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());}elses.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 stubwhile(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；