一元多项式加法链表实现

一元多项式加法的链表实现

作者：Duder

1.要求

使用链表实现一元多项式加法
并使用已有链表返回运算结果

2.算法分析

1.幂次有序算法

//一元多项式求和
void SumList(SList* &A,SList* B)
{
	SList *m,*n,*t;
	if(GetLine(A) > GetLine(B) )	
		{m=A;n=B;}
	else 
		{m=B;n=A;}
	//OutPut(m);OutPut(n);
	t = m->next;
	
	while(m->next != NULL && n->next != NULL)
	{
		if(m->next->exp == n->next->exp)
		{
			m->next->coef = m->next->coef + n->next->coef;
			m = m->next;n = n->next;
		}
		else if(m->next->exp < n->next->exp )
		{
			m=m->next;
		}
		else if(m->next->exp > n->next->exp)
		{
			n=n->next;
			Insert(m,n);
		}
	}
			
	while(n != NULL)
	{
		m->next = n->next;
		m = m->next;
		n = n->next;
	}
	
	A->next= t;
}

输入函数A:
$$f(x)=1+2x^1+3x^3+4x^5$$
输入函数B:
$$f(x)=2+x^2$$

运行结果

2.使用指针的有序相加算法

//一元多项式求和
void SumList(SList* &A,SList* B)
{
	SList *m,*n,*t,*p;
	if(GetLine(A) > GetLine(B) )	
		{m=A;n=B;}
	else 
		{m=B;n=A;}
	t = m->next;
	
	while(m->next != NULL && n->next != NULL)
	{
		if(m->next->exp == n->next->exp)
		{
			m->next->coef = m->next->coef + n->next->coef;
			m = m->next;n = n->next;
		}
		else if(m->next->exp < n->next->exp )
		{
			m=m->next;
		}
		else if(m->next->exp > n->next->exp)
		{
			p = n->next->next;
			n->next->next = m->next;
			m->next = n->next;
			n->next = p; 
		}
	}	
	while(n != NULL)
	{
		m->next = n->next;
		m = m->next;
		n = n->next;
	}
	
	A->next= t;
}

3.乱序幂次算法

//冒泡排序
void SortList(SList *head) 
{
    SList *p,*q,*t;
    for(p=head->next; p->next!=NULL; p=p->next)
	{
        for(q=p->next; q!=NULL; q=q->next)
        {
			if (p->exp > q->exp)
            {
                int t = p->coef; 
				p->coef = q->coef; 
				q->coef = t;
				
                t = p->exp;
				p->exp = q->exp;
				q->exp = t;
            }
            else {}
		}
	}
}

输入函数A:
$$f(x)=1x+2x^2+3x^3+4x^4$$

输入函数B:
$$f(x)=5x^5+4x^7+5x^2$$

3.完整代码

func.h

#include <iostream>
#include <stdlib.h>

using namespace std;
//#define MaxSize 20
typedef int ElemType;

//定义链表结构 
typedef struct SList{
	ElemType coef;
	int exp;
	struct SList *next;
}SList;

//链表的初始化
void InitList(SList* &head,int n);

//输出链表 
void OutPut(SList *head);

//释放链表 
void FreeList(SList *head);

//返回第n个节点的指针 
SList* GetPoint(SList* head);

//一元多项式求和
void SumList(SList* &A, SList* B);

//返回表长度 
int GetLine(SList* head);

//插入某处某数据
void Insert(SList* &m,SList* n);

void SortList(SList *head) ;

func.cpp

#include "func.h"
//#define MaxSize 20
//链表的初始化
void InitList(SList* &head,int n) 
{
	cout<<"please input the function:"<<endl;
	SList *node,*end;
	head = (SList*)malloc(sizeof(SList));
	end = head;
	for(int i=0;i<n;i++)
	{
		node = (SList*)malloc(sizeof(SList));
		cin >> node->coef;
		cin >> node->exp;
		end->next = node;
		end = node;
	}
	end->next = NULL; 
	cout << "The input is over"<<endl;
}


void OutPut(SList *head)
{
	SList *p;
	p = head->next;
	while(p != NULL)
	{
		cout <<p->coef<<"x^"<<p->exp<<" ";
		p = p->next; 
	}
	cout<<endl;
}

void FreeList(SList *head)
{
	SList *p,*t=NULL;
	p = head;
	if(p != NULL && p->next != NULL)
	{
		t = p->next;
		p->next = t->next;
		free(t);
		t=NULL;
	}	
	else
		cout << "该链表不存在"; 
	cout << endl;
}


int GetLine(SList *head)
{
	SList *p = head;
	SList *q;
	int i=0;
	while(p->next != NULL)
	{
		p=p->next;
		i++;
	}
	if(i == 0)	cout << "该链表不存在"<<endl; 
	return i;
}


//一元多项式求和
void SumList(SList* &A,SList* B)
{
	SList *m,*n,*t;
	if(GetLine(A) > GetLine(B) )	
		{m=A;n=B;}
	else 
		{m=B;n=A;}
	//OutPut(m);OutPut(n);
	t = m->next;
	
	while(m->next != NULL && n->next != NULL)
	{
		if(m->next->exp == n->next->exp)
		{
			m->next->coef = n->next->coef + n->next->coef;
			m = m->next;n = n->next;
		}
		else if(m->next->exp < n->next->exp )
		{
			m=m->next;
		}
		else if(m->next->exp > n->next->exp)
		{
			n=n->next;
			Insert(m,n);
		}
	}
			
	while(n != NULL)
	{
		m->next = n->next;
		m = m->next;
		n = n->next;
	}
	
	A->next= t;
}

//将n指针指向的数据插入到m指针后 
void Insert(SList* &m,SList* n)
{
	SList *note;
	note = (SList*)malloc(sizeof(SList));
	note->coef = n->coef;
	note->exp = n->exp;
	note->next = m->next;
	m->next = note;
}


//冒泡排序 节点值交换
void SortList(SList *head) 
{
    SList *p,*q,*t;
    for(p=head->next; p->next!=NULL; p=p->next)
	{
        for(q=p->next; q!=NULL; q=q->next)
        {
			if (p->exp > q->exp)
            {
                int t = p->coef; 
				p->coef = q->coef; 
				q->coef = t;
				
                t = p->exp;
				p->exp = q->exp;
				q->exp = t;
            }
            else {}
		}
	}
}

main.cpp

#include <iostream>
#include "func.h"
int main() 
{
	
	SList *A,*B;
	//FreeList(A);FreeList(B); 
	InitList(A,4);InitList(B,3);
	//cout<<GetLine(A);
	//OutPut(A);
	SortList(A);SortList(B);
	OutPut(A);OutPut(B);
	SumList(A, B);
	cout <<"求和结果：" ; 
	OutPut(A);
	//OutPut(B);
	FreeList(A);FreeList(B); 
	return 0;
}