所实现的一元多项式的结构如下图所示：
若只对多项式进行“求值”等不改变多项式系数和指数的运算，采用类似顺序表的顺序存储结构即可，否则应采用链式存储结构，本文因为要进行一元多项式的加法，加法，乘法，故采用的是链式存储结构
Polynomail.h
#include<stdio.h>
#include<assert.h>
struct Node
{
int coef; //系数
int expn; //指数
};
//节点结构
typedef struct PolynNode
{
Node data;
struct PolynNode *link;
}PolynNode;
typedef PolynNode* Polynmail;
void InitPolyn (Polynmail &head);
void CreatPolyn(Polynmail &head, int n);
void push_back (Polynmail &head, PolynNode *s);
void ShowPolyn (Polynmail head);
void AddPolyn(Polynmail &head, Polynmail pa, Polynmail pb);
void SubPolyn(Polynmail &head, Polynmail pa, Polynmail pb);
void MulPolyn(Polynmail &head, Polynmail pa, Polynmail pb);
int lenth(Polynmail head);
void destory(Polynmail &head);#include"Polynomail.h"
void InitPolyn(Polynmail &head)
{
PolynNode *s = new PolynNode;
assert(s != NULL);
s->data.coef = 0;
s->data.expn = -1;
s->link = NULL;
head = s;
}
void push_back(Polynmail &head, PolynNode *s)
{
PolynNode *p = head;
while (p->link != NULL)
{
p = p->link;
}
p->link = s;
}
//创建一元多项式
void CreatPolyn(Polynmail &head, int n)
{
int c;
int e;
for (int i = 0; i < n; ++i)
{
printf("请输入第%d项的系数和指数 >", i + 1);
scanf_s("%d%d", &c, &e);
PolynNode *s = new PolynNode;
s->data.coef = c;
s->data.expn = e;
s->link = NULL;
push_back(head, s);
}
}
//打印一元多项式
void ShowPolyn(Polynmail head)
{
PolynNode *s = head->link;
while (s != NULL)
{
if (s->data.expn == 0)//5x^0 ---->5
{
printf("%d", s->data.coef);
}
else if (s->data.expn == 1)//5x^1---->5x
{
printf("%dx", s->data.coef);
}
else//正常结果直接打印
{
printf("%dx^%d", s->data.coef, s->data.expn);
}
//下一项存在且系数为正数，需打印正号（负数会自带符号）
s = s->link;
if (s != NULL && s->data.coef > 0)
{
printf("+");
}
}
printf("\n");
}
//表达式pa + pb的结果保存在head中
void AddPolyn(Polynmail &head, Polynmail pa, Polynmail pb)
{
PolynNode *sa = pa->link;
PolynNode *sb = pb->link;
PolynNode *s;
while (sa != NULL && sb != NULL)
{
s = new PolynNode;
s->link = NULL;
//sa节点的指数 < sb节点的指数 ----------->
//1：将sa节点中的数据插入到结果中 2：指向下一个pa节点
if (sa->data.expn < sb->data.expn)
{
s->data.coef = sa->data.coef;
s->data.expn = sa->data.expn;
sa = sa->link;
}
//sa节点的指数 > sb节点的指数 ----------->
//1：将sb节点中的数据插入到结果中 2：指向下一个pb节点
else if (sa->data.expn > sb->data.expn)
{
s->data.coef = sb->data.coef;
s->data.expn = sb->data.expn;
sb = sb->link;
}
//sa节点的指数 == sb节点的指数
//1：将二者系数的和即相同的指数插入到结果中 2：pa、pb都指向下一个节点
else if (sa->data.expn == sb->data.expn)
{
s->data.coef = sb->data.coef + sa->data.coef;
s->data.expn = sb->data.expn;
sb = sb->link;
sa = sa->link;
}
//若所加结果的系数为0，不用插入结果中，反之需要插入到结果中
if (s->data.coef != 0)
{
push_back(head, s);
}
}
//将pa 或者pb当中表达式较长的剩余节点全部插入到结果中
if (sa != NULL)
{
while (sa != NULL)
{
s = new PolynNode;
s->link = NULL;
s->data.coef = sa->data.coef;
s->data.expn = sa->data.expn;
push_back(head, s);
sa = sa->link;
}
}
if (sb != NULL)
{
while (sb != NULL)
{
s = new PolynNode;
s->link = NULL;
s->data.coef = sb->data.coef;
s->data.expn = sb->data.expn;
push_back(head, s);
sb = sb->link;
}
}
}
//表达式pa - pb的结果保存在head中
void SubPolyn(Polynmail &head, Polynmail pa, Polynmail pb)
{
PolynNode *sa = pa->link;
PolynNode *sb = pb->link;
PolynNode *s;
while (sa != NULL && sb != NULL)
{
s = new PolynNode;
s->link = NULL;
//sa - sb sa中存在而sb中不存在的节点，相减后为正
if (sa->data.expn < sb->data.expn)
{
s->data.coef = sa->data.coef;
s->data.expn = sa->data.expn;
sa = sa->link;
}
//sa - sb sb中存在而sa中不存在的节点，相减后为负
else if (sa->data.expn > sb->data.expn)
{
s->data.coef = -(sb->data.coef);
s->data.expn = sb->data.expn;
sb = sb->link;
}
//sa - sb 两者都存在的节点，结果 = 二者相减后的结果
else if (sa->data.expn == sb->data.expn)
{
s->data.coef = sb->data.coef - sa->data.coef;
s->data.expn = sb->data.expn;
sb = sb->link;
sa = sa->link;
}
if (s->data.coef != 0)
{
push_back(head, s);
}
}
if (sa != NULL)
{
while (sa != NULL)
{
s = new PolynNode;
s->link = NULL;
s->data.coef = sa->data.coef;//sa - sb sa中存在而sb中不存在的节点，相减后为正
s->data.expn = sa->data.expn;
push_back(head, s);
sa = sa->link;
}
}
if (sb != NULL)
{
while (sb != NULL)
{
s = new PolynNode;
s->link = NULL;
s->data.coef = -(sb->data.coef);//sa - sb sb中存在而sa中不存在的节点，相减后为负
s->data.expn = sb->data.expn;
push_back(head, s);
sb = sb->link;
}
}
}
int lenth(Polynmail head)
{
int count = 0;
PolynNode *s = head->link;
while (s != NULL)
{
count++;
s = s->link;
}
return count;
}
//表达式pa * pb的结果保存在head中
void MulPolyn(Polynmail &head, Polynmail pa, Polynmail pb)
{
PolynNode *sb = pb->link;
while (sb != NULL)//sb中的每一个节点和sa中的所有节点相乘
{
PolynNode *sa = pa->link;//因为sb的每个节点都要和sa中的全部节点相乘，所以sb的每个节点
while (sa != NULL) //相乘时，sa总要从头开始
{
//创建相乘后的节点
PolynNode *p = new PolynNode;
p->data.coef = (sa->data.coef)*(sb->data.coef);//系数相乘
p->data.expn = (sa->data.expn)+(sb->data.expn);//指数相加
p->link = NULL;
//寻找已存在的节点中是否存在与刚创建的节点（指数）相同的节点
PolynNode *s = head->link;
while (s != NULL && (s->data.expn) != (p->data.expn))
{
s = s->link;
}
//不存在指数相同的节点，直接尾插即可
if (s == NULL)
{
push_back(head, p);
}
//存在指数相同的节点，修改系数即可
else
{
s->data.coef += p->data.coef;
}
//（sb的当前节点）为乘以sa中的下一个节点做准备
sa = sa->link;
}
//为sb中的下一个节点乘以sa的全部节点做准备
sb = sb->link;
}
}
void destory(Polynmail &head)
{
PolynNode *s = head->link;
while (s != NULL)
{
head->link = s->link;
delete s;
s = head->link;
}
delete head;
head = NULL;
}#include"Polynomail.h"
#include<cstdlib>
int main()
{
Polynmail pa;
Polynmail pb;
Polynmail pc;
InitPolyn(pa);
InitPolyn(pb);
InitPolyn(pc);
int select = 1;
int n;
while (select)
{
printf("*****************************************\n");
printf("* [1]创建多项式pa [2]创建多项式pb *\n");
printf("* [3]打印多项式pa [4]打印多项式pb *\n");
printf("* [5]AddPolyn [6]SubPolyn *\n");
printf("* [7]MulPolyn [8]打印多项式pc *\n");
printf("* [0]退出系统 [0]退出系统 *\n");
printf("*****************************************\n");
scanf_s("%d", &select);
switch (select)
{
case 1:
printf("请输入多项式的项数：>");
scanf_s("%d", &n);
CreatPolyn(pa, n);
break;
case 2:
printf("请输入多项式的项数：>");
scanf_s("%d", &n);
CreatPolyn(pb, n);
break;
case 3:
printf("pa = ");
ShowPolyn(pa);
break;
case 4:
printf("pb = ");
ShowPolyn(pb);
break;
case 5:
AddPolyn(pc, pa, pb);
break;
case 6:
SubPolyn(pc, pa, pb);
break;
case 7:
MulPolyn(pc, pa, pb);
break;
case 8:
printf("pc = ");
ShowPolyn(pc);
break;
default:
break;
}
}
destory(pa);
destory(pb);
destory(pc);
system("pause");
return 0;
}
版权声明：本文为博主原创文章，未经博主允许不得转载。
【c++版数据结构】之用带头节点的单链表实现一元多项式（C语言版）
原文地址：http://blog.csdn.net/zongyinhu/article/details/48009087
