C语言实现一元多项式的基本操作

函数声明（poly.h头文件）

//一元多项式的链式表达,利用带头节点的单链表实现
//多项式的插入和删除操作是比较频繁.用链式结构比顺序结构更好
//链表按照指数升序排列

typedef struct
{
     
	double cofe;//系数
	int expn;//指数
}term;//存放系数和指数的数对

typedef struct PNode
{
     
	term data;
	struct PNode* next;
}PNode, * Poly;//Poly == PNode *

//初始化
void InitPoly(Poly po);

//插入数据,cofe:系数,expn:指数.插入遵循指数升序
bool Insert(Poly po, double cofe, int expn);

//输出数据
void Show(Poly po);

//销毁多项式
void Destroy(Poly po);

//多项式加法,po1 += po2;
bool Add(Poly po1, Poly po2);

//多项式减法,po1 -= po2;
bool Sub(Poly po1, Poly po2);

//多项式乘法,po1 *= po2;
bool Mutil(Poly po1, Poly po2);

函数定义(poly.cpp文件)

#include
#include
#include
#include"poly.h"

/*初始化*/
void InitPoly(Poly po)
{
     
	assert(po != NULL);
	if (po == NULL)
	{
     
		return;
	}
	po->next = NULL;
}

//在多项式po里面查找指数为expn的前驱
static  PNode* SearchPrio(Poly po, int expn)
{
     
	PNode* p;
	for (p = po; p->next != NULL; p = p->next)
	{
     
		if (p->next->data.expn >= expn)
		{
     
			return p;
			//break;
		}
	}
	return p;
}

//插入数据, cofe:系数, expn : 指数.插入遵循指数升序
bool Insert(Poly po, double cofe, int expn)
{
     
#define EPS 0.0000001
	PNode* p = SearchPrio(po, expn);
	PNode* q;

	if (p->next != NULL && p->next->data.expn == expn)//合并同类项
	{
     
		q = p->next;
		q->data.cofe += cofe;
		if (-EPS <= q->data.cofe && q->data.cofe <= EPS)//系数为0就删除
		{
     
			p->next = q->next;
			free(q);
		}
	}
	else//创建新节点，插在p后面
	{
     
		q = (PNode*)malloc(sizeof(PNode));
		q->data.cofe = cofe;
		q->data.expn = expn;

		q->next = p->next;
		p->next = q;
	}
	return true;
}


//输出数据
void Show(Poly po)
{
     
	PNode* p = po->next;
	printf("%-4.1fx^%d", p->data.cofe, p->data.expn);
	po = po->next;
	for (p = po->next; p != NULL; p = p->next)
	{
     
		if (p->data.cofe < 0)
		{
     
			printf("%-4.1fx^%d", p->data.cofe, p->data.expn);
		}
		else
		{
     
			printf("+%-4.1fx^%d", p->data.cofe, p->data.expn);
		}
	}
	printf("\n");
}

//销毁多项式
void Destroy(Poly po)
{
     
	PNode* p ;
	while (po->next != NULL)
	{
     
		p = po->next;
		po->next = p->next;
		free(p);
	}
}

//多项式加法,po1 += po2;
bool Add(Poly po1, Poly po2)
{
     
	if (po1 == NULL || po2 == NULL)
		return false;
	for (PNode* p = po2->next; p != NULL; p = p->next)
	{
     
		Insert(po1, p->data.cofe, p->data.expn);
	}
	return true;
}

//多项式减法,po1 -= po2;
bool Sub(Poly po1, Poly po2)
{
     
	if (po1 == NULL || po2 == NULL)
		return false;
	for (PNode* p = po2->next; p != NULL; p = p->next)
	{
     
		p->data.cofe = -p->data.cofe;
		Insert(po1, p->data.cofe, p->data.expn);
	}
	return true;
}

//多项式乘法,po1 *= po2;
bool Mutil(Poly po1, Poly po2)
{
     
	if (po1 == NULL || po2 == NULL)
		return false;
	PNode po3;
	InitPoly(&po3);
	
	for (PNode*p2 = po2->next;  p2 != NULL; p2 = p2->next)//遍历po2的所有项,将其乘以po1的所有项
	{
     
		for(PNode* p1 = po1->next; p1 != NULL; p1 = p1->next)
		{
     
			Insert(&po3, (p2->data.cofe * p1->data.cofe ), (p1->data.expn + p2->data.expn));
		}
	}
	Destroy(po1);
	po1->next = po3.next;
	po3.next = NULL;

	return true;
}