C言語で一変数多項式の演算を実装の方法

C言語で、構造体を使用して一元多項式を表し、対応する操作関数を定義して多項式の演算を実行できます。以下に簡単な実装例を示します。

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

typedef struct PolyNode {
    float coef;  // 系数
    int exp;  // 指数
    struct PolyNode* next;  // 指向下一项的指针
} PolyNode;

typedef PolyNode* Polynomial;  // 多项式类型

// 创建一个新的项
PolyNode* createNode(float coef, int exp) {
    PolyNode* newNode = (PolyNode*)malloc(sizeof(PolyNode));
    newNode->coef = coef;
    newNode->exp = exp;
    newNode->next = NULL;
    return newNode;
}

// 插入一项到多项式的末尾
void insertTerm(Polynomial* poly, float coef, int exp) {
    PolyNode* newNode = createNode(coef, exp);
    if (*poly == NULL) {
        *poly = newNode;
    } else {
        PolyNode* curr = *poly;
        while (curr->next != NULL) {
            curr = curr->next;
        }
        curr->next = newNode;
    }
}

// 打印多项式
void printPolynomial(Polynomial poly) {
    PolyNode* curr = poly;
    while (curr != NULL) {
        printf("%.2fx^%d", curr->coef, curr->exp);
        if (curr->next != NULL) {
            printf(" + ");
        }
        curr = curr->next;
    }
    printf("\n");
}

// 相加两个多项式
Polynomial addPolynomials(Polynomial poly1, Polynomial poly2) {
    Polynomial sumPoly = NULL;
    PolyNode* curr1 = poly1;
    PolyNode* curr2 = poly2;

    while (curr1 != NULL && curr2 != NULL) {
        if (curr1->exp > curr2->exp) {
            insertTerm(&sumPoly, curr1->coef, curr1->exp);
            curr1 = curr1->next;
        } else if (curr1->exp < curr2->exp) {
            insertTerm(&sumPoly, curr2->coef, curr2->exp);
            curr2 = curr2->next;
        } else {
            float coefSum = curr1->coef + curr2->coef;
            if (coefSum != 0) {
                insertTerm(&sumPoly, coefSum, curr1->exp);
            }
            curr1 = curr1->next;
            curr2 = curr2->next;
        }
    }

    // 将剩余项加入和多项式中
    while (curr1 != NULL) {
        insertTerm(&sumPoly, curr1->coef, curr1->exp);
        curr1 = curr1->next;
    }
    while (curr2 != NULL) {
        insertTerm(&sumPoly, curr2->coef, curr2->exp);
        curr2 = curr2->next;
    }

    return sumPoly;
}

int main() {
    Polynomial poly1 = NULL;
    Polynomial poly2 = NULL;
    Polynomial sumPoly = NULL;

    // 初始化多项式1
    insertTerm(&poly1, 3.0, 2);
    insertTerm(&poly1, 4.0, 1);
    insertTerm(&poly1, 2.0, 0);

    // 初始化多项式2
    insertTerm(&poly2, 1.0, 3);
    insertTerm(&poly2, -2.0, 2);
    insertTerm(&poly2, 5.0, 0);

    // 打印多项式1和多项式2
    printf("Polynomial 1: ");
    printPolynomial(poly1);
    printf("Polynomial 2: ");
    printPolynomial(poly2);

    // 相加两个多项式
    sumPoly = addPolynomials(poly1, poly2);

    // 打印结果多项式
    printf("Sum of polynomials: ");
    printPolynomial(sumPoly);

    return 0;
}

上記の例では、多項式の各項を PolyNode 構造体で表しています。PolyNode 構造体は係数 (coef) および指数 (exp) の 2 つのメンバ変数と、次の項を指すポインター next を持っています。さらに、多項式の別名として Polynomial 型を定義し、createNode などの操作関数も定義しています。