02-线性结构2 一元多项式的乘法与加法运算

最新推荐文章于 2025-04-29 19:58:03 发布

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最新推荐文章于 2025-04-29 19:58:03 发布

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分类专栏： PTA 数据结构文章标签： c语言

本文链接：https://blog.youkuaiyun.com/WY200101/article/details/120750320

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这篇博客介绍了如何使用C语言实现多项式链表，包括多项式的输入、插入操作，以及两个多项式的求和与乘积。通过链表结构动态存储多项式，并提供了详细的代码实现。

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结果：
在这里插入图片描述

具体后面有时间再写吧，要找时间复习一下指针和结构体之类的了。

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

typedef struct PolyomialNode* PolyomialType;

struct PolyomialNode
{
    int coef;//系数coefficient
    int expon; //指数
    PolyomialType link;
};

PolyomialType input_init(int N) //接收输入
{
    PolyomialType P = (PolyomialType)malloc(sizeof(struct PolyomialNode));
    PolyomialType Header = NULL;
    PolyomialType S = NULL;

    for (int i = 0; i < N; i++)
    {
        S = (PolyomialType)malloc(sizeof(struct PolyomialNode));
        while(!scanf("%d", &(S->coef)));
        while(!scanf("%d", &(S->expon)));
        P->link = S;
        P = S;
        if (Header==NULL)
            Header = S;
    }
    S = (PolyomialType)malloc(sizeof(struct PolyomialNode));
    S->link = NULL;
    P->link = S;//使得链表最后一个元素时指向NULL
    P = S;
    //此处若直接P.link=NULL则会漏掉最后一个数
    return Header;
}

void Insert(PolyomialType *P, int expon, int coef) //插入元素
{
    PolyomialType S = NULL;
    S = (PolyomialType)malloc(sizeof(struct PolyomialNode));
    S->expon = expon;
    S->coef = coef;
    S->link = NULL;
    (*P)->link = S;
    (*P) = S;
    return ;
}

PolyomialType Sum(PolyomialType T1, PolyomialType T2) //求和多项式
{
    PolyomialType P = (PolyomialType)malloc(sizeof(struct PolyomialNode));
    PolyomialType S = NULL, Header = P;
    // PolyomialType T1 = *P1, T2 = *P2;

    while (T2->link && T1->link) //两边同时不为空时
    {
        if (T1->expon == T2->expon)
        {
            if((T1->coef+T2->coef)!=0) //同类项合并时有抵消则不添加
                Insert(&P, T1->expon, T1->coef+T2->coef);
            T1 = T1->link;
            T2 = T2->link;
        }
        else if(T1->expon > T2->expon)
        {
            Insert(&P, T1->expon, T1->coef);
            T1 = T1->link;
        }
        else if(T1->expon < T2->expon)
        {
            Insert(&P, T2->expon, T2->coef);
            T2 = T2->link;
        }
    }
    while (T2->link)
    {
        Insert(&P, T2->expon, T2->coef);
        T2 = T2->link;
    }
    while (T1->link)
    {
        Insert(&P, T1->expon, T1->coef);
        T1 = T1->link;
    }

    S = (PolyomialType)malloc(sizeof(struct PolyomialNode));
    S->link = NULL;
    P->link = S;//使得链表最后一个元素时指向NULL
    P = S;
    return Header->link;
}

PolyomialType Multiply(PolyomialType P1, PolyomialType P2) //求乘积多项式
{
    PolyomialType Sum_P = (PolyomialType)malloc(sizeof(struct PolyomialNode));
    Sum_P->link = NULL;
    PolyomialType S = NULL;
    PolyomialType T1 = P1, T2 = P2;

    while (T2->link) //两边同时不为空时
    {
        PolyomialType P = (PolyomialType)malloc(sizeof(struct PolyomialNode));
        P->link = NULL;
        PolyomialType S = NULL, Headers = P;
        
        while (T1->link)
        {
            Insert(&P, T1->expon+T2->expon, T1->coef*T2->coef);
            T1 = T1->link;
        }
        S = (PolyomialType)malloc(sizeof(struct PolyomialNode));
        S->link = NULL;
        P->link = S;//使得链表最后一个元素时指向NULL
        Sum_P = Sum(Sum_P,Headers->link);
        free(P);
        T2 = T2->link;
        T1 = P1;
    }

    return Sum_P;
}

int main()
{
    int N = 0;
    PolyomialType P1 = (PolyomialType)malloc(sizeof(struct PolyomialNode));
    PolyomialType P2 = (PolyomialType)malloc(sizeof(struct PolyomialNode));
    PolyomialType S;

    while(!scanf("%d",&N));
    if(N==0)//输入为零项时
    {
        P1->coef = 0;
        P1->expon = 0;
        S = (PolyomialType)malloc(sizeof(struct PolyomialNode));
        S->link = NULL;
        P2->link = S;//使得链表最后一个元素时指向NULL
    }
    else P1 = input_init(N);

    while(!scanf("%d",&N));
    if(N==0)
    {
        P2->coef = 0;
        P2->expon = 0;
        S = (PolyomialType)malloc(sizeof(struct PolyomialNode));
        S->link = NULL;
        P2->link = S;//使得链表最后一个元素时指向NULL
    }
    else P2 = input_init(N);

    PolyomialType Sum_P = Sum(P1, P2);
    PolyomialType Multiply_P = Multiply(P1, P2);

    if(!Multiply_P->link) // 系数和指数取上限，结果有零多项式
    {
        printf("0 0");
    }
    else
        while (Multiply_P->link)
        {
            printf("%d %d", (*Multiply_P).coef, (*Multiply_P).expon);
            Multiply_P = Multiply_P->link;
            if(Multiply_P->coef==0 && Multiply_P==0)
                break;
            if(Multiply_P->link)
                printf(" ");
        }
    printf("\n");
    if(!Sum_P->link) // 系数和指数取上限，结果有零多项式
        printf("0 0");
    while (Sum_P->link)
    {
        printf("%d %d", (*Sum_P).coef, (*Sum_P).expon);
        Sum_P = Sum_P->link;
        if(Multiply_P->coef==0 && Multiply_P==0)
            break;
        if(Sum_P->link)
            printf(" ");
    }
    
    return 0;
}