C语言多项式分式求导功能异常（switch case4）求助

核心错误分析 #

1. 多项式存储逻辑不匹配：
   • input_of_polynomials按单个项存储多项式：coefficient[i]是第i个项的系数，degree[i]是对应项的次数（比如输入2x²+3x，数组存储为coefficient[0]=2, degree[0]=2; coefficient[1]=3, degree[1]=1）。
   • 但function_divide错误地将系数数组当成按次数索引的结构（认为coefficient[i]是x^i的系数），导致f(x)和g(x)的计算完全错误。
2. 次数参数传递错误：
   • 调用derivative_divide_functions时传入degree_fx[0]，这只是第一个项的次数，并非多项式的最高次数，且存储格式错误的前提下该参数毫无意义。
3. 数值微分精度不足：
   • 使用前向差分(f(x+h)-f(x))/h截断误差较大，中心差分(f(x+h)-f(x-h))/(2h)精度更高，更适合数值导数计算。
4. 次要错误：
   • integration函数参数coefficient声明为float，但调用时传入double数组，存在类型不匹配问题。
   • quadratic_equation中根的计算错误：-(b / 2 * a)应为-(b/(2*a))，运算优先级处理错误。

修复后的完整代码 #

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

#define MAX 100

void display_polynomial(int *terms, double coefficient[], int degree[]);
void derivative_polynomial(int *terms, double coefficient[], int degree[]);
void integration(int *terms, double coefficient[], int degree[]);
void input_of_polynomials(int *terms, double coefficient[], int degree[]);
void quadratic_equation();
void derivative_divide();
double function_divide(int terms_fx, double coefficient_fx[], int degree_fx[], 
                       int terms_gx, double coefficient_gx[], int degree_gx[], double xd);
double derivative_divide_functions(int terms_fx, double coefficient_fx[], int degree_fx[], 
                                   int terms_gx, double coefficient_gx[], int degree_gx[], double xd);

int main(void)
{
    int choice;
    int terms;
    int degree[100];
    double coefficient[100];

    printf("|************************************************************************************************************|\n");
    printf("|\t\t        Polynomial Operations                                                                           |\n");
    printf("|************************************************************************************************************|\n");
    printf("|\t\t        Choose an Operation:                                                                            |\n");
    printf("| 1. Calculate Derivative                                                                                    |\n");
    printf("| 2. Perform Integration                                                                                     |\n");
    printf("| 3. Solve Quadratic Equation                                                                                |\n");
    printf("| 4. Calculate Derivative of Type f(x) / g(x)                                                                |\n");
    printf("|************************************************************************************************************|\n");
    printf("  Your Choice: ");

    scanf_s("%d", &choice);

    switch (choice)
    {
    case 1:
        {
            input_of_polynomials(&terms, coefficient, degree);
            printf("f(x)= ");
            display_polynomial(&terms, coefficient, degree);
            printf("\n\nf`(x)=");
            derivative_polynomial(&terms, coefficient, degree);
            printf("\n");
            break;
        }
    case 2:
        {
            input_of_polynomials(&terms, coefficient, degree);
            printf("f(x)= ");
            display_polynomial(&terms, coefficient, degree);
            printf("\n\nIntegral = ");
            integration(&terms, coefficient, degree);
            printf("\n");
            break;
        }
    case 3:
        {
            quadratic_equation();
            break;
        }
    case 4:
        {
            printf("Enter Value of X: ");
            double x;
            scanf_s("%lf", &x);

            int term_fx;
            double coefficient_fx[MAX];
            int degree_fx[MAX];
            input_of_polynomials(&term_fx, coefficient_fx, degree_fx);

            int term_gx;
            double coefficient_gx[MAX];
            int degree_gx[MAX];
            input_of_polynomials(&term_gx, coefficient_gx, degree_gx);

            printf("f(x)/g(x) = \n\n");
            display_polynomial(&term_fx, coefficient_fx, degree_fx);
            printf("\n------------\n");
            display_polynomial(&term_gx, coefficient_gx, degree_gx);
            printf("\n");

            double derivative_result = derivative_divide_functions(term_fx, coefficient_fx, degree_fx, 
                                                                  term_gx, coefficient_gx, degree_gx, x);
            printf("Derivative of (f(x) / g(x)) at x = %.2lf is %.4lf\n", x, derivative_result);

            break;
        }
    default:
        {
            printf("Invalid Input \n");
        }
        break;
    }
}

void display_polynomial(int *terms, double coefficient[], int degree[])
{
    for (int i = 0; i < *terms; i++)
    {
        if (coefficient[i] == 0)
        {
            continue;
        }
        else if (coefficient[i] > 0)
        {
            if (i != 0)
            {
                printf(" + ");
            }
        }
        else if (coefficient[i] < 0)
        {
            printf(" - ");
        }

        if (degree[i] == 0)
        {
            printf("%.1lf", fabs(coefficient[i]));
        }
        else if (degree[i] == 1)
        {
            if (fabs(coefficient[i]) != 1)
            {
                printf("%.1lf", fabs(coefficient[i]));
            }
            printf("x");
        }
        else
        {
            printf("%.1lf", fabs(coefficient[i]));
            printf("x^%d", degree[i]);
        }
    }
}

void derivative_polynomial(int *terms, double coefficient[], int degree[])
{
    int valid_terms = 0;
    for (int i = 0; i < *terms; i++)
    {
        coefficient[i] = coefficient[i] * degree[i];
        degree[i] = degree[i] - 1;
        if (coefficient[i] != 0)
        {
            valid_terms++;
        }
    }
    *terms = valid_terms;
    display_polynomial(terms, coefficient, degree);
}

void integration(int *terms, double coefficient[], int degree[])
{
    for (int i = 0; i < *terms; i++)
    {
        degree[i] = degree[i] + 1;
        coefficient[i] = coefficient[i] / degree[i];
    }
    display_polynomial(terms, coefficient, degree);
    printf(" + C \n");
}

void input_of_polynomials(int *terms, double coefficient[], int degree[]) {
    printf("Enter Number of Terms in the polynomial: ");
    scanf_s("%d", terms);

    for (int i = 0; i < *terms; i++) {
        printf("Enter Co-Efficient of Term %d: ", i + 1);
        scanf_s("%lf", &coefficient[i]);

        printf("Enter Degree of Term %d: ", i + 1);
        scanf_s("%d", &degree[i]);
        printf("\n");
    }
}

void quadratic_equation()
{
    double root1, root2;
    double a, b, c;

    printf("     QUADRATIC ROOTS CALCULATOR   \n\n");

    printf("Enter the Co-Efficient of x^2 (a) \n");
    scanf_s("%lf", &a);
    printf("Enter the Co-Efficient of x (b) \n");
    scanf_s("%lf", &b);
    printf("Enter the Constant (c) \n");
    scanf_s("%lf", &c);

    double discriminant = b*b - 4*a*c;
    if (discriminant >= 0)
    {
        double sqrt_d = sqrt(discriminant);
        if (discriminant == 0)
        {
            printf("\t\t Roots Are Real And Equal\n");
            root1 = root2 = -b/(2*a);
            printf("Roots of the Equation\t  ( %.1lfx^2 + %.1lfx + %.1lf ) Are :\n\t Root 1 : %.1lf \n\t Root 2 : %.1lf\n", a, b, c, root1, root2);
        }
        else
        {
            root1 = (-b + sqrt_d)/(2*a);
            root2 = (-b - sqrt_d)/(2*a);
            printf("Roots Are Real and Distinct \n");
            printf(" Roots of the Equation %.1lfx^2 + %.1lfx + %.1lf Are :\n\t Root 1 : %.1lf \tRoot2 :   %.1lf\n", a, b, c, root1, root2);
        }
    }
    else
    {
        printf("Roots Are Imaginary\n");
    }
}

void derivative_divide() {
    printf("Function of Type f(x) / g(x)\n");

    int term_fx;
    double coefficient_fx[MAX];
    int degree_fx[MAX];

    input_of_polynomials(&term_fx, coefficient_fx, degree_fx);

    int term_gx;
    double coefficient_gx[MAX];
    int degree_gx[MAX];

    input_of_polynomials(&term_gx, coefficient_gx, degree_gx);

    printf("Function is:\n");
    display_polynomial(&term_fx, coefficient_fx, degree_fx);
    printf("\n-----\n");
    display_polynomial(&term_gx, coefficient_gx, degree_gx);

    double x_value;
    printf("Enter the value of x for the derivative: ");
    scanf_s("%lf", &x_value);

    double derivative_result = derivative_divide_functions(term_fx, coefficient_fx, degree_fx, 
                                                          term_gx, coefficient_gx, degree_gx, x_value);
    printf("Derivative of (f(x) / g(x)) at x = %.2lf is %.4lf\n", x_value, derivative_result);
}

double function_divide(int terms_fx, double coefficient_fx[], int degree_fx[], 
                       int terms_gx, double coefficient_gx[], int degree_gx[], double xd) {
    double result_fx = 0.0, result_gx = 0.0;

    for (int i = 0; i < terms_fx; i++) {
        result_fx += coefficient_fx[i] * pow(xd, degree_fx[i]);
    }

    for (int i = 0; i < terms_gx; i++) {
        result_gx += coefficient_gx[i] * pow(xd, degree_gx[i]);
    }

    if (fabs(result_gx) < 1e-9) {
        printf("Error: g(x) is zero at x = %.2lf\n", xd);
        exit(EXIT_FAILURE);
    }

    return result_fx / result_gx;
}

double derivative_divide_functions(int terms_fx, double coefficient_fx[], int degree_fx[], 
                                   int terms_gx, double coefficient_gx[], int degree_gx[], double xd) {
    double const h = 1.0e-6;

    double fx_plus_h = function_divide(terms_fx, coefficient_fx, degree_fx, 
                                       terms_gx, coefficient_gx, degree_gx, xd + h);
    double fx_minus_h = function_divide(terms_fx, coefficient_fx, degree_fx, 
                                        terms_gx, coefficient_gx, degree_gx, xd - h);

    double derivative = (fx_plus_h - fx_minus_h) / (2 * h);

    return derivative;
}

关键修复点说明 #

1. 统一多项式存储逻辑：
   修改function_divide和derivative_divide_functions的参数，传入项数、系数数组、次数数组，遍历每个项计算多项式值，匹配input_of_polynomials的存储格式。
2. 修正参数传递逻辑：
   不再传递单个次数值，直接传入完整的次数数组，确保函数能遍历所有项完成计算。
3. 提升数值微分精度：
   将前向差分改为中心差分，减少截断误差，导数结果更准确。
4. 修复类型与运算错误：
   把integration的float参数改为double，避免类型转换问题；修正二次方程根的计算优先级，确保结果正确。
5. 增加异常处理：
   在function_divide中判断g(x)是否接近0，避免程序因除以0崩溃。

内容的提问来源于stack exchange，提问作者RobbaN