线性结构2 一元多项式的乘法与加法运算

 

设计函数分别求两个一元多项式的乘积与和。

输入格式:

输入分2行，每行分别先给出多项式非零项的个数，再以指数递降方式输入一个多项式非零项系数和指数（绝对值均为不超过1000的整数）。数字间以空格分隔。

输出格式:

输出分2行，分别以指数递降方式输出乘积多项式以及和多项式非零项的系数和指数。数字间以空格分隔，但结尾不能有多余空格。零多项式应输出0 0。

输入样例:

4 3 4 -5 2  6 1  -2 0
3 5 20  -7 4  3 1

 

输出样例:

15 24 -25 22 30 21 -10 20 -21 8 35 6 -33 5 14 4 -15 3 18 2 -6 1
5 20 -4 4 -5 2 9 1 -2 0

首先是多项式的表示：

struct PolyNode {
	int expon;    //指数 
	int coef;   //底数 
	struct PolyNode* Link;
};
typedef struct PolyNode* Polynomial;

然后程序的框架搭载

int main()
{
读入多项式1；
读入多项式2；
乘法预算并输出；
加法运算并输出；
return 0；
}

完整代码：

#include<iostream>
using namespace std;
struct PolyNode {
	int expon;    //指数 
	int coef;   //底数 
	struct PolyNode* Link;
};
typedef struct PolyNode* Polynomial;

void Attach(int c, int e, Polynomial* prear)
{
	Polynomial newp;
	newp = new struct PolyNode;
	newp->coef = c;
	newp->expon = e;
	newp->Link = NULL;
	(*prear)->Link = newp;
	(*prear) = newp;
}

Polynomial ReadPoly()
{
	int n;
	Polynomial p, rear, t;
	p = new struct PolyNode;
	p->Link = NULL;
	rear = p;
	cin >> n;
	while (n--) {
		int e, c;
		cin >> c >> e;
		Attach(c, e, &rear);
	}
	t = p;
	p = p->Link;
	delete t;
	return p;
}

Polynomial AddPoly(Polynomial P1, Polynomial P2)
{
	Polynomial P, t1, t2, rear;
	if (!P1 && !P2) return NULL;
	P = new struct PolyNode;
	P->Link = NULL;
	t1 = P1; t2 = P2; rear = P;
	while (t1 && t2)
	{
		if (t1->expon == t2->expon)  //指数相等 
		{
			if ((t1->coef + t2->coef) != 0)
			{
				Attach(t1->coef + t2->coef, t1->expon, &rear);//系数相加不为0
				t1 = t1->Link; t2 = t2->Link;
			}
		}
		else if (t1->expon > t2->expon)
		{
			Attach(t1->coef, t1->expon, &rear);
			t1 = t1->Link;
		}
		else {
			Attach(t2->coef, t2->expon, &rear);
			t2 = t2->Link;
		}
	}
	rear->Link = t1 ? t1 : t2;
	Polynomial t = P;
	P = t->Link;
	delete t;
	return P;
}

Polynomial MultPoly(Polynomial P1, Polynomial P2)
{
	Polynomial t1, t2, P, rear, t;
	int e, c;
	if (!P1 || !P2) return NULL;//P1,P2任意一个为零 多项式即为零
	t1 = P1; t2 = P2;
	P = new struct PolyNode;
	P->Link = NULL;
	rear = P;
	while (t2) //p1第一项与p2每一项相乘 
	{
		Attach(t1->coef * t2->coef, t1->expon + t2->expon, &rear);
		t2 = t2->Link;
	}
	t1 = t1->Link;
	while (t1)//p1接下来的每一项与t2所有项分别相乘 
	{
		rear = P;
		t2 = P2;
		while (t2)
		{
			c = t1->coef * t2->coef;
			e = t1->expon + t2->expon;
			/*  注意：这里都是先判断rear->Link是否存在，否则后面的判断语句可能会导致程序出错 */
			while (rear->Link && rear->Link->expon > e) rear = rear->Link;//如果rear的下一个结点大于e，则继续到下一个结点
			if (rear->Link && rear->Link->expon == e)
			{
				if (rear->Link->coef + c) rear->Link->coef += c;//系数相加不为0
				else {//系数相加为0 删除这个结点 
					t = rear->Link;
					rear = t->Link;
					delete t;
				}
			}
			else//rear的下一个结点指数比e小，新建结点加入到rear后面 
			{
				t = new struct PolyNode;
				t->coef = c;
				t->expon = e;
				t->Link = rear->Link;
				rear->Link = t;
				rear=rear->Link; 
			}
			t2 = t2->Link;
		}
		t1 = t1->Link;
	}
	t = P;
	P = P->Link;
	delete t;//删除头结点
	return P;
}



void Print(Polynomial p)
{
	if (!p) { cout << "0 0" << endl; return; }
	Polynomial t = p;
	cout << t->coef << " " << t->expon;
	t = t->Link;
	while (t)
	{
		cout <<" "<< t->coef << " " << t->expon ;
		t = t->Link;
	}
	cout << endl;
}

int main()
{
	Polynomial P1, P2;
	Polynomial PP, PS;
	P1 = ReadPoly();
	P2 = ReadPoly();
	PS = AddPoly(P1, P2);
	PP = MultPoly(P1, P2);
	Print(PP);
	Print(PS);
	//Print(NULL);
	return 0;
}

特别注意的是 ：

这个方法每次新建一个多项式都要在最后完成操作（加，乘）将空的头节点删掉。