我需要使用递归方法将两个多项式相加。 这是一个过期的任务（我想类似的事情将在测试中）。 主要课程：
public class Polynomial {
private Node poly;
public Polynomial(){
poly = new Node();
}
private Polynomial(Node node){
poly = node;
}
public void addTerm(int coef, int exp){
Term term = new Term(coef, exp);
Node node = new Node(term, null);
Node iterator = poly;
//if the list is empty just add the node
if (poly.next == null){
System.out.println("poly.next is null. adding node to first pos.");
poly.next = node;
return;
}
//if list isn't empty find the appropriate spot for it
while (iterator.next != null){
System.out.println("iterator.next != null...");
if (exp < iterator.next.data.exp){
System.out.println("\texp < iterator.next.data.exp");
node.next = iterator.next;
iterator.next = node;
return;
}
if (exp == iterator.next.data.exp){
System.out.println("\texp == iterator.next.data.exp");
iterator.next.data.coef += coef;
return;
}
iterator = iterator.next;
}
//if we get to this point then the list isn't empty
//and it doesn't fit inside the list, hence it must
//be added to the end of the list
System.out.println("list wasn't empty, didn't fit inside");
iterator.next = node;
return;
}
@Override
public String toString(){
Node iterator = poly;
String out = "";
if (poly.next == null){
return out;
}
while(iterator.next != null){
out += iterator.next.data.coef;
out += "*x^";
out += iterator.next.data.exp;
out += " + ";
iterator = iterator.next;
}
return out.substring(0, out.lastIndexOf('+'));
}
public Polynomial addPolynomial (Polynomial that){
Polynomial ret = new Polynomial();
Polynomial iterator = this;
return addPolynomial(that, ret, iterator);
}
public Polynomial addPolynomial(Polynomial that, Polynomial ret, Polynomial iterator){
if (iterator.poly.next == null){
return new Polynomial(that.poly);
}
if (that.poly.next == null){
return new Polynomial(iterator.poly);
}
if (iterator.poly.next.data.exp < that.poly.next.data.exp){
ret.addTerm(iterator.poly.next.data.coef, iterator.poly.next.data.exp);
iterator.poly = iterator.poly.next;
return iterator.addPolynomial(that);
}
if (iterator.poly.next.data.exp == that.poly.next.data.exp){
ret.addTerm(iterator.poly.next.data.coef + that.poly.next.data.coef, iterator.poly.next.data.exp);
iterator.poly = iterator.poly.next;
that.poly = that.poly.next;
return iterator.addPolynomial(that);
}
if (iterator.poly.next.data.exp > that.poly.next.data.exp){
ret.addTerm(that.poly.next.data.coef, that.poly.next.data.exp);
that.poly = that.poly.next;
return iterator.addPolynomial(that);
}
return ret;
}
/*
* Term
*/
private class Term implements Comparable{
int coef;
int exp;
public int getCoef() {
return coef;
}
public void setCoef(int coef) {
this.coef = coef;
}
public int getExp() {
return exp;
}
public void setExp(int exp) {
this.exp = exp;
}
public Term(int coef, int exp) {
this.coef = coef;
this.exp = exp;
}
public int compareTo(Object rhs){
Term that = (Term)rhs;
return this.exp - that.exp;
}
}//end Term
/*
* Node
*/
private class Node{
Term data;
Node next;
public Term getData() {
return data;
}
public void setData(Term data) {
this.data = data;
this.next = null;
}
public Node getNext() {
return next;
}
public void setNext(Node next) {
this.next = next;
}
public Node() {
this.data = null;
this.next = null;
}
public Node(Term data, Node next) {
this.data = data;
this.next = next;
}
}//end Node
}
测试类：
public class Polynomials {
/**
* @param args the command line arguments
*/
public static void main(String[] args) {
Polynomial p1 = new Polynomial();
Polynomial p2 = new Polynomial();
Polynomial p0 = new Polynomial();
p1.addTerm(1, 2);
p1.addTerm(1, 4);
p1.addTerm(1, 6);
p2.addTerm(1, 1);
p2.addTerm(1, 3);
p2.addTerm(1, 5);
System.out.println("p1 = " + p1.toString());
System.out.println("p2 = " + p2.toString());
System.out.println("Adding p1 to p2...");
p0 = p1.addPolynomial(p2);
System.out.println(p0.toString());
}
}
答案 0 :(得分：1)
您是否考虑过这种做法？
public class Polynomial {
public static void main(String[] args) {
Polynomial p1 = new Polynomial();
Polynomial p2 = new Polynomial();
Polynomial p0 = new Polynomial();
p1.addTerm(1, 2);
p1.addTerm(1, 4);
p1.addTerm(1, 6);
p2.addTerm(1, 1);
p2.addTerm(2, 3);
p2.addTerm(2, 2);
p2.addTerm(1, 5);
System.out.println("p1 = " + p1.toString());
System.out.println("p2 = " + p2.toString());
System.out.println("Adding p1 to p2...");
p0 = p1.addPolynomial(p2);
System.out.println(p0.toString());
for(int i = 0;i < 100;i++) {
p1 = new Polynomial();
p2 = new Polynomial();
for(int j = 0;j < 4;j++) {
p1.addTerm((int) (10 * Math.random()) - 5,
(int) (4 * Math.random()));
p2.addTerm((int) (10 * Math.random()) - 5,
(int) (4 * Math.random()));
}
p0 = p1.addPolynomial(p2);
System.out.println(p1 + "\n" + p2 + "\n" + p0 + "\n");
}
}
enum Comp {
LT, EQ, GT
}
static Comp cmp(int a, int b) {
return (a < b) ? Comp.LT : (a == b) ? Comp.EQ : Comp.GT;
}
private Term poly;
public Polynomial() {
poly = null;
}
public void addTerm(int coef, int exp) {
if (coef == 0) return;
Term term = new Term(coef, exp,null);
if (poly == null) {
poly = term;
} else {
poly = poly.add(term);
}
}
@Override
public String toString() {
if (poly == null) return "0";
StringBuilder buf = new StringBuilder();
poly.writeTo(buf);
return buf.toString();
}
public Polynomial addPolynomial(Polynomial that) {
Polynomial ret = new Polynomial();
if (poly != null) {
ret.poly = new Term(poly);
if (that.poly != null) {
ret.poly = ret.poly.add(new Term(that.poly));
}
} else if (that.poly != null) {
ret.poly = new Term(that.poly);
}
return ret;
}
private class Term {
final int coef;
final int exp;
final Term next;
Term(int coef, int exp, Term next) {
this.coef = coef;
this.exp = exp;
this.next = next;
}
Term(Term copy) {
this.coef = copy.coef;
this.exp = copy.exp;
if (copy.next == null) {
this.next = null;
} else {
this.next = new Term(copy.next);
}
}
Term add(Term other) {
if (other == null) return this;
switch (cmp(this.exp, other.exp)) {
case LT: {
Term n = other.add(this);
return n;
}
case GT: {
if (next == null) {
return new Term(coef,exp,other);
}
return new Term(coef,exp,next.add(other));
}
default: {
Term n = (next==null) ? other.next : next.add(other.next);
int nc = coef+other.coef;
return (nc!=0) ? new Term(nc,exp,n) : n;
}
}
}
public void writeTo(StringBuilder app) {
if (coef != 1 || exp == 0) app.append(coef);
if (exp == 1) {
app.append("x");
} else if (exp != 0) {
app.append("x^").append(exp);
}
if (next != null) {
app.append('+');
next.writeTo(app);
}
}
}
}
答案 1 :(得分：0)
那肯定比必要的复杂一点。
所以你想在已经存在的多项式中添加一个多项式，即： 4 * x ^ 2 + 4到5 * x ^ 4 + x + 5，结果为：5 * x ^ 4 + 4 * x ^ 2 + x + 9
你可以通过使用一个数组显然可以简化问题，但是对于链表也没那么难，代码看起来应该是这样的：
你有两个指针指向我们想要添加值（term1）的多项式中的当前位置，另一个指向我们想要添加的值（term2），两个指针都初始化为链表中的最低条目（其中我们假设根据指数排序。
while term1 != NULL && term2 != NULL do:
term1 > term2:
add term2 to list
term2 = term2.next()
term2 > term1:
term1 = term1.next()
term1 = term2:
add term2 to term1
term1 = term1.next()
term2 = term2.next()
while term1 == NULL && term2 != NULL:
add term2
term2 = term2.next()
您可以轻松地调整它以创建新的多项式，而不是将一个多项式添加到另一个。
好的，有关如何将迭代解决方案转换为递归解决方案的更多细节： 在考虑递归时，您始终要做的第一件事就是退出条件。
在这种情况下，如果您认为这很容易：只要term2不为NULL，我们才会工作，只要term2为NULL，我们就完成了。
下一步是考虑一个好的方法签名，这次也很容易，因为我们只需要这两个术语，所以你可以使用两个迭代器： void addTogether（Iterator term1，Iterator term2）; （假设您使用的是与ListIterator类似的接口，因为您需要在term1之前的位置插入 - 有几种方法可以实现它）
现在你已经摆脱了while循环并用递归调用替换它们（在这种情况下你可以区分不同的情况，做必要的操作并再次调用它）