重温数据结构：链表的应用之多项式的表示及相加和相乘

/*
* $filename: PolynAddAndMultiply.java,v $
* $Date: 2014-3-10  $
* Copyright (C) ZhengHaibo, Inc. All rights reserved.
* This software is Made by Zhenghaibo.
*/
package edu.njupt.zhb;

import java.util.LinkedList;
import java.util.List;

/*
*@author: ZhengHaibo
*web:     http://blog.csdn.net/nuptboyzhb *mail:    zhb931706659@126.com
*2014-3-10  Nanjing,njupt,China
*/
public class PolynAddAndMultiply {
public class Node{//表示k*x^n
public int k;//系数
public int n;//次方数
public Node(int k,int n) {
this.k=k;
this.n=n;
}
@Override
public String toString() {
// TODO Auto-generated method stub
return k+"*"+"x^"+n;
}
}
/**
* 计算多项式的和
* @param polyn1
* @param polyn2
* @return
*/
public List<Node> polynAdd(List<Node> polyn1,List<Node> polyn2){
List<Node> result = new LinkedList<Node>();
int p1 = 0;
int p2 = 0;
while(p1<polyn1.size()&&p2<polyn2.size()){
Node node1 = polyn1.get(p1);
Node node2 = polyn2.get(p2);
if(node1.n<node2.n){//node1的次方小于node2
result.add(node1);
p1++;
}else if(node1.n==node2.n){//同次幂
if(node1.k+node2.k!=0){//系数相加不为0
result.add(new Node(node1.k+node2.k,node1.n));
}
p1++;
p2++;
}else{//node2的次方小于node1
result.add(node2);
p2++;
}
}
while (p1<polyn1.size()) {//如果polyn1还有剩余
result.add(polyn1.get(p1));
p1++;
}
while (p2<polyn2.size()) {//如果polyn2还有剩余
result.add(polyn2.get(p2));
p2++;
}
return result;
}
/**
* 打印多项式
* @param list
*/
public void display(List<Node> list){
if(null==list||list.size()<1){
return;
}
System.out.print(list.get(0));
for(int i=1;i<list.size();i++){
Node node = list.get(i);
if(node.k<=0){
System.out.print(list.get(i));
}else{
System.out.print("+"+list.get(i));
}
}
System.out.println("");
}
/**
* 计算多项式的乘积
* 思路：逐个相乘，然后累加
* @param polyn1
* @param polyn2
* @return
*/
public List<Node> polynMultiply(List<Node> polyn1,List<Node> polyn2){
List<Node> resultList = new LinkedList<Node>();
for(int p1=0;p1<polyn1.size();p1++){//分别取出第一个多项式的每一项
Node node1 = polyn1.get(p1);
List<Node> tempList = new LinkedList<Node>();//用于保存第p1项与polyn2各项相乘的结果
for (int p2 = 0; p2 < polyn2.size(); p2++) {
Node node2 = polyn2.get(p2);
Node node = new Node(node1.k*node2.k, node1.n+node2.n);
tempList.add(node);
}
resultList=polynAdd(tempList,resultList);//求和
}
return resultList;
}
/**
* 测试上述的方法
*/
public void test(){
List<Node> polyn1 = new LinkedList<Node>();
polyn1.add(new Node(2,2));
polyn1.add(new Node(-100,3));
polyn1.add(new Node(45,5));
polyn1.add(new Node(3,20));
display(polyn1);//2*x^2-100*x^3+45*x^5+3*x^20
List<Node> polyn2 = new LinkedList<Node>();
polyn2.add(new Node(-8,2));
polyn2.add(new Node(7,3));
polyn2.add(new Node(4,4));
polyn2.add(new Node(6,18));
polyn2.add(new Node(7,20));
display(polyn2);//-8*x^2+7*x^3+4*x^4+6*x^18+7*x^20
List<Node> result = polynAdd(polyn1, polyn2);
display(result);//-6*x^2-93*x^3+4*x^4+45*x^5+6*x^18+10*x^20
List<Node> result2 = polynMultiply(polyn1, polyn2);
display(result2);
//-16*x^4+814*x^5-692*x^6-760*x^7+315*x^8+180*x^9+
//12*x^20-600*x^21-10*x^22-409*x^23+12*x^24+315*x^25+18*x^38+21*x^40
}
public static void main(String[] args) {
new PolynAddAndMultiply().test();
}
}