一元多项式的表示、求和，求值

在单链表的基础上实现：

1、一元多项式的表示（创建）CreatPolyn(Polynomial &, int);该创建在输入多项式时，按照指数递增方式输入

2、两个一元多项式的求和：Add(Polynomial &, Polynomial &);

3、求一元多项式的值：float ComputePolyn(const Polynomial &, float);要求时间复杂度O（n）

====main中：

1、创建一元多项式：PA=5 + 3x**2 + 4x**6 + 10x**9 + 11x**10 + x**12

2、创建一元多项式：PB=-5 + 2x + 4x**6 - 10x**9

3、遍历打印PA,PB（打印出类似上面形式的多项式，而不仅仅是打印系数和指数）

4、求PA+PB的和并遍历

#include <iostream>
#include<math.h>
using namespace std;
typedef int ElemType;
typedef struct PNode { //结点定义方式一
	float coef; //系数
	int exp; //指数
	PNode* next; //结点指针
}*Polynomial;
void InitPNode(Polynomial& P) {
	PNode* s = new PNode;
	s->next = NULL;
	P = s;
}
void Creat(Polynomial& P, int n) {
	PNode* r = P;
	for (int i = 0; i < n; i++) {
		PNode* s = new PNode;
		cout << "请分别输入系数和指数：";
		cin >> s->coef >> s->exp;
		r->next = s;
		r = s;
	}
	r->next = NULL;
}
void PrintPNode(const Polynomial& P) {
	PNode* s = P->next;
	while (s) {
		if(s!=P->next){
			if (s->coef > 0)cout << "+";
		}
		if (s->coef != 0) {
			if (s->coef != 1) {
				if (s->exp == 0)printf("%.0f", s->coef);
				else if (s->exp == 1)printf("%.0fx", s->coef);
				else {
					printf("%.0fx**%d", s->coef, s->exp);
				}
			}
		    else {
				if (s->exp == 0)printf("%d", 1);
				else if (s->exp == 1)printf("%.0fx", s->coef);
			    else {
				    	printf("x**%d", s->exp);
				}
			}
		}
		s = s->next;
	}
	printf("\n");
}
void Add(const Polynomial &A,const Polynomial &B,Polynomial& C) {
	PNode * pa,* pb,	* pc,* q;
	pc =C; //结果存放指针与C工作指针
	pa = A->next; //A 的工作指针
	pb = B->next; // B 的工作指针
	delete B; //删去 B 的表头结点
	while (pa && pb) {
		if (pa->exp == pb->exp) {
			pa->coef = pa->coef + pb->coef;//系数相加
			q = pb; pb = pb->next; delete q;
			//指数相等，仅保留一个，因此pb项一定删
				if (pa->coef) { //相加不为零, 加入 C 链
					pc->next = pa; pc = pa;
					pa = pa->next;
				}
				else //相加为零, pa项也删
				{
					q = pa; pa = pa->next; delete q;
				}
		}
		else if (pa->exp < pb->exp) {//链接pb项
			pc->next = pa; pc = pa;
			pa = pa->next;
		}
		else { //链接pa项
			pc->next = pb; pc = pb;
			pb = pb->next;
		}
	} //while结束
	if (!pa) pc->next = pb;
	else pc->next = pa; //剩余部分链入 C 链
}
//5 0 3 2 4 6 10 9 11 10 1 12
//-5 0 2 1 4 6 -10 9
float ComputePolyn(const Polynomial& P, float n){
	float  SUM = 0;
	PNode* s ;
	s = P->next;
	float a;
	int  b;
	while (s) {
		a = s->coef;
		b = s->exp;
		SUM = SUM + a*(pow(n, b));
		s = s->next;
	}
	return SUM;
}
int main() {
	Polynomial PA;
	Polynomial PB;
	Polynomial PC;
	InitPNode(PA);
	InitPNode(PB);
	InitPNode(PC);
	cout << "创建多项式PA" << endl;
	Creat(PA, 6);//1、创建一元多项式：PA=5 + 3x**2 + 4x**6 + 10x**9 + 11x**10 + x**12
	cout << "创建多项式PB"<< endl;
	Creat(PB, 4);//2、创建一元多项式：PB=-5 + 2x + 4x**6 - 10x**9
	cout << "PA=";
	PrintPNode(PA);//3、遍历打印PA,PB（打印出类似上面形式的多项式，而不仅仅是打印系数和指数）
	cout << "PB=";
	PrintPNode(PB);
	Add(PA, PB, PC);//4、求PA+PB的和并遍历
	cout << "PA+PB的和PC=";
	PrintPNode(PC); //4、求PA + PB的和并遍历
}