c语言实现多项式的求和与乘积

由于一些时间原因和个人英语水平有限,在这个代码里面并没有做申请空间是否成功的判断和启明有些LOW,不要介意,而且输入的多项式只能是指数非递增的,嘻嘻,直接进入正题:

本程序用的是C语言链表实现的多项式的求和与乘积计算。

结构体:

typedef struct Node
{
    int zs;
    int xs;
    struct Node* next;
}poly;
typedef poly* poly_node;
typedef poly* polynomial;

创建并赋值多项式链表函数:

polynomial GetPoly()
{
    int n;
    scanf("%d",&n);
    poly_node head,end,temp;
    head = (poly*)malloc(sizeof(poly));            //申请头节点
    end = head;
    for(;n>0;n--)
    {
        end->next = (poly*)malloc(sizeof(poly));    //申请节点,并且是一条空头的链表
        end = end->next;
        scanf("%d%d",&end->xs,&end->zs);            
    }
    end->next = NULL;                    //封尾,方便后序的遍历
    temp = head;                        //中间变量
    head = head->next;                    //头为空,不影响数据
    free(temp);                            //释放空头节点空间
    return head;                
}

多项式求和函数:

polynomial polySum(polynomial p1,polynomial p2)
{
    poly_node head,end,temp;
    head = (poly*)malloc(sizeof(poly));
    end = head;
    while( p1 && p2 )
    {                        //此处遵循多项式求和规律
        if(p1->zs > p2->zs)                
        {
            polyNodeAdd(p1->zs , p1->xs , &end);   //调用追加函数,添加多项式结果
            p1 = p1->next;
        }
        else if(p1->zs < p2->zs)
        {
            polyNodeAdd(p2->zs , p2->xs , &end);     //调用追加函数,添加多项式结果
            p2 = p2->next;
        }
        else
        {
            if((p1->xs + p2->xs) != 0)        //如果指数相等,系数不为零执行此步
                polyNodeAdd(p1->zs , (p1->xs) + (p2->xs) , &end);
            p1 = p1->next;
            p2 = p2->next;
        }
    }
    for( ; p1; p1 = p1->next)        //如果链表在上面的while没有遍历完,则在此处完成遍历添加
        polyNodeAdd(p1->zs , p1->xs , &end);
    for( ; p2; p2 = p2->next)
    {
        polyNodeAdd(p2->zs , p2->xs , &end);
    }
    end->next = NULL;
    temp = head;
    head = head->next;
    free(temp);
    return head;
}

多项式乘法函数:

polynomial polyProduct(polynomial p1,polynomial p2)
{
    poly_node head,end,temp,head2;
    head2 = (poly*)malloc(sizeof(poly));
    head2 = NULL;
    for(; p1 ;p1 = p1->next)    //调用多项式求和函数,将第一个多项式的第n项与第二条多项式的乘积加上第一个多项式的第n+1项与第二条多项式的乘积的和。
    {
        head = (poly*)malloc(sizeof(poly));
        end = head;
        for(temp = p2;temp;temp = temp->next)
            polyNodeAdd( (p1->zs)+(temp->zs),(p1->xs)*(temp->xs) , &end);
        head2 = polySum(head2,head->next);
        free_poly(head->next);  //释放掉上一条多项式链表
    }

    return head2;
}

多项式链表节点追加函数:

void polyNodeAdd(int zs,int xs,poly_node* end)        //二级指针
{
    poly_node temp;
    temp = (poly*)malloc(sizeof(poly));
    temp->zs = zs;
    temp->xs = xs;
    (*end)->next = temp;
    (*end) = (*end)->next;
    (*end)->next=NULL;                //封口
}

多项式链表打印函数:

void polyOutput(polynomial temp)
{
    printf("\n");
    if(!temp)printf("0 0");                //如果得出的多项式为空时输出0  0.
    while(temp)
    {
        printf("%d %d ",temp->xs,temp->zs);
        temp = temp->next;
    }
}

完整程序:

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

typedef struct Node
{
    int zs;
    int xs;
    struct Node* next;
}poly;

typedef poly* poly_node;
typedef poly* polynomial;

polynomial GetPoly();
void free_poly(polynomial);
void polyNodeAdd(int,int,poly_node*);
polynomial polySum(polynomial,polynomial);
polynomial polyProduct(polynomial,polynomial);
void polyOutput(polynomial);


int main()
{
    polynomial p1,p2,temp;
    p1=GetPoly();
    p2=GetPoly();
    temp = polyProduct(p1,p2);
    polyOutput(temp);
    free_poly(temp);
    temp = polySum(p1,p2);
    polyOutput(temp);
    free_poly(temp);

    return 0;
}

polynomial GetPoly()
{

    int n;
    scanf("%d",&n);
    poly_node head,end,temp;
    head = (poly*)malloc(sizeof(poly));
    end = head;
    for(;n>0;n--)
    {
        end->next = (poly*)malloc(sizeof(poly));
        end = end->next;
        scanf("%d%d",&end->xs,&end->zs);
    }
    end->next = NULL;
    temp = head;
    head = head->next;
    free(temp);
    return head;
}

polynomial polySum(polynomial p1,polynomial p2)
{

    poly_node head,end,temp;
    head = (poly*)malloc(sizeof(poly));
    end = head;
    while( p1 && p2 )
    {
        if(p1->zs > p2->zs)
        {
            polyNodeAdd(p1->zs , p1->xs , &end);
            p1 = p1->next;
        }
        else if(p1->zs < p2->zs)
        {
            polyNodeAdd(p2->zs , p2->xs , &end);
            p2 = p2->next;
        }
        else
        {
            if((p1->xs + p2->xs) != 0)
                polyNodeAdd(p1->zs , (p1->xs) + (p2->xs) , &end);
            p1 = p1->next;
            p2 = p2->next;
        }
    }
    for( ; p1; p1 = p1->next)
        polyNodeAdd(p1->zs , p1->xs , &end);
    for( ; p2; p2 = p2->next)
    {
        polyNodeAdd(p2->zs , p2->xs , &end);
    }
    end->next = NULL;
    temp = head;
    head = head->next;
    free(temp);
    return head;
}

void polyNodeAdd(int zs,int xs,poly_node* end)
{
    poly_node temp;
    temp = (poly*)malloc(sizeof(poly));
    temp->zs = zs;
    temp->xs = xs;
    (*end)->next = temp;
    (*end) = (*end)->next;
    (*end)->next=NULL;
}

void polyOutput(polynomial temp)
{
    printf("\n");
    if(!temp)printf("0 0");
    while(temp)
    {
        printf("%d %d ",temp->xs,temp->zs);
        temp = temp->next;
    }
}

void free_poly(polynomial p)
{
    poly_node temp;
    while(p)
    {
        temp = p;
        p=p->next;
        free(temp);
    }
}
polynomial polyProduct(polynomial p1,polynomial p2)
{
    poly_node head,end,temp,head2;
    head2 = (poly*)malloc(sizeof(poly));
    head2 = NULL;
    for(; p1 ;p1 = p1->next)
    {
        head = (poly*)malloc(sizeof(poly));
        end = head;
        for(temp = p2;temp;temp = temp->next)
            polyNodeAdd( (p1->zs)+(temp->zs),(p1->xs)*(temp->xs) , &end);
        head2 = polySum(head2,head->next);
        free_poly(head->next);

    }

    return head2;
}
测试用例:

项数 系数 指数 系数 指数……
4 3 4 -5 2 6 1 -2 0
3 5 20 -7 4 3 1
(一般情况)

2 1 2 1 0
2 1 2 -1 0
(同类项合并时有抵消)

2 -1000 1000 1000 0
2 1000 1000 -1000 0
(系数和指数取上限,结果有零多项式)

0
1 999 1000
(输入有零多项式和常数多项式)

输出结果:

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还有最最重要的一点,记得加空间申请是否成功的判断哟。

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最后修改:2021 年 09 月 16 日 05 : 57 PM