单链表实现多项式的表示及运算

  1 //单链表类，实现一些基本单链表的操作
  2 public class SinglyList<T> extends Object {
  3     public Node<T> head; // 头指针，指向单链表的头结点
  4 
  5     public SinglyList() {
  6         this.head = new Node<T>();
  7     }
  8 
  9     public SinglyList(T[] values) { // values数组中的值构成结点
 10         this();
 11         Node<T> rear = this.head;
 12         for (int i = 0; i < values.length; i++) {
 13             rear.next = new Node<T>(values[i], null);
 14             rear = rear.next;
 15         }
 16     }
 17 
 18     public boolean isEmpty() {
 19         return this.head.next == null;
 20     }
 21 
 22     public T get(int i) {
 23         Node<T> p = this.head.next;
 24         for (int j = 0; p != null && j < i; j++) {
 25             p = p.next;
 26         }
 27         return (i >= 0 && p != null) ? p.data : null;
 28     }
 29 
 30     public void set(int i, T x) {
 31         if (i < 0 || i > size())
 32             throw new IndexOutOfBoundsException(i + "");
 33         if (x == null)
 34             throw new NullPointerException("x==null");
 35         Node<T> p = this.head.next;
 36         for (int j = 0; p != null && j < i; j++) {
 37             p = p.next;
 38         }
 39         p.data = x;
 40 
 41     }
 42 
 43     public int size() {
 44         int len = 0;
 45         Node<T> p = this.head.next;
 46         if (p == null)
 47             return -1;
 48         while (p != null) {
 49             len++;
 50             p = p.next;
 51 
 52         }
 53         return len;
 54     }
 55 
 56     public Node<T> insert(int i, T x) {
 57         if (x == null)
 58             throw new NullPointerException("x==null");
 59         Node<T> front = this.head;
 60         for (int j = 0; front.next != null && j < i; j++) {
 61             front = front.next;
 62         }
 63         front.next = new Node<T>(x, front.next);
 64         return front.next;
 65 
 66     }
 67 
 68     public Node<T> insert(T t) {
 69         return insert(Integer.MAX_VALUE, t);
 70     }
 71 
 72     public T remove(int i) {
 73         Node<T> front = this.head;
 74         for (int j = 0; front.next != null && j < i; j++) {
 75             front = front.next;
 76         }
 77         if (i >= 0 && front.next != null) {
 78             T old = front.next.data;
 79             front.next = front.next.next;
 80             return old;
 81         }
 82         return null;
 83 
 84     }
 85 
 86     public void clear() {
 87         this.head.next = null;
 88     }
 89 
 90 }
 91 // 排序单链表，对于一些结点可以实现按顺序插入排序
 92 public class SortedSinglyList<T extends Comparable<? super T>> extends
 93         SinglyList<T> {
 94     public SortedSinglyList() {
 95         super();
 96     }
 97 
 98     public SortedSinglyList(T[] values) { // values的数组中的对象按值插入
 99         super();
100         for (int i = 0; i < values.length; i++) {
101             this.insert(values[i]);
102         }
103     }
104 
105     public SortedSinglyList(SinglyList<T> list) { // 单链表的深拷贝
106         super();
107         for (Node<T> p = list.head.next; p != null; p = p.next)
108             this.insert(p.data);
109     }
110 
111     public Node<T> insert(T x) { // 覆盖父类的insert方法
112         Node<T> front = this.head, p = front.next;
113         while (p != null && x.compareTo(p.data) > 0) {
114             front = p;
115             p = p.next;
116         }
117         front.next = new Node<T>(x, p); // 在front之后，p之前插入x节点
118         return front.next;
119     }
120 
121 }
122 
123 //可相加接口
124 public interface Addible<T> {
125     public void add(T t); // 两元素相加
126 
127     public boolean removable(); // 删除元素
128 
129 }
130 //比较大小接口
131 public interface Comparable<T> {
132     int compareTo(T obj);
133 
134 }
135 
136 /*
137  * 一元多项式节点类 存储多项式的系数(coefficient)和指数(exponential)
138  */
139 public class PolyNode implements Comparable<PolyNode>, Addible<PolyNode> {
140     private int coef;// 系数
141     private int expo;// 指数
142 
143     protected PolyNode next;
144 
145     public PolyNode() {
146         this(0, 0);
147     }
148 
149     public PolyNode(int coef, int expo) { // 带参数的构造函数
150 
151         this.coef = coef;
152         this.expo = expo;
153         // this.next = null;
154     }
155 
156     public PolyNode(PolyNode po) { // 拷贝构造函数
157         this(po.coef, po.expo);
158     }
159 
160     public boolean equals(Object obj) // 比较两项是否相等
161     {
162         if (this == obj)
163             return true;
164         if (!(obj instanceof PolyNode))
165             return false;
166         PolyNode term = (PolyNode) obj;
167         return this.coef == term.coef && this.expo == term.expo;
168     }
169 
170     public PolyNode(String str) { // 参数为一个项时，得到项的系数和指数
171         if (str.charAt(0) == ‘+‘)
172             str = str.substring(1); // 去掉‘+’号
173         int i = str.indexOf(‘x‘);
174         if (i == -1) {
175             this.coef = Integer.parseInt(str); // 没有x,指数就为0
176             this.expo = 0;
177         } else {
178             if (i == 0) { // x在开头，系数为1
179                 this.coef = 1;
180             } else {
181                 String str1 = str.substring(0, i);// 截取x符号之前的系数
182                 if (str1.equals("-")) { // 为‘-’，系数为-1
183                     this.coef = -1;
184                 } else {
185                     this.coef = Integer.parseInt(str1);
186                 }
187                 i = str.indexOf(‘^‘);// 找^符号
188                 if (i == -1)
189                     this.expo = 1;
190                 else
191                     this.expo = Integer.parseInt(str.substring(i + 1));
192             }
193         }
194     }
195 
196     public String toString() { // 显示多项式的样式
197         String sy = this.coef > 0 ? "+" : "-";
198         if (this.expo == 0 || this.expo > 0 && this.coef != 1
199                 && this.coef != -1) {
200             sy += Math.abs(this.coef); // 系数绝对值，系数为-1或1不能显示
201         }
202         if (this.expo > 0)
203             sy += "x";// 指数为0不能输出x
204         if (this.expo > 1)
205             sy += "^" + this.expo;// 指数为1不能输出^
206         return sy;
207     }
208 
209     public int compareTo(PolyNode a) { // 比较两项的大小
210         return (this.expo < a.expo ? -1 : (this.expo == a.expo ? 0 : 1));
211     }
212 
213     public void add(PolyNode po) { // 相加
214         if (this.compareTo(po) == 0)
215             this.coef += po.coef;
216 
217     }
218 
219     public boolean removable() { // 删除
220         return this.coef == 0;
221     }
222 
223     public int getCoef() {
224         return coef;
225     }
226 
227     public void setCoef(int coef) {
228         this.coef = coef;
229     }
230 
231     public int getExpo() {
232         return expo;
233     }
234 
235     public void setExpo(int expo) {
236         this.expo = expo;
237     }
238 
239 }
240 /*
241  * 一元多项式排序链表类，提供排序单链表的多项式相加运算；
242  */
243 public class PolySort<T extends Comparable<? super T> & Addible<T>> extends
244         SortedSinglyList<T> {
245 
246     public PolySort() {
247         super(); // 构造空单链表
248     }
249 
250     public PolySort(T value[]) { // 构造方法，项的组来指定各项的值
251         super(value);
252     }
253 
254     public PolySort(PolySort<T> list) {// 调用父类的深拷贝函数，复制所有结点
255         super(list);
256     }
257 
258     // 多项式相加函数
259     public void addAll(PolySort<T> list) {
260         Node<T> front = this.head, p = front.next;
261         Node<T> q = list.head.next;
262         while (p != null && q != null) {
263             if (p.data.compareTo(q.data) == 0) { // 两项大小相同
264                 p.data.add(q.data);
265                 if (p.data.removable()) { // 删除系数为0的结点
266                     front.next = p.next;
267                     p = front.next;
268                 } else {
269                     front = p;
270                     p = p.next;
271 
272                 }
273                 q = q.next;
274             } else if (p.data.compareTo(q.data) < 0) {
275                 front = p;
276                 p = p.next;
277             } else {
278                 front.next = new Node<T>(q.data, p);
279                 q = q.next;
280             }
281         }
282         while (q != null) // 将list单链表中剩余结点复制并插入到当前链表尾
283         {
284             front.next = new Node<T>(q.data, null);
285             front = front.next;
286             q = q.next;
287         }
288     }
289 
290 }
291 // 多项式类，使用多项式排序单链表类作为成员变量，提供多项式相加运算
292 public class Polynomial {
293     private PolySort<PolyNode> list; // 多项式排序单链表
294 
295     public Polynomial() // 构造方法
296     {
297         this.list = new PolySort<PolyNode>(); // 创建空单链表，执行排序单链表默认构造方法
298     }
299 
300     public Polynomial(PolyNode terms[]) // 构造方法，由项数组指定多项式各项值
301     {
302         this.list = new PolySort<PolyNode>(terms);
303     }
304 
305     public Polynomial(String polystr) // 构造方法，参数指定多项式表达式字符串
306     {
307         this();
308         if (polystr == null || polystr.length() == 0)
309             return;
310         Node<PolyNode> rear = this.list.head;
311         int start = 0, end = 0; // 序号start～end的子串为一项
312         while (start < polystr.length() && end < polystr.length()) {
313             int i = polystr.indexOf(‘+‘, end + 1); // 返回字符+在字符串中从end+1开始的序号
314             if (i == -1) // 未找到指定字符
315                 i = polystr.length();
316             int j = polystr.indexOf(‘-‘, end + 1);
317             if (j == -1)
318                 j = polystr.length();
319             end = i < j ? i : j; // end为下一个+或-号的序号
320             rear.next = new Node<PolyNode>(new PolyNode(polystr.substring(
321                     start, end)), null);
322             // 尾插入，以序号start～end的子串作为一项，创建结点，创建元素对象
323             rear = rear.next;
324             start = end;
325         }
326     }
327 
328     public Polynomial(Polynomial poly) // 深度拷贝构造方法，复制所有结点和对象
329     {
330         this(); // 创建空单链表，只有头结点
331         Node<PolyNode> rear = this.list.head;
332         for (Node<PolyNode> p = poly.list.head.next; p != null; p = p.next) // p遍历poly单链表
333         {
334             rear.next = new Node<PolyNode>(new PolyNode(p.data), null);// 复制结点，复制对象
335             rear = rear.next;
336         }
337     }
338 
339     public String toString() // 返回多项式的描述字符串
340     {
341         String str = "";
342         for (Node<PolyNode> p = this.list.head.next; p != null; p = p.next)
343             str += p.data.toString();
344         return str;
345     }
346 
347     public void addAll(Polynomial poly) // 多项式相加，this＋=poly
348     {
349         this.list.addAll(poly.list);
350     }
351 
352     public Polynomial union(Polynomial poly) // 加法＋，C=this＋poly
353     {
354         Polynomial polyc = new Polynomial(this); // 深度拷贝，复制所有结点和对象
355         polyc.addAll(poly); // polyc＋=poly
356         return polyc; // 返回对象引用
357     }
358 
359     public boolean equals(Object obj) // 比较两个多项式是否相等
360     {
361         return this == obj || obj instanceof Polynomial
362                 && this.list.equals(((Polynomial) obj).list);
363         // 比较两条单链表是否相等
364     }
365 }
366 // 测试类，完成多项式的相加结果并显示
367 public class Poly extends PolySort {
368 
369     public static void main(String[] args) {
370 
371         System.out.println("//一元多项式");
372         PolyNode aterms[] = { new PolyNode(-7, 9), new PolyNode(2, 7),
373                 new PolyNode(-9, 4), new PolyNode(1, 2), new PolyNode(-1, 1),
374                 new PolyNode(2, 0) };
375         Polynomial apoly = new Polynomial(aterms);
376 
377         PolyNode bterms[] = { new PolyNode(9, 11), new PolyNode(5, 10),
378                 new PolyNode(-3, 8), new PolyNode(10, 4), new PolyNode(-1, 2),
379                 new PolyNode(1, 1), new PolyNode(-1, 0) };
380         Polynomial bpoly = new Polynomial(bterms);
381 
382         // Polynomial bpoly = new Polynomial("-1+x-x^2+10x^4-3x^8+5x^10+9x^11");
383         System.out.println("A=" + apoly.toString() + "\nB=" + bpoly.toString());
384 
385         Polynomial cpoly = apoly.union(bpoly);
386         System.out.println("C=A+B，C=" + cpoly.toString());
387         apoly.addAll(bpoly);
388         System.out.println("A+=B，A=" + apoly.toString());
389 
390     }
391 }