一元多项式加减乘用链表

以下是使用链表实现一元多项式的加减乘的示例代码：

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

// 定义多项式的节点结构
typedef struct Node {
    int coef;  // 系数
    int exp;   // 指数
    struct Node* next;  // 指向下一个节点的指针
} Node;

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

// 在多项式的末尾添加一个节点
void appendNode(Node** poly, int coef, int exp) {
    Node* newNode = createNode(coef, exp);
    if (*poly == NULL) {
        *poly = newNode;
    } else {
        Node* curr = *poly;
        while (curr->next != NULL) {
            curr = curr->next;
        }
        curr->next = newNode;
    }
}

// 打印多项式
void printPoly(Node* poly) {
    Node* curr = poly;
    while (curr != NULL) {
        printf("%dx^%d ", curr->coef, curr->exp);
        if (curr->next != NULL) {
            printf("+ ");
        }
        curr = curr->next;
    }
    printf("\n");
}

// 多项式相加
Node* addPoly(Node* poly1, Node* poly2) {
    Node* result = NULL;
    Node* curr1 = poly1;
    Node* curr2 = poly2;
    while (curr1 != NULL && curr2 != NULL) {
        if (curr1->exp > curr2->exp) {
            appendNode(&result, curr1->coef, curr1->exp);
            curr1 = curr1->next;
        } else if (curr1->exp < curr2->exp) {
            appendNode(&result, curr2->coef, curr2->exp);
            curr2 = curr2->next;
        } else {
            int coefSum = curr1->coef + curr2->coef;
            if (coefSum != 0) {
                appendNode(&result, coefSum, curr1->exp);
            }
            curr1 = curr1->next;
            curr2 = curr2->next;
        }
    }
    while (curr1 != NULL) {
        appendNode(&result, curr1->coef, curr1->exp);
        curr1 = curr1->next;
    }
    while (curr2 != NULL) {
        appendNode(&result, curr2->coef, curr2->exp);
        curr2 = curr2->next;
    }
    return result;
}

// 多项式相减
Node* subtractPoly(Node* poly1, Node* poly2) {
    Node* result = NULL;
    Node* curr1 = poly1;
    Node* curr2 = poly2;
    while (curr1 != NULL && curr2 != NULL) {
        if (curr1->exp > curr2->exp) {
            appendNode(&result, curr1->coef, curr1->exp);
            curr1 = curr1->next;
        } else if (curr1->exp < curr2->exp) {
            appendNode(&result, -curr2->coef, curr2->exp);
            curr2 = curr2->next;
        } else {
            int coefDiff = curr1->coef - curr2->coef;
            if (coefDiff != 0) {
                appendNode(&result, coefDiff, curr1->exp);
            }
            curr1 = curr1->next;
            curr2 = curr2->next;
        }
    }
    while (curr1 != NULL) {
        appendNode(&result, curr1->coef, curr1->exp);
        curr1 = curr1->next;
    }
    while (curr2 != NULL) {
        appendNode(&result, -curr2->coef, curr2->exp);
        curr2 = curr2->next;
    }
    return result;
}

// 多项式相乘
Node* multiplyPoly(Node* poly1, Node* poly2) {
    Node* result = NULL;
    Node* curr1 = poly1;
    while (curr1 != NULL) {
        Node* curr2 = poly2;
        while (curr2 != NULL) {
            int coefProd = curr1->coef * curr2->coef;
            int expSum = curr1->exp + curr2->exp;
            appendNode(&result, coefProd, expSum);
            curr2 = curr2->next;
        }
        curr1 = curr1->next;
    }
    return result;
}

int main() {
    // 创建多项式1: 2x^3 + 3x^2 + 4x^1 + 5x^0
    Node* poly1 = NULL;
    appendNode(&poly1, 2, 3);
    appendNode(&poly1, 3, 2);
    appendNode(&poly1, 4, 1);
    appendNode(&poly1, 5, 0);

    // 创建多项式2: 1x^2 + 2x^1 + 3x^0
    Node* poly2 = NULL;
    appendNode(&poly2, 1, 2);
    appendNode(&poly2, 2, 1);
    appendNode(&poly2, 3, 0);

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

    // 多项式相加
    Node* sum = addPoly(poly1, poly2);
    printf("多项式相加: ");
    printPoly(sum);

    // 多项式相减
    Node* diff = subtractPoly(poly1, poly2);
    printf("多项式相减: ");
    printPoly(diff);

    // 多项式相乘
    Node* prod = multiplyPoly(poly1, poly2);
    printf("多项式相乘: ");
    printPoly(prod);

    return 0;
}