数据结构学习----稀疏矩阵(Java实现)

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