链表的应用1--多项式求和

     今天学数据结构学到的链表应用于多项式相加，但是书上的代码没看懂，在看了点资料和问ChatGPT以后想到的一个算法，后面有更好的想法在回来更新算法

1.链表相关结构：

//链表结点结构
typedef struct linknode
{
	int coef;//系数 
	int exp;//指数
	linknode* next;//指针
}LinkNode;

//链表头结点结构
typedef struct header
{
	int length;//链表长度(结点数)
	LinkNode* next;//指针
}Header;

2.多项式相加算法：

使用前提：

1.多项式各项按照指数大小降次排序

2.不能出现多个含有相同次幂的项数，例如在一个多项式中不能出现3+5这样，必须为8

，但是这个算法计算结果是没错的，就是输出的时候不太美观，后续会继续完善

//多项式相加
Header* PolyAdd(Header* &A,Header* &B)
{
	//创建新链表头结点
	Header* C = new Header();
	C->length = 0;
	C->next = NULL;
	
	LinkNode* pa = A->next;
	LinkNode* pb = B->next;
	LinkNode* pc = NULL;
	int flag2 = 1;
	while(pa != NULL && pb != NULL)
	{
		LinkNode* new_node = new LinkNode();
		if(pa->exp > pb->exp)
		{
			new_node->coef = pa->coef;
			new_node->exp = pa->exp;
			pa = pa->next;
		}
		else if(pa->exp == pb->exp)
		{
			new_node->coef = pa->coef + pb->coef;
			new_node->exp = pa->exp;
			pa = pa->next;
			pb = pb->next;
		}
		else
		{
			new_node->coef = pb->coef;
			new_node->exp = pb->exp;
			pb = pb->next;
		}
		
		if(flag2)
		{
			C->next = new_node;
			pc = new_node;
			flag2 = 0;
		}
		else
		{
			pc->next = new_node;
			pc = pc->next;
		}
	} 
	
	//将剩余的没有进行加和的项数结点依次添加到C链表后
	//这里由于在上面的循环结束后，A和B链表中必定有一个
	//已经到尾了，所以下面对谁先进行排查的顺序无所谓 
	while(pa != NULL)
	{
		pc->next = new LinkNode();
		pc->next->coef = pa->coef;
		pc->next->exp = pa->exp;
		pc = pc->next; 
		pa = pa->next;
	}
	
	while(pb != NULL)
	{
		pc->next = new LinkNode();
		pc->next->coef = pb->coef;
		pc->next->exp = pb->exp;
		pc = pc->next; 
		pb = pb->next; 
	}
	pc->next = NULL;
	return C;
}

3.完整代码：

#include

using namespace std;

//链表结点结构
typedef struct linknode
{
	int coef;//系数 
	int exp;//指数
	linknode* next;//指针
}LinkNode;

//链表头结点结构
typedef struct header
{
	int length;//链表长度(结点数)
	LinkNode* next;//指针
}Header;


//创建链表
Header* CreateLinkList()
{
	//创建头结点并初始化
	Header* header = new Header();
	header->length = 0;
	header->next = NULL;
	
	//添加链表结点或结束
	int choice = 2;
	cout << "(1)添加结点 (2)离开：";
	cin >> choice;
	
	if(choice == 2)
	{
		return header;
	}
	
	int flag1 = 1;
	LinkNode* ptr = NULL;
	while(choice == 1)
	{
		LinkNode* node = new LinkNode();
		cout << "系数coef：";
		cin >> node->coef;
		cout << "指数exp:";
		cin >> node->exp;
		
		if(flag1)
		{
			header->next = node;
			ptr = node;
			flag1 = 0;
		}
		else
		{
			ptr->next = node;
			ptr = node;
		}
		header->length++;
		cout << "(1)添加结点 (2)离开：";
		cin >> choice;
	}
	ptr->next = NULL;
	return header;
}

//多项式相加
Header* PolyAdd(Header* &A,Header* &B)
{
	//创建新链表头结点
	Header* C = new Header();
	C->length = 0;
	C->next = NULL;
	
	LinkNode* pa = A->next;
	LinkNode* pb = B->next;
	LinkNode* pc = NULL;
	int flag2 = 1;
	while(pa != NULL && pb != NULL)
	{
		LinkNode* new_node = new LinkNode();
		if(pa->exp > pb->exp)
		{
			new_node->coef = pa->coef;
			new_node->exp = pa->exp;
			pa = pa->next;
		}
		else if(pa->exp == pb->exp)
		{
			new_node->coef = pa->coef + pb->coef;
			new_node->exp = pa->exp;
			pa = pa->next;
			pb = pb->next;
		}
		else
		{
			new_node->coef = pb->coef;
			new_node->exp = pb->exp;
			pb = pb->next;
		}
		
		if(flag2)
		{
			C->next = new_node;
			pc = new_node;
			flag2 = 0;
		}
		else
		{
			pc->next = new_node;
			pc = pc->next;
		}
	} 
	
	//将剩余的没有进行加和的项数结点依次添加到C链表后
	//这里由于在上面的循环结束后，A和B链表中必定有一个
	//已经到尾了，所以下面对谁先进行排查的顺序无所谓 
	while(pa != NULL)
	{
		pc->next = new LinkNode();
		pc->next->coef = pa->coef;
		pc->next->exp = pa->exp;
		pc = pc->next; 
		pa = pa->next;
	}
	
	while(pb != NULL)
	{
		pc->next = new LinkNode();
		pc->next->coef = pb->coef;
		pc->next->exp = pb->exp;
		pc = pc->next; 
		pb = pb->next; 
	}
	pc->next = NULL;
	return C;
}

//输出链表内容 
void Print(Header* &header)
{
	LinkNode* ph = header->next;
	while(ph != NULL)
	{
		cout << ph->coef << 'X' << ph->exp;
		ph = ph->next;
		if(ph != NULL)
		{
			cout << " + ";
		}
	}
	cout << endl;
	system("pause");
	system("cls");
}

//清空链表 
void FreeLinkList(Header* header)
{
	if(header == NULL)
	{
		cout << "链表不存在或已清空！\n";
		return; 
	}
	LinkNode* p = header->next;
	LinkNode* temp = NULL;
	while(p != NULL)
	{
		temp = p;
		p = p->next;
		delete temp;
	}
	delete header;
	header = NULL;
	if(header == NULL)
	{
		cout << "链表已清空！\n";
	}
}

//测试函数 
void test()
{
	cout << "输入多项式A的结点数据：\n";
	Header* A = CreateLinkList();
	system("pause");
	system("cls");
	Print(A);
	
	cout << "输入多项式B的结点数据：\n";
	Header* B = CreateLinkList();
	system("pause");
	system("cls");
	Print(B);
	
	Header* C = PolyAdd(A,B);
	cout << "多项式A+B的结果为：\n";
	Print(C);
	
	//销毁链表释放空间
	FreeLinkList(A); 
	FreeLinkList(B);
	FreeLinkList(C);
}

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