C语言实现一元多项式的表示和实现

一元多项式可以表示为：

a0 + a1*x + a2*x^2 + ... + an*x^n

其中 a0, a1, ..., an 为系数，n 为最高次数，x 为未知数。

实现一元多项式可以定义一个结构体，包含系数和次数两个成员变量。具体实现如下：

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

typedef struct Node *PtrToNode;
typedef PtrToNode Polynomial;
struct Node {
    int coef;  // 系数
    int expon; // 次数
    Polynomial Next;
};

Polynomial CreatePoly();         // 创建多项式
Polynomial AddPoly(Polynomial P1, Polynomial P2); // 多项式相加
void PrintPoly(Polynomial P);   // 输出多项式

int main()
{
    Polynomial P1, P2, PP;

    printf("创建第一个多项式：\n");
    P1 = CreatePoly();
    printf("第一个多项式：");
    PrintPoly(P1);

    printf("创建第二个多项式：\n");
    P2 = CreatePoly();
    printf("第二个多项式：");
    PrintPoly(P2);

    PP = AddPoly(P1, P2);
    printf("两个多项式相加的结果为：");
    PrintPoly(PP);

    return 0;
}

Polynomial CreatePoly()
{
    Polynomial P, Rear, t;
    int c, e;

    P = (Polynomial)malloc(sizeof(struct Node));
    P->Next = NULL;
    Rear = P;

    printf("请输入多项式系数和指数，以 -1 -1 结束\n");
    scanf("%d %d", &c, &e);
    while (c != -1) {
        t = (Polynomial)malloc(sizeof(struct Node));
        t->coef = c;
        t->expon = e;
        t->Next = NULL;
        Rear->Next = t;
        Rear = t;
        scanf("%d %d", &c, &e);
    }

    return P;
}

Polynomial AddPoly(Polynomial P1, Polynomial P2)
{
    Polynomial Front, Rear, temp;
    int sum;

    Front = (Polynomial)malloc(sizeof(struct Node));
    Rear = Front;
    P1 = P1->Next;
    P2 = P2->Next;

    while (P1 && P2) {
        if (P1->expon == P2->expon) {
            sum = P1->coef + P2->coef;
            if (sum) {
                temp = (Polynomial)malloc(sizeof(struct Node));
                temp->coef = sum;
                temp->expon = P1->expon;
                Rear->Next = temp;
                Rear = temp;
            }
            P1 = P1->Next;
            P2 = P2->Next;
        } else if (P1->expon > P2->expon) {
            temp = (Polynomial)malloc(sizeof(struct Node));
            temp->coef = P1->coef;
            temp->expon = P1->expon;
            Rear->Next = temp;
            Rear = temp;
            P1 = P1->Next;
        } else {
            temp = (Polynomial)malloc(sizeof(struct Node));
            temp->coef = P2->coef;
            temp->expon = P2->expon;
            Rear->Next = temp;
            Rear = temp;
            P2 = P2->Next;
        }
    }

    while (P1) {
        temp = (Polynomial)malloc(sizeof(struct Node));
        temp->coef = P1->coef;
        temp->expon = P1->expon;
        Rear->Next = temp;
        Rear = temp;
        P1 = P1->Next;
    }

    while (P2) {
        temp = (Polynomial)malloc(sizeof(struct Node));
        temp->coef = P2->coef;
        temp->expon = P2->expon;
        Rear->Next = temp;
        Rear = temp;
        P2 = P2->Next;
    }

    Rear->Next = NULL;
    temp = Front;
    Front = Front->Next;
    free(temp);

    return Front;
}

void PrintPoly(Polynomial P)
{
    int flag = 0;

    if (!P) {
        printf("0 0\n");
        return;
    }

    while (P) {
        if (!flag) {
            flag = 1;
        } else {
            printf(" ");
        }
        printf("%d %d", P->coef, P->expon);
        P = P->Next;
    }
    printf("\n");
}

以上代码中，CreatePoly() 函数用于创建多项式，AddPoly() 函数用于相加两个多项式，PrintPoly() 函数用于输出多项式。

在主函数中，先分别创建两个多项式，然后将它们相加，最后输出结果。