Java数据结构之稀疏矩阵定义与用法示例

本文实例讲述了Java数据结构之稀疏矩阵定义与用法。分享给大家供大家参考，具体如下：

稀疏矩阵非零元素的三元组类:

package com.clarck.datastructure.matrix;
/**
 * 稀疏矩阵的压缩存储
 *
 * 稀疏矩阵非零元素的三元组类
 *
 * @author clarck
 *
 */
public class Triple implements Comparable<Triple> {
  // 行号，列号， 元素值，默认访问权限
  int row, colum, value;
  public Triple(int row, int colum, int value) {
    if (row < 0 || colum < 0) {
      throw new IllegalArgumentException("稀疏矩阵元素三元组的行/列序号非正数");
    }
    this.row = row;
    this.colum = colum;
    this.value = value;
  }
  /**
   * 拷贝构造方法，复制一个三元组
   *
   * @param elem
   */
  public Triple(Triple elem) {
    this(elem.row, elem.colum, elem.value);
  }
  @Override
  public String toString() {
    return "(" + row + ", " + colum + ", " + value + ")";
  }
  /**
   * 两个三元组是否相等，比较位置和元素值
   */
  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;
  }
  /**
   * 根据三元组位置比较两个三元组的大小，与元素值无关，约定三元组排序次序
   */
  @Override
  public int compareTo(Triple elem) {
    //当前三元组对象小
    if (this.row < elem.row || this.row == elem.row && this.colum < elem.colum)
      return -1;
    //相等，与equals方法含义不同
    if (this.row == elem.row && this.colum == elem.colum)
      return 0;
    //当前三元组对象大
    return 1;
  }
  /**
   * 加法， +=运算符作用
   * @param term
   */
  public void add(Triple term) {
    if (this.compareTo(term) == 0)
      this.value += term.value;
    else
      throw new IllegalArgumentException("两项的指数不同，不能相加");
  }
  /**
   * 约定删除元素
   *
   * @return
   */
  public boolean removable() {
    //不存储为0的元素
    return this.value == 0;
  }
  /**
   * 返回对称位置矩阵元素的三元组
   * @return
   */
  public Triple toSymmetry() {
    return new Triple(this.colum, this.row, this.value);
  }
  /**
   * 加法运算，重载运算符+
   * @return
   */
  public Triple plus(Triple term) {
    Triple tmp = new Triple(this);
    tmp.add(term);
    return tmp;
  }
}

三元组顺序存储的稀疏矩阵类:

package com.clarck.datastructure.matrix;
import com.clarck.datastructure.linear.SeqList;
/**
 * 稀疏矩阵的压缩存储
 *
 * 稀疏矩阵三元组顺序表
 *
 * 三元组顺序存储的稀疏矩阵类
 *
 * @author clarck
 *
 */
public class SeqSparseMatrix {
  // 矩阵行数、列数
  private int rows, columns;
  // 稀疏矩阵三元组顺序表
  private SeqList<Triple> list;
  /**
   * 构造rows行，colums列零矩阵
   *
   * @param rows
   * @param columns
   */
  public SeqSparseMatrix(int rows, int columns) {
    if (rows <= 0 || columns <= 0)
      throw new IllegalArgumentException("矩阵行数或列数为非正数");
    this.rows = rows;
    this.columns = columns;
    // 构造空顺序表，执行SeqList()构造方法
    this.list = new SeqList<Triple>();
  }
  public SeqSparseMatrix(int rows, int columns, Triple[] elems) {
    this(rows, columns);
    // 按行主序插入一个元素的三元组
    for (int i = 0; i < elems.length; i++)
      this.set(elems[i]);
  }
  /**
   * 返回矩阵第i行第j列元素，排序顺序表的顺序查找算法，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("矩阵元素的行或列序号越界");
    Triple item = new Triple(i, j, 0);
    int k = 0;
    Triple elem = this.list.get(k);
    // 在排序顺序表list中顺序查找item对象
    while (k < this.list.length() && item.compareTo(elem) >= 0) {
      // 只比较三元组元素位置，即elem.row == i && elem.column == j
      if (item.compareTo(elem) == 0)
        return elem.value;
      // 查找到(i, j), 返回矩阵元素
      k++;
      elem = this.list.get(k);
    }
    return 0;
  }
  /**
   * 以三元组设置矩阵元素
   *
   * @param elem
   */
  public void set(Triple elem) {
    this.set(elem.row, elem.colum, elem.value);
  }
  /**
   * 设置矩阵第row行第column列的元素值为value，按行主序在排序顺序表list中更改或插入一个元素的三元组， O(n)
   *
   * @param row
   * @param column
   * @param value
   */
  public void set(int row, int column, int value) {
    // 不存储值为0元素
    if (value == 0)
      return;
    if (row >= this.rows || column >= this.columns)
      throw new IllegalArgumentException("三元组的行或列序号越界");
    Triple elem = new Triple(row, column, value);
    int i = 0;
    // 在排序的三元组顺序表中查找elem对象，或更改或插入
    while (i < this.list.length()) {
      Triple item = this.list.get(i);
      // 若elem存在，则更改改位置矩阵元素
      if (elem.compareTo(item) == 0) {
        // 设置顺序表第i个元素为elem
        this.list.set(i, elem);
        return;
      }
      // elem 较大时向后走
      if (elem.compareTo(item) >= 0)
        i++;
      else
        break;
    }
    this.list.insert(i, elem);
  }
  @Override
  public String toString() {
    String str = "三元组顺序表：" + this.list.toString() + "\n";
    str += "稀疏矩阵" + this.getClass().getSimpleName() + "(" + rows + " * "
        + columns + "): \n";
    int k = 0;
    // 返回第k个元素，若k指定序号无效则返回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;
  }
  /**
   * 返回当前矩阵与smat相加的矩阵， smatc=this+smat,不改变当前矩阵，算法同两个多项式相加
   *
   * @param smat
   * @return
   */
  public SeqSparseMatrix plus(SeqSparseMatrix smat) {
    if (this.rows != smat.rows || this.columns != smat.columns)
      throw new IllegalArgumentException("两个矩阵阶数不同，不能相加");
    // 构造rows*columns零矩阵
    SeqSparseMatrix smatc = new SeqSparseMatrix(this.rows, this.columns);
    int i = 0, j = 0;
    // 分别遍历两个矩阵的顺序表
    while (i < this.list.length() && j < smat.list.length()) {
      Triple elema = this.list.get(i);
      Triple elemb = smat.list.get(j);
      // 若两个三元组表示相同位置的矩阵元素，则对应元素值相加
      if (elema.compareTo(elemb) == 0) {
        // 相加结果不为零，则新建元素
        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) { // 将较小三元组复制添加到smatc顺序表最后
        // 复制elema元素执行Triple拷贝构造方法
        smatc.list.append(new Triple(elema));
        i++;
      } else {
        smatc.list.append(new Triple(elemb));
        j++;
      }
    }
    // 将当前矩阵顺序表的剩余三元组复制添加到smatc顺序表最后
    while (i < this.list.length())
      smatc.list.append(new Triple(this.list.get(i++)));
    // 将smat中剩余三元组复制添加到smatc顺序表最后
    while (j < smatc.list.length()) {
      Triple elem = smat.list.get(j++);
      if (elem != null) {
        smatc.list.append(new Triple(elem));
      }
    }
    return smatc;
  }
  /**
   * 当前矩阵与smat矩阵相加，this+=smat, 改变当前矩阵，算法同两个多项式相加
   *
   * @param smat
   */
  public void add(SeqSparseMatrix smat) {
    if (this.rows != smat.rows || this.columns != smat.columns)
      throw new IllegalArgumentException("两个矩阵阶数不同，不能相加");
    int i = 0, j = 0;
    // 将mat的各三元组依次插入(或相加)到当前矩阵三元组顺序表中
    while (i < this.list.length() && j < smat.list.length()) {
      Triple elema = this.list.get(i);
      Triple elemb = smat.list.get(j);
      // 若两个三元组表示相同位置的矩阵元素，则对应元素值相加
      if (elema.compareTo(elemb) == 0) {
        // 相加结果不为0,则新建元素
        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) { // 继续向后寻找elemb元素的插入元素
        i++;
      } else {
        // 复制elemb元素插入作为this.list的第i个元素
        this.list.insert(i++, new Triple(elemb));
        j++;
      }
    }
    // 将mat中剩余三元组依次复制插入当前矩阵三元组顺序表中
    while (j < smat.list.length()) {
      this.list.append(new Triple(smat.list.get(j++)));
    }
  }
  // 深拷贝
  public SeqSparseMatrix(SeqSparseMatrix smat) {
    this(smat.rows, smat.columns);
    // 创建空顺序表，默认容量
    this.list = new SeqList<Triple>();
    // 复制smat中所有三元组对象
    for (int i = 0; i < smat.list.length(); i++)
      this.list.append(new Triple(smat.list.get(i)));
  }
  /**
   * 比较两个矩阵是否相等
   */
  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);
  }
  /**
   * 返回转置矩阵
   * @return
   */
  public SeqSparseMatrix transpose() {
    //构造零矩阵，指定行数和列数
    SeqSparseMatrix trans = new SeqSparseMatrix(columns, rows);
    for (int i = 0; i < this.list.length(); i++) {
      //插入矩阵对称位置元素的三元组
      trans.set(this.list.get(i).toSymmetry());
    }
    return trans;
  }
}

测试类：

package com.clarck.datastructure.matrix;
/**
 * 稀疏矩阵的压缩存储
 *
 * 稀疏矩阵三元组顺序表
 *
 * 三元组顺序表表示的稀疏矩阵及其加法运算
 *
 * @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转置" + smata.transpose().toString());
  }
}

运行结果：

A 三元组顺序表：((0, 2, 11), (0, 4, 17), (1, 1, 20), (3, 0, 19), (3, 5, 28), (4, 4, 50))
稀疏矩阵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  0
B 三元组顺序表：((0, 2, -11), (0, 4, -17), (2, 3, 51), (3, 0, 10), (4, 5, 99))
稀疏矩阵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 99
C=A+B三元组顺序表：((1, 1, 20), (2, 3, 51), (3, 0, 29), (3, 5, 28), (4, 4, 50), (4, 5, 99))
稀疏矩阵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 99
A+=B三元组顺序表：((1, 1, 20), (2, 3, 51), (3, 0, 29), (3, 5, 28), (4, 4, 50), (4, 5, 99))
稀疏矩阵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 99
C.equals(A)?true
B 三元组顺序表：((0, 2, 1), (0, 4, -17), (2, 3, 51), (3, 0, 10), (4, 5, 99))
稀疏矩阵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 99
D 三元组顺序表：((0, 2, -11), (0, 4, -17), (2, 3, 51), (3, 0, 10), (4, 5, 99))
稀疏矩阵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 99
A转置三元组顺序表：((0, 3, 29), (1, 1, 20), (3, 2, 51), (4, 4, 50), (5, 3, 28), (5, 4, 99))
稀疏矩阵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

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