问题描述 按照升幂排列的一元多项式P n ​ (x)=p 1 ​ x+p 2 ​ x 2 +⋯+p n ​ x n 可以用线性表来表示P=(p 1 ​ ,p 2 ​ ,…,p n ​ )，对于一元多项式各种操作，实际上可以利用线性表来处理。若多项式的非零项指数很高并且非零项很少称之为稀疏多项式，此时使用链式存储结构较为方便。设计一个程序，实现一元稀疏多项式简单计算器。 基本要求 稀疏多项式简单计算器的基本功能是： （1）输入并建立多项式； （2）输出多项式，输出形式为整数序列：n,p 1 ​ ,e 1 ​ ,p 2 ​ ,e 2 ​ …,p n ​ ,e n ​ ，其中n是多项式的项数，p i ​ 和e i ​ 分别是第i项的系数和指数，序列按指数升幂排列； （3） 多项式a和b相加，建立多项式a+b； （4） 多项式a和c相减，建立多项式a-b； （5） 计算多项式在x处的值。使用C语言写

以下是一元稀疏多项式简单计算器的代码实现：

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

// 定义多项式项的结构体
typedef struct PolyNode {
    int coef;   // 系数
    int expo;   // 指数
    struct PolyNode* next;  // 指向下一项的指针
} PolyNode, *Polynomial;

// 函数声明
Polynomial createPoly();
void printPoly(Polynomial P);
Polynomial addPoly(Polynomial P1, Polynomial P2);
Polynomial subPoly(Polynomial P1, Polynomial P2);
int calcPoly(Polynomial P, int x);

int main() {
    // 输入并建立多项式
    printf("请输入第一个多项式（按指数降幂输入，输入-1结束）：");
    Polynomial P1 = createPoly();
    printf("第一个多项式为：");
    printPoly(P1);

    printf("请输入第二个多项式（按指数降幂输入，输入-1结束）：");
    Polynomial P2 = createPoly();
    printf("第二个多项式为：");
    printPoly(P2);

    // 多项式相加
    Polynomial P_add = addPoly(P1, P2);
    printf("两个多项式相加的结果为：");
    printPoly(P_add);

    // 多项式相减
    Polynomial P_sub = subPoly(P1, P2);
    printf("第一个多项式减去第二个多项式的结果为：");
    printPoly(P_sub);

    // 计算多项式在x处的值
    int x;
    printf("请输入x的值：");
    scanf("%d", &x);
    int result = calcPoly(P1, x);
    printf("第一个多项式在x=%d处的值为：%d\n", x, result);

    return 0;
}

// 创建多项式
Polynomial createPoly() {
    Polynomial P = (Polynomial)malloc(sizeof(PolyNode));  // 头结点
    P->next = NULL;
    Polynomial Rear = P;

    int c, e;
    scanf("%d %d", &c, &e);
    while (e != -1) {
        Polynomial newNode = (Polynomial)malloc(sizeof(PolyNode));
        newNode->coef = c;
        newNode->expo = e;
        newNode->next = NULL;
        Rear->next = newNode;
        Rear = newNode;

        scanf("%d %d", &c, &e);
    }

    return P;
}

// 输出多项式
void printPoly(Polynomial P) {
    if (P->next == NULL) {
        printf("0\n");
        return;
    }

    int flag = 0;
    while (P->next != NULL) {
        P = P->next;
        if (P->coef > 0 && flag != 0) {
            printf("+");
        }
        if (P->coef != 1 && P->coef != -1) {
            printf("%d", P->coef);
        } else if (P->expo == 0) {
            printf("%d", P->coef);
        } else if (P->coef == -1) {
            printf("-");
        }
        if (P->expo == 0) {
            flag = 1;
            continue;
        } else if (P->expo == 1) {
            printf("x");
        } else {
            printf("x^%d", P->expo);
        }
        flag = 1;
    }
    printf("\n");
}

// 多项式相加
Polynomial addPoly(Polynomial P1, Polynomial P2) {
    Polynomial P = (Polynomial)malloc(sizeof(PolyNode));  // 头结点
    P->next = NULL;
    Polynomial Rear = P;

    Polynomial p1 = P1->next;
    Polynomial p2 = P2->next;
    while (p1 != NULL && p2 != NULL) {
        if (p1->expo > p2->expo) {
            Polynomial newNode = (Polynomial)malloc(sizeof(PolyNode));
            newNode->coef = p1->coef;
            newNode->expo = p1->expo;
            newNode->next = NULL;
            Rear->next = newNode;
            Rear = newNode;
            p1 = p1->next;
        } else if (p1->expo < p2->expo) {
            Polynomial newNode = (Polynomial)malloc(sizeof(PolyNode));
            newNode->coef = p2->coef;
            newNode->expo = p2->expo;
            newNode->next = NULL;
            Rear->next = newNode;
            Rear = newNode;
            p2 = p2->next;
        } else {
            int sum = p1->coef + p2->coef;
            if (sum != 0) {
                Polynomial newNode = (Polynomial)malloc(sizeof(PolyNode));
                newNode->coef = sum;
                newNode->expo = p1->expo;
                newNode->next = NULL;
                Rear->next = newNode;
                Rear = newNode;
            }
            p1 = p1->next;
            p2 = p2->next;
        }
    }

    while (p1 != NULL) {
        Polynomial newNode = (Polynomial)malloc(sizeof(PolyNode));
        newNode->coef = p1->coef;
        newNode->expo = p1->expo;
        newNode->next = NULL;
        Rear->next = newNode;
        Rear = newNode;
        p1 = p1->next;
    }
    while (p2 != NULL) {
        Polynomial newNode = (Polynomial)malloc(sizeof(PolyNode));
        newNode->coef = p2->coef;
        newNode->expo = p2->expo;
        newNode->next = NULL;
        Rear->next = newNode;
        Rear = newNode;
        p2 = p2->next;
    }

    return P;
}

// 多项式相减
Polynomial subPoly(Polynomial P1, Polynomial P2) {
    Polynomial P = (Polynomial)malloc(sizeof(PolyNode));  // 头结点
    P->next = NULL;
    Polynomial Rear = P;

    Polynomial p1 = P1->next;
    Polynomial p2 = P2->next;
    while (p1 != NULL && p2 != NULL) {
        if (p1->expo > p2->expo) {
            Polynomial newNode = (Polynomial)malloc(sizeof(PolyNode));
            newNode->coef = p1->coef;
            newNode->expo = p1->expo;
            newNode->next = NULL;
            Rear->next = newNode;
            Rear = newNode;
            p1 = p1->next;
        } else if (p1->expo < p2->expo) {
            Polynomial newNode = (Polynomial)malloc(sizeof(PolyNode));
            newNode->coef = -p2->coef;
            newNode->expo = p2->expo;
            newNode->next = NULL;
            Rear->next = newNode;
            Rear = newNode;
            p2 = p2->next;
        } else {
            int diff = p1->coef - p2->coef;
            if (diff != 0) {
                Polynomial newNode = (Polynomial)malloc(sizeof(PolyNode));
                newNode->coef = diff;
                newNode->expo = p1->expo;
                newNode->next = NULL;
                Rear->next = newNode;
                Rear = newNode;
            }
            p1 = p1->next;
            p2 = p2->next;
        }
    }

    while (p1 != NULL) {
        Polynomial newNode = (Polynomial)malloc(sizeof(PolyNode));
        newNode->coef = p1->coef;
        newNode->expo = p1->expo;
        newNode->next = NULL;
        Rear->next = newNode;
        Rear = newNode;
        p1 = p1->next;
    }
    while (p2 != NULL) {
        Polynomial newNode = (Polynomial)malloc(sizeof(PolyNode));
        newNode->coef = -p2->coef;
        newNode->expo = p2->expo;
        newNode->next = NULL;
        Rear->next = newNode;
        Rear = newNode;
        p2 = p2->next;
    }

    return P;
}

// 计算多项式在x处的值
int calcPoly(Polynomial P, int x) {
    int result = 0;
    while (P->next != NULL) {
        P = P->next;
        result += P->coef * pow(x, P->expo);
    }

    return result;
}

代码中使用了链式存储结构来表示多项式，分别实现了创建多项式、输出多项式、多项式相加、多项式相减和计算多项式在x处的值的功能。