本文将讲解利用单链表 将多项式相加。

假设现有多项式A与多项式B：

（注意：这两个多项式的项按照指数已经从小到大排列）

1. 新建一个链表c,用于存储加和后的多项式， 初始化
2. 利用链表将多项式的数据存储起来
3. 相加
4. 输出

#pragma once
#include<iostream>
using namespace std;

typedef struct LinkNode
{
	int coef;//系数
	int index;//指数
	LinkNode* next;
}LN;

typedef class Polonomial
{
public:
	void PNInit();//初始化函数
	void PNInput();//数据输入函数
	void PNPrint();//输出函数
	 
	void PNAdd();//加和函数
private:
	int length_a;
	int length_b;
	int length_c;
	
	LN* La;
	LN* Lb;
	LN* Lc;//用于存储加和后的多项式
   void PNInseert(int whichOne, int xishu, int zhishu)//定义为私有函数，便于调用
	{
		LN* phead = NULL;
		int len = 0;

		
		switch (whichOne)
		{
		case 1:
			phead = La;
			len = length_a;
			break;
		case 2:
			phead = Lb;
			len = length_b;
			break;
		case 3:
			phead = Lc;
			len = length_c;
			break;
			
		default:
			break;
		}
		//找到尾节点，将新节点插入在尾节点之后
		LN* tail =phead;
		for (int i = 0; i < len; i++)
		{
			tail = tail->next;
		}

		LN* newNode = new LN;

		newNode->coef = xishu;
		newNode->index = zhishu;
		newNode->next = NULL;
		//newNode->next = tail->next;
		tail->next = newNode;

		//插入后长度加一
		switch (whichOne)
		{
		case 1:
			length_a++;
			break;
		case 2:
			length_b++;
			break;
		case 3:
			length_c++;
			break;
		default:
			break;
		}
	}


	
}PN;

#include"polynomial.h"

void PN::PNInit()
{
	 La = new LN;
	if (La == NULL)
	{
		cout << "a分配失败" << endl;
		exit(-1);
	}
	La->next = NULL;
	length_a = 0;

	
	Lb = new LN;
	if (Lb == NULL)
	{
		cout << "b分配失败" << endl;
		exit(-1);
	}
	Lb->next = NULL;
	length_b = 0;

	Lc = new LN;
	if (Lc == NULL)
	{
		cout << "c分配失败" << endl;
		exit(-1);
	}
	Lc->next = NULL;
	length_c = 0;

}


void PN::PNInput()
{
	int num;//项数
	int x, y;

	cout << "请输入第一个多项式的项数：";
	cin >> num;
	for (int i = 0; i < num; i++)
	{
		cout << "请输入" << i + 1 << "个项的系数";
		cin >> x;
		cout << "请输入" << i + 1 << "个项的指数";
		cin >> y;
		PNInseert(1, x, y);
	}
	
	cout << "请输入第二个多项式的项数：";
	cin >> num;
	for (int i = 0; i < num; i++)
	{
		cout << "请输入" << i + 1 << "个项的系数";
		cin >> x;
		cout << "请输入" << i + 1 << "个项的指数";
		cin >> y;
		PNInseert(2, x, y);
	}
}

void PN::PNPrint()
{
	LN*cur;

	cout << "第一个多项式的长度为：" <<length_a <<endl;
	if (length_a > 0)
	{
		cur = La->next;
		for (int i = 0; i < length_a; i++)
		{
			//为了输出美观，分类输出
			if (i != length_a - 1)
				cout << cur->coef << "X(" << cur->index << ")+";
			else
				cout << cur->coef << "X(" << cur->index << ")";
			cur = cur->next;
		}
		cout << endl;
	}

	cout << "第二个多项式的长度为：" << length_b << endl;
	if (length_b > 0)
	{
		cur = Lb->next;
		for (int i = 0; i < length_b; i++)
		{
			if (i != length_b - 1)
				cout << cur->coef << "X(" << cur->index << ")+";
			else
				cout << cur->coef << "X(" << cur->index << ")";
			cur = cur->next;
		}
		cout << endl;
	}

	cout << "相加后多项式的长度为：" << length_c << endl;
	if (length_c > 0)
	{
		cur = Lc->next;
		for (int i = 0; i < length_c; i++)
		{
			if (i != length_c - 1)
				cout << cur->coef << "X(" << cur->index << ")+";
			else
				cout << cur->coef << "X(" << cur->index << ")";
			cur = cur->next;
		}
		cout << endl;
	}

}


void PN::PNAdd()
{
	LN* pa = La->next;
	LN* pb = Lb->next;

	while (pa && pb)
	{
		if (pa->index < pb->index)
		{
			PNInseert(3, pa->coef, pa->index);
			pa = pa->next;
		}
		else if(pa->index > pb->index)
		{
			PNInseert(3, pb->coef, pb->index);
			pb = pb->next;
		}
		else
		{
			int result = pa->coef + pb->coef;
			if (result)
			{
				PNInseert(3, result, pa->index);
				pa = pa->next;
				pb = pb->next;
			}
			else
			{
				pa = pa->next;
				pb = pb->next;
			}
		}
	}
	//
	LN* p = (pa == NULL) ? pb : pa;
	while (p != NULL)
	{
		PNInseert(3, p->coef, p->index);
		p = p->next;
	}
}

#include"polynomial.h"

void PN_Test()
{
	PN s;
	s.PNInit();
	s.PNInput();
	
	s.PNAdd();
	s.PNPrint();
}

int main()
{
	PN_Test();
	return 0;
}