链表的经典应用，程序在多项式相加同类项合并还有小的瑕疵，有待改进。

代码如下：

package 一元多项式计算器;

public class PolyNode {

	private double a;

    private int i;

    PolyNode next;  

    public PolyNode(double a,int i){  

         this.a=a;

         this.i=i;

         this.next=null;

    }

    public PolyNode(){  

        this(0,0);

    }

    public double getA() {

        return a;

    }

    public int getI() {

        return i;

    }

    public void setA(double a) {

        this.a = a;

    }

    public void setI(int i) {

        this.i = i;

    }  

}

package 一元多项式计算器;

public class PolyList {

	PolyNode head;

    PolyNode current;  

    public PolyList(){  

        head=new PolyNode();

        current=head;

        head.next=null;

    }  

    //是否为空

    public boolean isEmpty(){  

        return head.next==null;

    }

    //这里只考虑按顺序插入元素

    public void insert(PolyNode node){  

        current.next=node;

        current=node;

    }

    //打印多项式

    public String printS(){  

        StringBuilder s=new StringBuilder("");

        StringBuilder a=new StringBuilder("");

        StringBuilder i=new StringBuilder("");

        StringBuilder theOne=new StringBuilder("");

        current=head.next;

        int count1=0;

        int count2=0;

        while(current!=null){

        	if(current.getA() == 0){

        		count1++;

        	}

        	count2++;

        	current = current.next;

        }

          if(count1 == count2){

        	  s.append("0");

          }else{

         current=head.next;

         while(current!=null){  

             a.delete(0, a.length());

             i.delete(0, i.length());

             theOne.delete(0, theOne.length());  

                 if((current.getA()==1 || current.getA()==-1) && current.getI()!=0)

                     a.append("");

                 else if(current.getA() < 0){

                	 a.append(String.valueOf((-current.getA())));

                 }else{

                     a.append(String.valueOf(current.getA()));

                 }

                 if(current.getI()==1)

                 {

                     i.append("");

                     theOne.append(a.toString()).append("x").append(i.toString());

                 } else if(current.getI()==0){

                     i.append("");

                     theOne.append(a.toString());

                 } else{

                	 i.append(String.valueOf(current.getI()));

                     theOne.append(a.toString()).append("x^").append(i.toString());

                 }

            if(current.getA() == 0){

            	s.append("");

            }else{

            if(current==head.next && current.getA()<0){

            	s.append("-").append(theOne.toString());

            }else if(current==head.next && current.getA()>0){

                 s.append(theOne.toString());

            }

            else if(current.getA() < 0){

            	s.append(" - ").append(theOne.toString());

            }else

                s.append(" + ").append(theOne.toString());

            }

             current = current.next;

         }

          }

         return s.toString();

    }  

    //加法运算

    public static PolyList add(PolyList p1,PolyList p2){  

         PolyList result=new PolyList();

         //分别指向p1 p2的第一个元素

         p1.current=p1.head.next;

         p2.current=p2.head.next;

         while(p1.current!=null && p2.current!=null){  

              if(p1.current.getI()==p2.current.getI()){  

                  result.insert(new PolyNode(p1.current.getA()+p2.current.getA(),p1.current.getI()));

                  p1.current=p1.current.next;

                  p2.current=p2.current.next;

              }

              else if(p1.current.getI()<p2.current.getI()){  

                  result.insert(p1.current);

                  p1.current=p1.current.next;  

              }else{

                  result.insert(p2.current);

                  p2.current=p2.current.next;

              }

         }

         while(p1.current!=null){  

              result.insert(p1.current);

              p1.current=p1.current.next;

         }

         while(p2.current!=null){  

              result.insert(p2.current);

              p2.current=p2.current.next;

         }

         //return result;  

         result.current=result.head.next;

         PolyNode tempPrevious=result.current;

         PolyNode temp=result.current.next;

         while(result.current.next!=null){  

             while(temp!=null)

             {

                 if(temp.getI()!=result.current.getI())

                 {

                     temp=temp.next;

                     tempPrevious=tempPrevious.next;

                 }else{

                     result.current.setA(result.current.getA()+temp.getA());

                     tempPrevious.next=temp.next;

                     temp=temp.next;

                 }  

             }

             result.current=result.current.next;

             tempPrevious=result.current;

             temp=result.current.next;

         }

         return result;  

    }

    //减法运算

    public static PolyList sub(PolyList p1,PolyList p2){  

        PolyList result=new PolyList();

        p2.current = p2.head.next;

        while(p2.current!=null){

        	p2.current.setA(-(p2.current.getA()));

        	p2.current=p2.current.next;

        }

        //System.out.println(p2.printS());

        //分别指向p1 p2的第一个元素

        p1.current=p1.head.next;

        p2.current=p2.head.next;

        while(p1.current!=null && p2.current!=null){  

             if(p1.current.getI()==p2.current.getI()){  

                 result.insert(new PolyNode(p1.current.getA()+p2.current.getA(),p1.current.getI()));

                 p1.current=p1.current.next;

                 p2.current=p2.current.next;

             }

             else if(p1.current.getI()<p2.current.getI()){  

                 result.insert(p1.current);

                 p1.current=p1.current.next;  

             }else{

                 result.insert(p2.current);

                 p2.current=p2.current.next;

             }

        }

        while(p1.current!=null){  

             result.insert(p1.current);

             p1.current=p1.current.next;

        }

        while(p2.current!=null){  

             result.insert(p2.current);

             p2.current=p2.current.next;

        }

        return result;  

   }

    //乘法运算

    public static PolyList multiply(PolyList p1,PolyList p2){  

         PolyList result=new PolyList();

         //分别指向p1 p2的第一个元素

         p1.current=p1.head.next;

         p2.current=p2.head.next;

         while(p1.current!=null){  

               while(p2.current!=null)

               {

                   double a=p1.current.getA()*p2.current.getA();

                   int i=p1.current.getI()+p2.current.getI();

                   result.insert(new PolyNode(a,i));

                   p2.current=p2.current.next;

               }

               p1.current=p1.current.next;

               p2.current=p2.head.next;

         }

         //合并同类项

         result.current=result.head.next;

         PolyNode tempPrevious=result.current;

         PolyNode temp=result.current.next;

         PolyNode t = result.current.next;

         while(result.current.next!=null){  

             while(temp!=null)

             {

                 if(temp.getI()!=result.current.getI())

                 {

                     temp=temp.next;

                     tempPrevious=tempPrevious.next;

                 }else{

                     result.current.setA(result.current.getA()+temp.getA());

                     tempPrevious.next=temp.next;

                     temp=temp.next;

                 }  

             }

             result.current=result.current.next;

             tempPrevious=result.current;

             temp=result.current.next;

         }

         return result;

    }

    //就地逆置单链表

    public static void reverse(PolyList p_){

    	PolyNode p,q;

    	p = p_.head.next;

        p_.head.next = null;

        while(p!=null){

        	q = p.next;

        	p.next = p_.head.next;//让p.next变成p_.head.next;

        	p_.head.next = p;//让p_.head.next变成p;

        	p = q;//让p变成q;

        }

    }

}

package 一元多项式计算器;

import java.util.*;

public class Testclass {

	public static void main(String[] args) {

		// TODO Auto-generated method stub

		while(true){

		PolyList p1 = new PolyList();

		PolyList p2 = new PolyList();

		Scanner scan = new Scanner(System.in);

		System.out.print("请输入要计算的第一个多项式的系数和指数，以0,0结束：");

		double a = scan.nextDouble();

		int i = scan.nextInt();

		while(a!=0 || i!=0){

			p1.insert(new PolyNode(a,i));

			a = scan.nextDouble();

			i = scan.nextInt();

		}

        System.out.println("您输入的第一个多项式为：");

        System.out.println("p1 = " + p1.printS());

		System.out.print("请输入要计算的第二个多项式的系数和指数，以0,0结束：");

		a = scan.nextDouble();

		i = scan.nextInt();

		while(a!=0 || i!=0){

			p2.insert(new PolyNode(a,i));

			a = scan.nextDouble();

			i = scan.nextInt();

		}

		System.out.println("您输入的第二个多项式为：");

		System.out.println("p2 = " + p2.printS());

		System.out.println("请按提示选择您想要进行的运算：");

		System.out.println("0 -----> +");

		System.out.println("1 -----> -");

		System.out.println("2 -----> x");

		int n;

		n = scan.nextInt();

		if(n == 0){

			PolyList resultList= PolyList.add(p1, p2);

			PolyList.reverse(resultList);

	        System.out.println("p1 + p2 = "+resultList.printS());

		}else if(n == 1){

			PolyList resultList= PolyList.sub(p1, p2);

			PolyList.reverse(resultList);

	        System.out.println("p1 - p2 = "+resultList.printS());

		}else{

			PolyList resultList= PolyList.multiply(p1, p2);

			//PolyList.reverse(resultList);

	        System.out.println("p1 x p2 = "+resultList.printS());

		}

		}

	}

}

//还存在的bug：1-当系数为0的时候应该删去一整项；   已解决！

//          2-当一个多项式只有0时，应该输出一个0；已解决！

//          3-计算器的仿真界面。已解决！使用不方便！

//          4-合并同类项有空指针错误，待解决，错误数据如1 1 1 1 0 0+1 1 1 1 0 0；
            

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