设有一元多项式Am(x) 和Bn(x)。 Am(x) = A0+A1x1+A2x2+A3x3+… +Amxm Bn(x) = B0+B1x1+B2x2+B3x3+… +Bnxn 试求M(x)= Am(x)+Bn(x)、N(x)= Am(x)-Bn(x)。利用C语言实现 (1)要求结果M(x)中无重复阶项和无零系数项。 (2)要求输出结果的升幂和降幂两种排列情况。 (3)设计实现菜单方式的交互界面，界面友好，可反复操作。

以下是实现此功能的C语言代码，其中使用了结构体来表示多项式：

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

#define MAX_DEGREE 100

typedef struct {
    int degree; // 多项式最高阶次数
    float coefficient[MAX_DEGREE + 1]; // 多项式系数
} Polynomial;

// 多项式相加
Polynomial add(Polynomial a, Polynomial b) {
    Polynomial result;
    int i;
    for (i = 0; i <= MAX_DEGREE; i++) {
        result.coefficient[i] = 0;
    }
    result.degree = a.degree > b.degree ? a.degree : b.degree;
    for (i = 0; i <= result.degree; i++) {
        result.coefficient[i] = a.coefficient[i] + b.coefficient[i];
    }
    return result;
}

// 多项式相减
Polynomial subtract(Polynomial a, Polynomial b) {
    Polynomial result;
    int i;
    for (i = 0; i <= MAX_DEGREE; i++) {
        result.coefficient[i] = 0;
    }
    result.degree = a.degree > b.degree ? a.degree : b.degree;
    for (i = 0; i <= result.degree; i++) {
        result.coefficient[i] = a.coefficient[i] - b.coefficient[i];
    }
    return result;
}

// 输出多项式
void print(Polynomial p) {
    int i;
    printf("Degree: %d\n", p.degree);
    printf("Coefficients: ");
    for (i = 0; i <= p.degree; i++) {
        printf("%g ", p.coefficient[i]);
    }
    printf("\n");
}

// 多项式去重和去零
Polynomial simplify(Polynomial p) {
    int i, j;
    Polynomial result;
    result.degree = p.degree;
    for (i = 0; i <= p.degree; i++) {
        result.coefficient[i] = p.coefficient[i];
    }
    // 去重
    for (i = 0; i <= result.degree; i++) {
        for (j = i + 1; j <= result.degree; j++) {
            if (i != j && result.coefficient[i] != 0 && result.coefficient[i] == result.coefficient[j]) {
                result.coefficient[j] = 0;
            }
        }
    }
    // 去零
    for (i = 0; i <= result.degree; i++) {
        if (result.coefficient[i] == 0) {
            result.degree--;
            for (j = i; j <= result.degree; j++) {
                result.coefficient[j] = result.coefficient[j + 1];
            }
        }
    }
    return result;
}

int main() {
    Polynomial a, b, m, n;
    int choice;
    do {
        printf("Menu:\n");
        printf("1. Input polynomials\n");
        printf("2. Add polynomials\n");
        printf("3. Subtract polynomials\n");
        printf("4. Print polynomials (ascending order)\n");
        printf("5. Print polynomials (descending order)\n");
        printf("0. Exit\n");
        printf("Enter your choice: ");
        scanf("%d", &choice);
        switch (choice) {
            case 1:
                // 输入多项式
                int i;
                printf("Enter the degree of polynomial A (<= %d): ", MAX_DEGREE);
                scanf("%d", &a.degree);
                printf("Enter the coefficients of polynomial A:\n");
                for (i = 0; i <= a.degree; i++) {
                    scanf("%f", &a.coefficient[i]);
                }
                printf("Enter the degree of polynomial B (<= %d): ", MAX_DEGREE);
                scanf("%d", &b.degree);
                printf("Enter the coefficients of polynomial B:\n");
                for (i = 0; i <= b.degree; i++) {
                    scanf("%f", &b.coefficient[i]);
                }
                break;
            case 2:
                // 多项式相加
                m = simplify(add(a, b));
                printf("M(x) = A(x) + B(x):\n");
                print(m);
                break;
            case 3:
                // 多项式相减
                n = simplify(subtract(a, b));
                printf("N(x) = A(x) - B(x):\n");
                print(n);
                break;
            case 4:
                // 升幂排序输出
                printf("Polynomial A:\n");
                print(a);
                printf("Polynomial B:\n");
                print(b);
                printf("Polynomial M:\n");
                print(m);
                printf("Polynomial N:\n");
                print(n);
                break;
            case 5:
                // 降幂排序输出
                printf("Polynomial A:\n");
                int j;
                printf("Degree: %d\n", a.degree);
                printf("Coefficients: ");
                for (j = a.degree; j >= 0; j--) {
                    printf("%g ", a.coefficient[j]);
                }
                printf("\n");
                printf("Polynomial B:\n");
                printf("Degree: %d\n", b.degree);
                printf("Coefficients: ");
                for (j = b.degree; j >= 0; j--) {
                    printf("%g ", b.coefficient[j]);
                }
                printf("\n");
                printf("Polynomial M:\n");
                printf("Degree: %d\n", m.degree);
                printf("Coefficients: ");
                for (j = m.degree; j >= 0; j--) {
                    printf("%g ", m.coefficient[j]);
                }
                printf("\n");
                printf("Polynomial N:\n");
                printf("Degree: %d\n", n.degree);
                printf("Coefficients: ");
                for (j = n.degree; j >= 0; j--) {
                    printf("%g ", n.coefficient[j]);
                }
                printf("\n");
                break;
            case 0:
                // 退出程序
                break;
            default:
                printf("Invalid choice!\n");
        }
        printf("\n");
    } while (choice != 0);

    return 0;
}

在程序中，首先定义了一个结构体 `Polynomial` 表示多项式，包括最高阶次数和系数数组。然后分别实现了多项式相加、多项式相减、输出多项式、多项式去重和去零等函数。在主函数中，使用菜单方式的交互界面，根据用户输入的选择进行相应的操作。其中，升幂排序输出和降幂排序输出使用不同的方式实现。