一元多项式的表示及加减乘除运算

例如：如何实现用线性链表表示多项式的加法运算？

根据一元多项式相加的运算规则：对于两个一元多项式中所有指数相同的项，对应系数相加，若其和不为零，则构成“和多项式”中的一项；对于两个一元多项式中所有指数不相同的项，则分别复抄到“和多项式”中去。

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

typedef struct polyn
{
    float coef;
    int expn;
    struct polyn* next;
}PolyNode,*PLinkList;  

PLinkList CreatePolyn();//创建一元多项式，使一元多项式呈指数递减
void OutPut(PLinkList head);//输出一元多项式
PLinkList Addition(PLinkList L1,PLinkList L2);//多项式的加法
PLinkList Subtraction(PLinkList L1,PLinkList L2);//多项式的减法
PLinkList Reverse(PLinkList head);//将生成的链表逆置，使一元多项式呈指数递增形式
PLinkList MultiplyPolyn(PLinkList L1,PLinkList L2);//多项式的乘法 

#include "test.h"  

PLinkList CreatePolyn()//创建一元多项式，使一元多项式呈指数递减
{
    PolyNode *p,*q,*s;
    PolyNode *head = NULL;
    int expn2;
    float coef2;
    head = (PLinkList)malloc(sizeof(PolyNode));//动态生成头结点
    if(!head)
    {
        return NULL;
    }
    head->coef = 0.0;//初始化
    head->expn = 0;
    head->next = NULL;
    do
    {
        printf("输入系数coef(系数和指数都为0结束)");
        scanf("%f",&coef2);
        printf("输入指数数exp(系数和指数都为0结束)");
        scanf("%d",&expn2);
        if((long)coef2 == 0 && expn2 == 0)
        {
            break;
        }
        s = (PLinkList)malloc(sizeof(PolyNode));
        if(!s)
        {
            return NULL;
        }
        s->expn = expn2;
        s->coef = coef2;
        q = head->next ;
        p = head;
        while(q && expn2 < q->expn)
        {
            p = q;
            q = q->next ;
        }
        if(q == NULL || expn2 > q->expn)
        {
            p->next = s;
            s->next = q;
        }
        else
        {
            q->coef += coef2;
        }
    }while(1);
    return head;
}  

void OutPut(PLinkList head)//输出一元多项式
{
    PolyNode *p = head->next ;
    while(p)
    {
        printf("%1.1f",p->coef);
        if(p->expn)
        {
            printf("*x^%d",p->expn);
        }
        if(p->next && p->next->coef > 0)
        {
            printf("+");
        }
        p = p->next ;
    }
}  

PolyNode *Addition(PLinkList L1,PLinkList L2)//多项式的加法
{
    PolyNode *pa,*pb,*pc,*u,*head;
    head = (PLinkList)malloc(sizeof(PolyNode));
    if(!head)
    {
        return NULL;
    }
    head->coef = 0.0;
    head->expn = 0;
    head->next = NULL;
    pc = head;
    L2 = Reverse(L2);
    pa = L1->next ;
    pb = L2->next ;
    while(pa != NULL && pb != NULL)
    {
        if(pa->expn == pb->expn)
        {
            u = (PLinkList)malloc(sizeof(PolyNode));
            if(!u)
            {
                return NULL;
            }
            u->coef = pa->coef + pb->coef ;
            u->expn = pa->expn ;
            pa = pa->next ;
            pb = pb->next ;
            u->next = pc->next ;
            pc->next = u;
            pc = u;
        }
        else if(pa->expn > pb->expn)
        {
            u = (PLinkList)malloc(sizeof(PolyNode));
            if(!u)
            {
                return NULL;
            }
            u->coef = pa->coef ;
            u->expn = pa->expn ;
            pa = pa->next ;
            u->next = pc->next ;
            pc->next = u;
            pc = u;
        }
        else
        {
            u = (PLinkList)malloc(sizeof(PolyNode));
            if(!u)
            {
                return NULL;
            }
            u->coef = pb->coef ;
            u->expn = pb->expn ;
            pb = pb->next ;
            u->next = pc->next ;
            pc->next = u;
            pc = u;
        }
    }
    L2 = Reverse(L2);
    return head;
}  

PolyNode *Subtraction(PLinkList L1,PLinkList L2)//多项式的减法
{
    PolyNode *pa,*pb,*pc,*u,*head;
    head = (PLinkList)malloc(sizeof(PolyNode));
    if(!head)
    {
        return NULL;
    }
    head->coef = 0.0;
    head->expn = 0;
    head->next = NULL;
    pc = head;
    pa = L1->next ;
    pb = L2->next ;
    while(pa != NULL && pb != NULL)
    {
        if(pa->expn == pb->expn)
        {
            u = (PLinkList)malloc(sizeof(PolyNode));
            if(!u)
            {
                return NULL;
            }
            u->coef = pa->coef - pb->coef ;
            u->expn = pa->expn ;
            pa = pa->next ;
            pb = pb->next ;
            u->next = pc->next ;
            pc->next = u;
            pc = u;
        }
        else if(pa->expn > pb->expn)
        {
            u = (PLinkList)malloc(sizeof(PolyNode));
            if(!u)
            {
                return NULL;
            }
            u->coef = pa->coef ;
            u->expn = pa->expn ;
            pa = pa->next ;
            u->next = pc->next ;
            pc->next = u;
            pc = u;
        }
        else
        {
            u = (PLinkList)malloc(sizeof(PolyNode));
            if(!u)
            {
                return NULL;
            }
            u->coef = pb->coef ;
            u->expn = pb->expn ;
            pb = pb->next ;
            u->next = pc->next ;
            pc->next = u;
            pc = u;
        }
    }
    return head;
}  

PolyNode *Reverse(PLinkList head)//将生成的链表逆置，使一元多项式呈指数递增形式
{
    PolyNode *q,*r,*p = NULL;
    q = head->next ;
    while(q)
    {
        r = q->next ;
        q->next = p;
        p = q;
        q = r;
    }
    head->next = p;
    return head;
}  

PolyNode *MultiplyPolyn(PLinkList L1,PLinkList L2)//多项式的乘法
{
    PolyNode *pa,*pb,*pc,*u,*head;
    int k,maxExp;
    float coef;
    head = (PLinkList)malloc(sizeof(PolyNode));
    if(!head)
    {
        return NULL;
    }
    head->coef = 0.0;
    head->expn = 0;
    head->next = NULL;
    if(L1->next != NULL && L2->next != NULL)
    {
        maxExp = L1->next->expn +L2->next->expn ;
    }
    else
    {
        return head;
    }
    pc = head;
    L2 = Reverse(L2);
    for(k = maxExp;k >= 0;k--)
    {
        pa = L1->next ;
        while(pa != NULL && pa->expn > k)
        {
            pa = pa->next ;
        }
        pb = L2->next ;
        while(pb != NULL && pa != NULL && pa->expn+pb->expn < k)
        {
            pb= pb->next ;
        }
        coef = 0.0;
        while(pa != NULL && pb != NULL)
        {
            if(pa->expn +pb->expn == k)
            {
                coef += pa->coef *pb->coef ;
                pa = pa->next ;
                pb = pb->next ;
            }
            else if(pa->expn +pb->expn > k)
            {
                pa = pa->next ;
            }
            else
            {
                pb = pb->next ;
            }
        }
        if(coef != 0.0)
        {
            u = (PLinkList)malloc(sizeof(PolyNode));
            u->coef = coef;
            u->expn = k;
            u->next = pc->next ;
            pc->next = u;
            pc = u;
        }
    }
    L2 = Reverse(L2);
    return head;
}  

#include "test.h"  

int main(void)
{
    PLinkList A,B,C,D,E;
    A = CreatePolyn();
    printf("A(x) =");
    OutPut(A);
    printf("\n");
    B = CreatePolyn();
    printf("B(x) =");
    OutPut(B);
    printf("\n");
    C = MultiplyPolyn(A,B);
    printf("C(x) = A(x)*B(x) =");
    OutPut(C);
    printf("\n");
    D = Addition(A,B);
    printf("D(x) = A(x)+B(x) =");
    OutPut(D);
    printf("\n");
    E = Subtraction(A,B);
    printf("E(x) = A(x)-B(x) =");
    OutPut(E);
    printf("\n");
    return 0;
}

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