实验5特殊矩阵的存储和运算

1、.实验报告五 特殊矩阵和广义表的存储和运算班级： 姓名： 学号： 专业： 一、 实验目的：1、 了解多维数组的存储方式和存取特点2、 熟悉稀疏矩阵的存储方式3、 用三元组法实现稀疏矩阵的相、减、转置算法。二、 实验内容：1、 在矩阵类Matrix中，增加下列操作：1) 判断一个矩阵是否为上（下）三角矩阵、对称矩阵。2) 判断两个矩阵是否相等。3) 计算两个矩阵的乘积。算法原代码：public class Matrix private int matrix; private int row; private int column; public Matrix(int matrix) row =

2、matrix.length; column = matrix0.length; this.matrix = new introwcolumn; for(int i=0;imatrix.length;i+) for(int j=0;jmatrixi.length;j+) this.matrixij = matrixij; public Matrix(int row, int column) this.row = row; this.column = column; matrix = new introwcolumn; /* * 判断上三角 * param matrix * return */ p

3、ublic static boolean isUpTri(Matrix matrix) if(matrix.column!=matrix.row) throw new IllegalArgumentException(矩阵的行列不相等); for(int i=0;imatrix.getRow();i+) for(int j=i+1;jmatrix.getColumn();j+) if(0 = matrix.getElement(i, j) return false; return true; /* * 判断下三角 * param matrix * return */ public static

4、 boolean isDownTri(Matrix matrix) /先判断行列相不相等 if(matrix.column!=matrix.row) throw new IllegalArgumentException(矩阵的行列不相等); for(int j=0;jmatrix.getColumn();j+) for(int i=j+1;imatrix.getColumn();i+) if(matrix.getElement(i,j)=0) return false; return true; /* * 判断matrix是不是对称矩阵 * param matrix * return */ p

5、ublic static boolean isSymmetry(Matrix matrix) for(int i=0;imatrix.getRow();i+) for(int j=i+1;jmatrix.getColumn();j+) if(matrix.getElement(i,j) != matrix.getElement(j,i) return false; return true; /* * 判断两个矩阵是否相等 * param matrix1 * param matrix2 * return */ public static boolean equals(Matrix matrix1

6、, Matrix matrix2) if(matrix1.getRow()!=matrix2.getRow()|matrix1.getColumn()!=matrix2.getColumn() return false; for(int i=0;imatrix1.row;i+) for(int j=0;jmatrix1.column;j+) if(matrix1.getElement(i,j)!=matrix2.getElement(i,j) return false; return true; /* * 将两个矩阵相乘 * param TemPMatrix * return */ publi

7、c Matrix multiply(Matrix TemPMatrix) if(column!=TemPMatrix.row) throw new IllegalArgumentException(行列不匹配，两个矩阵无法相乘); Matrix matrix1 = new Matrix(row,TemPMatrix.column); for(int i=0;imatrix1.row;i+) for(int j=0;jmatrix1.column;j+) int sum = 0; for(int k=0;kcolumn;k+) sum += (this.matrixik)*(TemPMatrix

8、.getElement(k,j); matrix1.setElement(i,j,sum); return matrix1; /* * 两个矩阵相加 * param matrix * return */ public Matrix plus(Matrix matrix) if(row!=matrix.getRow()&column!=matrix.getColumn() throw new IllegalArgumentException(行列不匹配); int tempMatrix = new introwcolumn; for(int i=0;irow;i+) for(int j=0;jc

9、olumn;j+) tempMatrixij = this.matrixij+ matrix.getElement(i,j); return new Matrix(tempMatrix); Override public boolean equals(Object o) if (this = o) return true; if (o = null | getClass() != o.getClass() return false; Matrix matrix1 = (Matrix) o; if (row != matrix1.row) return false; if (column !=

10、matrix1.column) return false; return Arrays.deepEquals(matrix, matrix1.matrix); public void setElement(int row, int column, int element) matrixrowcolumn = element; public int getElement(int row, int column) return matrixrowcolumn; public int getRow() return row; public int getColumn() return column;

11、 Override public String toString() String string = new String(); for(int i=0;irow;i+) for(int j=0;jcolumn;j+) string += matrixij+ ; string += n; return string; public class Test public static void main(String args) throws Exception Matrix matrix1 = new Matrix(new int1,0,0,0,0,1,2,0,0,0,1,2,3,0,0,1,2

12、,3,4,0,1,2,3,4,5); Matrix matrix2 = new Matrix(new int1,2,3,4,5,0,2,3,4,5,0,0,3,4,5,0,0,0,4,5,0,0,0,0,5); Matrix matrix3 = new Matrix(new int1,2,3,4,5,2,1,6,7,8,3,6,1,9,10,4,7,9,1,11,5,8,10,11,1); Matrix matrix4 = new Matrix(new int1,0,0,0,0,1,2,0,0,0,1,2,3,0,0,1,2,3,4,0,1,2,3,4,5); System.out.print

13、ln(matrix1); System.out.println(matrix2); System.out.println(matrix1是否是上三角:+Matrix.isUpTri(matrix1); System.out.println(matrix2是否是上三角:+Matrix.isUpTri(matrix2); System.out.println(matrix1是否是下三角:+Matrix.isDownTri(matrix1); System.out.println(matrix2是否是下三角:+Matrix.isDownTri(matrix2); System.out.println

14、(matrix3是否是对称矩阵+Matrix.isSymmetry(matrix3); System.out.println(matrix2是否是对称矩阵+Matrix.isSymmetry(matrix2); System.out.println(matrix1是否等于matrix2:+matrix1.equals(matrix2); System.out.println(matrix1是否等于matrix4:+matrix1.equals(matrix4); System.out.println(); System.out.println(matrix1*matrix2); System.

15、out.println(matrix1.multiply(matrix2); 测试结果如下：2、在三元组行的单链表表示的稀疏矩阵类LinkedMatrix中，增加判断矩阵相等、判断对称矩阵、计算矩阵乘积等操作。算法源代码：public interface IPlus public void plus(E object);/* * 用于表示稀疏矩阵中的元素 * Created by 74062 on 2017/4/16. */public class Element implements Comparable,IPlus private int column; private int value

16、; public Element(int column, int value) this.column = column; this.value = value; public int getColumn() return column; public int getValue() return value; public void setValue(int value) this.value = value; Override public int compareTo(Element o) if(columno.getColumn() return 1; else return 0; /*

17、* 将原本的value覆盖掉 * param object */ Override public void plus(Element object) this.value = this.value+object.getValue(); Override public boolean equals(Object o) if (this = o) return true; if (o = null | getClass() != o.getClass() return false; Element element = (Element) o; return column = element.col

18、umn & Objects.equals(value, element.value); /* * 用于表示矩阵中的一行 继承了多项式的链表 * Created by 74062 on 2017/4/17. */public class LinkedMatrixRow extends Multple /* * 将一个新元素添加到矩阵中，如果该位置上已经存在元素，则将其里面的数值覆盖 * param element * return */ Override public boolean add(Comparable element) Node node = findNode(element); i

19、f(node!=null) if(node!=getHead()&pareTo(E) element)=0) node.data.setValue(E) element).getValue(); else add(node,element); else add(size-1,element); return true; /* * 根据column来获得该行的元素，如果该行中column列有元素，则返回该元素，没有则返回null * param column * return */ public int getByColumn(int column) Node node

20、 = getHead().next; for(int i=0;isize;i+) if(node.data.getColumn()=column) return node.data.getValue(); node = node.next; return 0; /* * 实现两个元素的相加 * param element * return */ public boolean plus(Element element) Node node = findNode(element); if(node!=null) if(node!=getHead()&pareTo(elem

21、ent)=0) node.data.plus(element); else add(node,element); else add(size-1,element); return true; /* * 将一行相加 * param linkedMatrixRow * return */ public boolean plus(LinkedMatrixRow linkedMatrixRow) Node node = linkedMatrixRow.getHead().next; for(int i=0;ilinkedMatrixRow.size;i+) plus(node.data); node

22、= node.next; return true; /* * 稀疏矩阵 * Created by 74062 on 2017/4/16. */public class LinkedMatrix private int row; private int column; private ListLinkedMatrixRow rowList; public ListLinkedMatrixRow getRowList() return rowList; public LinkedMatrix(int row, int column) this.row = row; this.column = co

23、lumn; rowList = new ArrayList(row); for(int i=0;irow;i+) rowList.add(new LinkedMatrixRow(); public int getRow() return row; public int getColumn() return column; /* * 设置row, column位置上的元素 * param row * param column * param data */ public void setElement(int row,int column, int data) if(row0|columnthi

24、s.row|columnthis.column) throw new IllegalArgumentException(row,column超出范围); MyList list = rowList.get(row); list.add(new Element(column,data); /* * 获取row行，column列上的值 * param row * param column * return */ public int getElement(int row,int column) return rowList.get(row).getByColumn(column); public

25、static boolean isDownTri(LinkedMatrix linkedMatrix) int row = linkedMatrix.getRow(); int column = linkedMatrix.getColumn(); /先判断行列相不相等 if(column!=row) throw new IllegalArgumentException(矩阵的行列不相等); for(int j=0;jcolumn;j+) for(int i=j+1;irow;i+) if(linkedMatrix.getElement(i,j)=0) return false; return

26、true; public static boolean isUpTri(LinkedMatrix linkedMatrix) int row = linkedMatrix.getRow(); int column = linkedMatrix.getColumn(); if(column!=row) throw new IllegalArgumentException(矩阵的行列不相等); for(int i=0;irow;i+) for(int j=i+1;jcolumn;j+) if(0 = linkedMatrix.getElement(i, j) return false; retur

27、n true; /* * 判断是不是对称矩阵 * return */ public static boolean isSymmetry(LinkedMatrix linkedMatrix) int row = linkedMatrix.getRow(); ListLinkedMatrixRow rowList = linkedMatrix.getRowList(); for(int i=0;irow;i+) LinkedMatrixRow list = rowList.get(i); if(!list.isEmpty() for (int j = 0; j list.size(); j+) /

28、获取第i行的第j个元素 j不不代表列的位置 只是用来表示该行元素的顺序 Element element = (Element) list.getNode(j).data; /获取element的列位置 int column = element.getColumn(); /获取对称元素的那一行 LinkedMatrixRow symmetryList = rowList.get(column); /根据列位置来得到对称元素 int symmetryElement = symmetryList.getByColumn(i); if(symmetryElement=0) return false;

29、if (element.getValue()!=symmetryElement) return false; return true; /* * 将两个矩阵相乘 * param linkedMatrix * return */ public LinkedMatrix multiply(LinkedMatrix linkedMatrix) if(column!=linkedMatrix.row) throw new IllegalArgumentException(行列不匹配，无法相乘); /获取参数linkedMatrix中的链表 ListLinkedMatrixRow tempRowList

30、 = linkedMatrix.getRowList(); /声明一个返回矩阵 LinkedMatrix tempLinkedMatrix = new LinkedMatrix(row,linkedMatrix.column); for(int i=0;itempLinkedMatrix.row;i+) /获取this的第i行 LinkedMatrixRow linkedMatrixLine = rowList.get(i); /如果该行不是全0行则继续 if(linkedMatrixLine!=null) for(int j=0;jtempLinkedMatrix.column;j+) in

31、t sum = 0; /挨个获取第i行中的元素 for (int k = 0; k linkedMatrixLine.size(); k+) Element element = (Element) linkedMatrixLine.getNode(k).data; int value = element.getValue(); int column = element.getColumn(); /根据矩阵相乘的规律，获得第column行第j列的元素 int element1 = tempRowList.get(column).getByColumn(j); if (element1 != 0)

32、 sum += value * element1; if (sum != 0) tempLinkedMatrix.setElement(i, j, sum); this.rowList = tempLinkedMatrix.rowList; return this; /* * 将this对象转化为Matrix类 * return */ private Matrix toMatrix() Matrix matrix = new Matrix(row,column); for(int i=0;irow;i+) MyList list = rowList.get(i); for(int j=0;jl

33、ist.size();j+) Element element = list.getNode(j).data; matrix.setElement(i,element.getColumn(),element.getValue(); return matrix; /* * 将 linkedMatrix 转化为Matrix * param linkedMatrix * return */ public static Matrix toMatrix(LinkedMatrix linkedMatrix) int row = linkedMatrix.row; int column = linkedMat

34、rix.column; Matrix matrix = new Matrix(row,column); for(int i=0;irow;i+) MyList list = (MyList) linkedMatrix.rowList.get(i); for(int j=0;jlist.size();j+) Element element = list.getNode(j).data; matrix.setElement(i,element.getColumn(),(int)element.getValue(); return matrix; /* * 将matrix类转化为linkedMatr

35、ix类 * param matrix * return */ public LinkedMatrix toLinkedMatrix(Matrix matrix) int row = matrix.getRow(); int column = matrix.getColumn(); LinkedMatrix linkedMatrix = new LinkedMatrix(row,column); for(int i=0;irow;i+) for(int j=0;jcolumn;j+) if(matrix.getElement(i,j)!=0) linkedMatrix.setElement(i,

36、 j, matrix.getElement(i, j); return linkedMatrix; Override public String toString() Matrix matrix = toMatrix(); return matrix.toString(); Override public boolean equals(Object o) if (this = o) return true; if (o = null | getClass() != o.getClass() return false; if(row != (LinkedMatrix) o).row| column != (LinkedMatrix) o).column) return false; LinkedMatrix linkedMatrix = (LinkedMatrix)o; for(int i=0;irow;i+) if(!(