode));
    P->next = NULL;
    Rear = P;
    while(temp2){
        c = temp1->coefficient * temp2->coefficient;
        e = temp1->exponent + temp2->exponent;
        if(c != 0){
            Attach(c, e, &Rear);
            temp2 = temp2->next;
        }
    }
    temp1 = temp1->next;
    while(temp1){
        temp2 = P2, Rear = P;
        while(temp2){
            c = temp1->coefficient * temp2->coefficient;
            e = temp1->exponent + temp2->exponent;
            if(c != 0){
                while(Rear->next && Rear->next->exponent > e)
                    Rear = Rear->next;
                if(Rear->next && Rear->next->exponent == e){
                    if(Rear->next->coefficient + c)
                        Rear->next->coefficient += c;
                    else{
                        temp = Rear->next;
                        Rear->next = temp->next;
                        free(temp);
                    }
                }else{
                    temp = (PolyNode*)malloc(sizeof(PolyNode));
                    temp->coefficient = c;
                    temp->exponent = e;
                    temp->next = Rear->next;
                    Rear->next = temp;
                    Rear = Rear->next;
                }
                temp2 = temp2->next;
            }
        }
        temp1 = temp1->next;
    }
    temp = P;
    P = P->next;
    free(temp);
    return P;
}

Polynomial AddPoly(Polynomial P1, Polynomial P2){
    Polynomial P, temp1, temp2, Rear, temp;
    if(!P1 && !P2){
        if(!P1)
            return P2;
        else
            return P1;
    }
    P = (PolyNode*)malloc(sizeof(PolyNode));
    P->next = NULL;
    Rear = P;
    temp1 = P1;
    temp2 = P2;
    while(temp1 && temp2){
        if(temp1->exponent > temp2->exponent){
            if(temp1->coefficient){
                Attach(temp1->coefficient, temp1->exponent, &Rear);
            }
            temp1 = temp1->next;
        }else if(temp1->exponent == temp2->exponent){
            if(temp1->coefficient + temp2->coefficient){
                Attach(temp1->coefficient + temp2->coefficient, temp1->exponent, &Rear);
            }
            temp1 = temp1->next;
            temp2 = temp2->next;
        }else{
            if(temp2->coefficient){
                Attach(temp2->coefficient, temp2->exponent, &Rear);
            }
            temp2 = temp2->next;
        }
    }
    while(temp1){
        Attach(temp1->coefficient, temp1->exponent, &Rear);
        temp1 = temp1->next;
    }
    while(temp2){
        Attach(temp2->coefficient, temp2->exponent, &Rear);
        temp2 = temp2->next;
    }
    temp = P;
    P = P->next;
    free(temp);
    return P;
}
void PrintPoly(Polynomial P){
    int flag = 0;
    if(!P){
        printf("0 0");
    }
    while(P){
        if (!flag)
            flag = 1;
        else
            printf(" ");
        printf("%d %d", P->coefficient, P->exponent);
        P = P->next;
    }
    printf("
");
}

测试结果：