1.简单一元多项式的求导问题

#define _CRT_SECURE_NO_WARNINGS
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <ctype.h>

#define MAX_TERMS 100

// 结构体用于表示单项式
typedef struct {
    int coefficient; // 系数
    int exponent;    // 指数
} Term;

// 函数声明
void parsePolynomial(char* input, Term* polynomial, int* numTerms);
void derivative(Term* polynomial, int* numTerms);
void printPolynomial(Term* polynomial, int numTerms);

int main() {
    char input[100];
    Term polynomial[MAX_TERMS];
    int numTerms = 0;

    // 获取用户输入
    printf("请输入一元多项式：");
    fgets(input, sizeof(input), stdin);

    // 解析多项式
    parsePolynomial(input, polynomial, &numTerms);
    if (numTerms == 0) {
        printf("输入格式有误！\n");
        return 1;
    }

    // 求导
    derivative(polynomial, &numTerms);

    // 输出结果
    printf("求导后的多项式为：");
    printPolynomial(polynomial, numTerms);

    return 0;
}

// 解析多项式
void parsePolynomial(char* input, Term* polynomial, int* numTerms) {
    char* token = strtok(input, "+-\n");

    while (token != NULL) {
        int coefficient = 0;
        int exponent = 0;

        if (sscanf(token, "%dx^%d", &coefficient, &exponent) == 2) {
            // 处理正确格式的单项式
            polynomial[*numTerms].coefficient = coefficient;
            polynomial[*numTerms].exponent = exponent;
            (*numTerms)++;
        }
        else if (sscanf(token, "%dx", &coefficient) == 1) {
            // 单项式只有 x
            polynomial[*numTerms].coefficient = coefficient;
            polynomial[*numTerms].exponent = 1;
            (*numTerms)++;
        }
        else if (sscanf(token, "%d", &coefficient) == 1) {
            // 处理常数项
            polynomial[*numTerms].coefficient = coefficient;
            polynomial[*numTerms].exponent = 0;
            (*numTerms)++;
        }

        token = strtok(NULL, "+-\n");
    }
}

// 求导
void derivative(Term* polynomial, int* numTerms) {
    for (int i = 0; i < *numTerms; i++) {
        polynomial[i].coefficient *= polynomial[i].exponent;
        polynomial[i].exponent--;
    }

    // 去除指数为负数的项
    for (int i = 0; i < *numTerms; i++) {
        if (polynomial[i].exponent < 0) {
            for (int j = i; j < *numTerms - 1; j++) {
                polynomial[j] = polynomial[j + 1];
            }
            (*numTerms)--;
            i--; 
        }
    }

    // 处理减法项的导数
    for (int i = 0; i < *numTerms; i++) {
        if (i > 0 && polynomial[i].coefficient < 0) {
            polynomial[i].coefficient = -polynomial[i].coefficient;
        }
    }
}



// 打印多项式
void printPolynomial(Term* polynomial, int numTerms) {
    for (int i = 0; i < numTerms; i++) {
        if (polynomial[i].coefficient > 0 && i != 0) {
            printf("+");
        }
        if (polynomial[i].exponent == 0) {
            printf("%d", polynomial[i].coefficient);
        }
        else if (polynomial[i].exponent == 1) {
            printf("%dx", polynomial[i].coefficient);
        }
        else {
            printf("%dx^%d", polynomial[i].coefficient, polynomial[i].exponent);
        }
    }
    printf("\n");
}