一元多项式 加法 减法 乘法

#include<stdio.h>
#include<stdlib.h>
//系数 coefficient，coef
//指数 exponent, expon
typedef struct polyNode* polynomial;
struct polyNode {
    int coef;
    int expon;
    polynomial link;
};

polynomial readPoly();
//输入 必须是从幂的降幂 输入
void attach(int c, int e, polynomial* prear);
//把这一项插入到链表中
polynomial polyAdd(polynomial p1, polynomial p2);
//主要进行多项式加法运算
polynomial polyMul(polynomial p1, polynomial p2);
//主要进行多项式乘法运算
polynomial polySub(polynomial p1, polynomial p2);
//主要进行多项式减法运算
int compare(int a, int b);//比较两个项的指数
void printPoly(polynomial p);
void display();//显示计算器的选项


int main(void) {
    polynomial p1, p2, ps;
    int t;
    while (1) {
        display();
        scanf("%d", &t);
        switch (t) {
        case 1:
            p1 = readPoly();
            p2 = readPoly();
            ps = polyAdd(p1, p2);
            printPoly(ps);
            printf("是否继续操作: 是请输入1，否则输出0:");
            scanf("%d", &t);
            if (t == 1)
                system("cls");
            else if (t == 0)
                return 0;
            break;
        case 2:
            p1 = readPoly();
            p2 = readPoly();
            ps = polySub(p1, p2);
            printPoly(ps);
            printf("是否继续操作: 是请输入1，否则输出0:");
            scanf("%d", &t);
            if (t == 1)
                system("cls");
            else if (t == 0)
                return 0;
            break;
        case 3:
            p1 = readPoly();
            p2 = readPoly();
            ps = polyMul(p1, p2);
            printPoly(ps);
            printf("是否继续操作: 是请输入1，否则输出0:");
            scanf("%d", &t);
            if (t == 1)
                system("cls");
            else if (t == 0)
                return 0;
            break;
        }
    }
    return 0;
}

void display() {
    printf("1.多项式加法

");
    printf("2.多项式减法

");
    printf("3.多项式乘法

");
    printf("请输入所执行内容：");
}

polynomial readPoly() {
    int n, c, e;
    polynomial rear, p, t;

    p = (polynomial)malloc(sizeof(struct polyNode));
    p->link = NULL;
    rear = p;
    scanf("%d", &n);//这个语句用来说明有几项
    while (n--) {
        scanf("%d%d", &c, &e);
        attach(c, e, &rear);
    }
    t = p; p = p->link; free(t);
    return p;
}

void attach(int c, int e, polynomial* prear) {
    polynomial p;

    p = (polynomial)malloc(sizeof(struct polyNode));
    p->coef = c;
    p->expon = e;
    p->link = NULL;
    (*prear)->link = p;
    *prear = p;//修改prear的值
}

polynomial polyAdd(polynomial p1, polynomial p2) {
    polynomial front, rear, t;
    int sum;

    rear = (polynomial)malloc(sizeof(struct polyNode));
    front = rear;
    //对比相应项的指数，若指数相同，则把系数相加
    //否则，把指数大的先插入链表，再指针后移一位
    while (p1 && p2) {
        switch (compare(p1->expon, p2->expon)) {
        case 1:
            attach(p1->coef, p1->expon, &rear);
            p1 = p1->link;
            break;
        case -1:
            attach(p2->coef, p2->expon, &rear);
            p2 = p2->link;
            break;
        case 0:
            sum = p1->coef + p2->coef;
            if (sum)    attach(sum, p1->expon, &rear);
            p1 = p1->link;
            p2 = p2->link;
            break;
        }
    }
    //因为肯定最多有一个多项式剩余项，所以把残留的也存入链表
    for (; p1; p1 = p1->link)    attach(p1->coef, p1->expon, &rear);
    for (; p2; p2 = p2->link)    attach(p2->coef, p2->expon, &rear);
    rear->link = NULL;
    t = front;
    front = front->link;
    free(t);//把头空节点释放
    return front;
}

int compare(int a, int b) {
    if (a == b)    return 0;
    else if (a > b)    return 1;
    else return -1;
}

void printPoly(polynomial p) {
    int flag = 0;

    if (!p) {
        printf("0 0
");
        return;
    }

    while (p) {
        if (!flag)    flag = 1;
        else printf(" ");//主要在每一组数据之后输出一个空格隔开
        printf("%d %d", p->coef, p->expon);
        p = p->link;
    }

    printf("
");
}

polynomial polyMul(polynomial p1, polynomial p2) {
    polynomial p, rear, t1, t2, t;
    int c, e;

    if (!p1 || !p2)    return NULL;
    t1 = p1; t2 = p2;
    p = (polynomial)malloc(sizeof(struct polyNode));
    p->link = NULL;
    rear = p;
    //先用p1的第一项 乘以p2，得到p
    while (t2) {
        attach(t1->coef * t2->coef, t1->expon + t2->expon, &rear);
        t2 = t2->link;
    }
    t1 = t1->link;
    //下面这一大部分 是用t1的 从第二项开始，每一项乘以整个t2。
    while (t1) {
        t2 = p2; rear = p;
        while (t2) {
            e = t1->expon + t2->expon;
            c = t1->coef * t2->coef;
            //把该结点插入到正确的位置，因为指数是按降序排列的
            while (rear->link && rear->link->expon > e)
                rear = rear->link;
            //若找到位置，则需要和下一项比，因为指数可能会相同
            //相同则系数相加
            //否则直接插入即可
            if (rear->link && rear->link->expon == e) {
                if (rear->link->coef + c)
                    rear->link->coef += c;
                else {
                    t = rear->link;
                    rear->link = t->link;
                    free(t);
                }
            }
            else {
                t = (polynomial)malloc(sizeof(struct polyNode));
                t->coef = c; t->expon = e;
                t->link = rear->link;
                rear->link = t;
                rear = rear->link;
            }
            t2 = t2->link;
        }
        t1 = t1->link;
    }
    t2 = p; p = p->link; free(t2);//删除头空节点
    return p;
}

polynomial polySub(polynomial p1, polynomial p2) {
    polynomial p = p2;
    while (p) {
        p->coef *= -1;
        p = p->link;
    }
    //下面是加法运算的代码，因为根据多项式减法法则
    //也只是 类似减数的那一个多项式，把每一项的系数取相反数
    //再相加即可
    polynomial front, rear, t;
    int sum;

    rear = (polynomial)malloc(sizeof(struct polyNode));
    front = rear;
    while (p1 && p2) {
        switch (compare(p1->expon, p2->expon)) {
        case 1:
            attach(p1->coef, p1->expon, &rear);
            p1 = p1->link;
            break;
        case -1:
            attach(p2->coef, p2->expon, &rear);
            p2 = p2->link;
            break;
        case 0:
            sum = p1->coef + p2->coef;
            if (sum)    attach(sum, p1->expon, &rear);
            p1 = p1->link;
            p2 = p2->link;
            break;
        }
    }

    for (; p1; p1 = p1->link)    attach(p1->coef, p1->expon, &rear);
    for (; p2; p2 = p2->link)    attach(p2->coef, p2->expon, &rear);
    rear->link = NULL;
    t = front;
    front = front->link;
    free(t);
    return front;
}