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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