一元多项式的表示及加减乘除运算

Posted 2020-09-23 zhchoutai

比如：怎样实现用线性链表表示多项式的加法运算？

依据一元多项式相加的运算规则：对于两个一元多项式中全部指数同样的项。相应系数相加，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全部指数不同样的项，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;  
}