package com.clarck.datastructure.matrix;/** * 稀疏矩陣的壓縮存儲 * * 稀疏矩陣非零元素的三元組類 * * @author clarck * */public class Triple implements Comparable<Triple> {  // 行號，列號， 元素值，默認訪問權限  int row, colum, value;  public Triple(int row, int colum, int value) {    if (row < 0 || colum < 0) {      throw new IllegalArgumentException("稀疏矩陣元素三元組的行/列序號非正數");    }    this.row = row;    this.colum = colum;    this.value = value;  }  /**   * 拷貝構造方法，復制一個三元組   *   * @param elem   */  public Triple(Triple elem) {    this(elem.row, elem.colum, elem.value);  }  @Override  public String toString() {    return "(" + row + ", " + colum + ", " + value + ")";  }  /**   * 兩個三元組是否相等，比較位置和元素值   */  public boolean equals(Object obj) {    if (!(obj instanceof Triple))      return false;    Triple elem = (Triple) obj;    return this.row == elem.row && this.colum == elem.colum        && this.value == elem.value;  }  /**   * 根據三元組位置比較兩個三元組的大小，與元素值無關，約定三元組排序次序   */  @Override  public int compareTo(Triple elem) {    //當前三元組對象小    if (this.row < elem.row || this.row == elem.row && this.colum < elem.colum)      return -1;    //相等，與equals方法含義不同    if (this.row == elem.row && this.colum == elem.colum)      return 0;    //當前三元組對象大    return 1;  }  /**   * 加法， +=運算符作用   * @param term   */  public void add(Triple term) {    if (this.compareTo(term) == 0)      this.value += term.value;    else      throw new IllegalArgumentException("兩項的指數不同，不能相加");  }  /**   * 約定刪除元素   *   * @return   */  public boolean removable() {    //不存儲為0的元素    return this.value == 0;  }  /**   * 返回對稱位置矩陣元素的三元組   * @return   */  public Triple toSymmetry() {    return new Triple(this.colum, this.row, this.value);  }  /**   * 加法運算，重載運算符+   * @return   */  public Triple plus(Triple term) {    Triple tmp = new Triple(this);    tmp.add(term);    return tmp;  }}

package com.clarck.datastructure.matrix;import com.clarck.datastructure.linear.SeqList;/** * 稀疏矩陣的壓縮存儲 * * 稀疏矩陣三元組順序表 * * 三元組順序存儲的稀疏矩陣類 * * @author clarck * */public class SeqSparseMatrix {  // 矩陣行數、列數  private int rows, columns;  // 稀疏矩陣三元組順序表  private SeqList<Triple> list;  /**   * 構造rows行，colums列零矩陣   *   * @param rows   * @param columns   */  public SeqSparseMatrix(int rows, int columns) {    if (rows <= 0 || columns <= 0)      throw new IllegalArgumentException("矩陣行數或列數為非正數");    this.rows = rows;    this.columns = columns;    // 構造空順序表，執行SeqList()構造方法    this.list = new SeqList<Triple>();  }  public SeqSparseMatrix(int rows, int columns, Triple[] elems) {    this(rows, columns);    // 按行主序插入一個元素的三元組    for (int i = 0; i < elems.length; i++)      this.set(elems[i]);  }  /**   * 返回矩陣第i行第j列元素，排序順序表的順序查找算法，O(n)   *   * @param i   * @param j   * @return   */  public int get(int i, int j) {    if (i < 0 || i >= rows || j < 0 || j >= columns)      throw new IndexOutOfBoundsException("矩陣元素的行或列序號越界");    Triple item = new Triple(i, j, 0);    int k = 0;    Triple elem = this.list.get(k);    // 在排序順序表list中順序查找item對象    while (k < this.list.length() && item.compareTo(elem) >= 0) {      // 只比較三元組元素位置，即elem.row == i && elem.column == j      if (item.compareTo(elem) == 0)        return elem.value;      // 查找到(i, j), 返回矩陣元素      k++;      elem = this.list.get(k);    }    return 0;  }  /**   * 以三元組設置矩陣元素   *   * @param elem   */  public void set(Triple elem) {    this.set(elem.row, elem.colum, elem.value);  }  /**   * 設置矩陣第row行第column列的元素值為value，按行主序在排序順序表list中更改或插入一個元素的三元組， O(n)   *   * @param row   * @param column   * @param value   */  public void set(int row, int column, int value) {    // 不存儲值為0元素    if (value == 0)      return;    if (row >= this.rows || column >= this.columns)      throw new IllegalArgumentException("三元組的行或列序號越界");    Triple elem = new Triple(row, column, value);    int i = 0;    // 在排序的三元組順序表中查找elem對象，或更改或插入    while (i < this.list.length()) {      Triple item = this.list.get(i);      // 若elem存在，則更改改位置矩陣元素      if (elem.compareTo(item) == 0) {        // 設置順序表第i個元素為elem        this.list.set(i, elem);        return;      }      // elem 較大時向后走      if (elem.compareTo(item) >= 0)        i++;      else        break;    }    this.list.insert(i, elem);  }  @Override  public String toString() {    String str = "三元組順序表：" + this.list.toString() + "/n";    str += "稀疏矩陣" + this.getClass().getSimpleName() + "(" + rows + " * "        + columns + "): /n";    int k = 0;    // 返回第k個元素，若k指定序號無效則返回null    Triple elem = this.list.get(k++);    for (int i = 0; i < this.rows; i++) {      for (int j = 0; j < this.columns; j++)        if (elem != null && i == elem.row && j == elem.colum) {          str += String.format("%4d", elem.value);          elem = this.list.get(k++);        } else {          str += String.format("%4d", 0);        }      str += "/n";    }    return str;  }  /**   * 返回當前矩陣與smat相加的矩陣， smatc=this+smat,不改變當前矩陣，算法同兩個多項式相加   *   * @param smat   * @return   */  public SeqSparseMatrix plus(SeqSparseMatrix smat) {    if (this.rows != smat.rows || this.columns != smat.columns)      throw new IllegalArgumentException("兩個矩陣階數不同，不能相加");    // 構造rows*columns零矩陣    SeqSparseMatrix smatc = new SeqSparseMatrix(this.rows, this.columns);    int i = 0, j = 0;    // 分別遍歷兩個矩陣的順序表    while (i < this.list.length() && j < smat.list.length()) {      Triple elema = this.list.get(i);      Triple elemb = smat.list.get(j);      // 若兩個三元組表示相同位置的矩陣元素，則對應元素值相加      if (elema.compareTo(elemb) == 0) {        // 相加結果不為零，則新建元素        if (elema.value + elemb.value != 0)          smatc.list.append(new Triple(elema.row, elema.colum,              elema.value + elemb.value));        i++;        j++;      } else if (elema.compareTo(elemb) < 0) { // 將較小三元組復制添加到smatc順序表最后        // 復制elema元素執行Triple拷貝構造方法        smatc.list.append(new Triple(elema));        i++;      } else {        smatc.list.append(new Triple(elemb));        j++;      }    }    // 將當前矩陣順序表的剩余三元組復制添加到smatc順序表最后    while (i < this.list.length())      smatc.list.append(new Triple(this.list.get(i++)));    // 將smat中剩余三元組復制添加到smatc順序表最后    while (j < smatc.list.length()) {      Triple elem = smat.list.get(j++);      if (elem != null) {        smatc.list.append(new Triple(elem));      }    }    return smatc;  }  /**   * 當前矩陣與smat矩陣相加，this+=smat, 改變當前矩陣，算法同兩個多項式相加   *   * @param smat   */  public void add(SeqSparseMatrix smat) {    if (this.rows != smat.rows || this.columns != smat.columns)      throw new IllegalArgumentException("兩個矩陣階數不同，不能相加");    int i = 0, j = 0;    // 將mat的各三元組依次插入(或相加)到當前矩陣三元組順序表中    while (i < this.list.length() && j < smat.list.length()) {      Triple elema = this.list.get(i);      Triple elemb = smat.list.get(j);      // 若兩個三元組表示相同位置的矩陣元素，則對應元素值相加      if (elema.compareTo(elemb) == 0) {        // 相加結果不為0,則新建元素        if (elema.value + elemb.value != 0)          this.list.set(i++, new Triple(elema.row, elema.colum,              elema.value + elemb.value));        else          this.list.remove(i);        j++;      } else if (elema.compareTo(elemb) < 0) { // 繼續向后尋找elemb元素的插入元素        i++;      } else {        // 復制elemb元素插入作為this.list的第i個元素        this.list.insert(i++, new Triple(elemb));        j++;      }    }    // 將mat中剩余三元組依次復制插入當前矩陣三元組順序表中    while (j < smat.list.length()) {      this.list.append(new Triple(smat.list.get(j++)));    }  }  // 深拷貝  public SeqSparseMatrix(SeqSparseMatrix smat) {    this(smat.rows, smat.columns);    // 創建空順序表，默認容量    this.list = new SeqList<Triple>();    // 復制smat中所有三元組對象    for (int i = 0; i < smat.list.length(); i++)      this.list.append(new Triple(smat.list.get(i)));  }  /**   * 比較兩個矩陣是否相等   */  public boolean equals(Object obj) {    if (this == obj)      return true;    if (!(obj instanceof SeqSparseMatrix))      return false;    SeqSparseMatrix smat = (SeqSparseMatrix) obj;    return this.rows == smat.rows && this.columns == smat.columns        && this.list.equals(smat.list);  }  /**   * 返回轉置矩陣   * @return   */  public SeqSparseMatrix transpose() {    //構造零矩陣，指定行數和列數    SeqSparseMatrix trans = new SeqSparseMatrix(columns, rows);    for (int i = 0; i < this.list.length(); i++) {      //插入矩陣對稱位置元素的三元組      trans.set(this.list.get(i).toSymmetry());    }    return trans;  }}

package com.clarck.datastructure.matrix;/** * 稀疏矩陣的壓縮存儲 * * 稀疏矩陣三元組順序表 * * 三元組順序表表示的稀疏矩陣及其加法運算 * * @author clarck * */public class SeqSparseMatrix_test {  public static void main(String args[]) {    Triple[] elemsa = { new Triple(0, 2, 11), new Triple(0, 4, 17),        new Triple(1, 1, 20), new Triple(3, 0, 19),        new Triple(3, 5, 28), new Triple(4, 4, 50) };    SeqSparseMatrix smata = new SeqSparseMatrix(5, 6, elemsa);    System.out.print("A " + smata.toString());    Triple[] elemsb = { new Triple(0, 2, -11), new Triple(0, 4, -17),        new Triple(2, 3, 51), new Triple(3, 0, 10),        new Triple(4, 5, 99), new Triple(1, 1, 0) };    SeqSparseMatrix smatb = new SeqSparseMatrix(5,6,elemsb);    System.out.print("B " + smatb.toString());    SeqSparseMatrix smatc = smata.plus(smatb);    System.out.print("C=A+B"+smatc.toString());    System.out.println();    smata.add(smatb);    System.out.print("A+=B" + smata.toString());    System.out.println("C.equals(A)?" + smatc.equals(smata));    SeqSparseMatrix smatd = new SeqSparseMatrix(smatb);    smatb.set(0,2,1);    System.out.print("B " + smatb.toString());    System.out.print("D " + smatd.toString());    System.out.println("A轉置" + smata.transpose().toString());  }}

A 三元組順序表：((0, 2, 11), (0, 4, 17), (1, 1, 20), (3, 0, 19), (3, 5, 28), (4, 4, 50))稀疏矩陣SeqSparseMatrix(5 * 6):  0  0 11  0 17  0  0 20  0  0  0  0  0  0  0  0  0  0 19  0  0  0  0 28  0  0  0  0 50  0B 三元組順序表：((0, 2, -11), (0, 4, -17), (2, 3, 51), (3, 0, 10), (4, 5, 99))稀疏矩陣SeqSparseMatrix(5 * 6):  0  0 -11  0 -17  0  0  0  0  0  0  0  0  0  0 51  0  0 10  0  0  0  0  0  0  0  0  0  0 99C=A+B三元組順序表：((1, 1, 20), (2, 3, 51), (3, 0, 29), (3, 5, 28), (4, 4, 50), (4, 5, 99))稀疏矩陣SeqSparseMatrix(5 * 6):  0  0  0  0  0  0  0 20  0  0  0  0  0  0  0 51  0  0 29  0  0  0  0 28  0  0  0  0 50 99A+=B三元組順序表：((1, 1, 20), (2, 3, 51), (3, 0, 29), (3, 5, 28), (4, 4, 50), (4, 5, 99))稀疏矩陣SeqSparseMatrix(5 * 6):  0  0  0  0  0  0  0 20  0  0  0  0  0  0  0 51  0  0 29  0  0  0  0 28  0  0  0  0 50 99C.equals(A)?trueB 三元組順序表：((0, 2, 1), (0, 4, -17), (2, 3, 51), (3, 0, 10), (4, 5, 99))稀疏矩陣SeqSparseMatrix(5 * 6):  0  0  1  0 -17  0  0  0  0  0  0  0  0  0  0 51  0  0 10  0  0  0  0  0  0  0  0  0  0 99D 三元組順序表：((0, 2, -11), (0, 4, -17), (2, 3, 51), (3, 0, 10), (4, 5, 99))稀疏矩陣SeqSparseMatrix(5 * 6):  0  0 -11  0 -17  0  0  0  0  0  0  0  0  0  0 51  0  0 10  0  0  0  0  0  0  0  0  0  0 99A轉置三元組順序表：((0, 3, 29), (1, 1, 20), (3, 2, 51), (4, 4, 50), (5, 3, 28), (5, 4, 99))稀疏矩陣SeqSparseMatrix(6 * 5):  0  0  0 29  0  0 20  0  0  0  0  0  0  0  0  0  0 51  0  0  0  0  0  0 50  0  0  0 28 99