山东大学数据结构实验报告矩阵和散列表

1、山东大学计算机科学与技术学院数据结构课程实验报告 学号：姓名：徐大鹏班级：实验题目：实验四_矩阵和散列表实验学时：2实验日期：2015.11.24实验目的：掌握特殊矩阵和稀疏矩阵。掌握散列表及其应用。硬件环境： 略软件环境：Ubuntu Kylin 15.04 64-bitLinux GCC 4.9.2Java SE Runtime Environment (build 1.8.0_60-b27)Eclipse IDE for C/C+ Developers Mars.1 Release (4.5.1)实验内容与设计：1. 实验内容（题目内容，输入要求，输出要求）(1)创建

2、三对角矩阵类，采用按列映射方式，提供store和retrieve 方法。(2)创建下三角矩阵类，采用按列映射方式，提供store和retrieve 方法。(3)创建稀疏矩阵类，采用行主顺序把稀疏矩阵映射到一维数组中，实现稀疏矩阵的转置和两个稀疏矩阵的加法操作。(4)使用散列表设计实现一个字典，假设关键字为整数且D为961，在字典中插入随机产生的500个不同的整数，实现字典的建立和搜索操作。分别使用线性开型寻址和链表散列解决溢出。2.数据结构与算法描述（整体思路描述，所需要的数据结构与算法）对问题一，从数学上推导得出三对角方阵列主映射的函数关系式i = 2c + r - 3其中i为元素在数组e中

3、的下标， c为列数， r为行数，c1且r1。以此关系式为TridiagonalMatrix类编写了Store和Retrieve函数，并扩展编写了Input函数和Output函数。对问题二，从数学上推导得出下三角方阵列主映射的函数关系式i = n × (c - 1) - 1 + r + c × (1 - c) / 2其中i为元素在数组e中的下标，n为方阵的大小，c为列数， r为行数，c1且r1。以此关系式为LowerTriangularMatrix类编写了Store和Retrieve函数，并扩展编写了Input函数和Output函数。对问题三，仿课本所述，定义Term类作为S

4、parseMatrix类的友元类，包含行、列、值三个要素的成员变量，用Term类的数组实现稀疏矩阵的行主映射存储。查找行为的实现方式是，找到位于目标元素前一行的最后一个元素，再从这个元素开始向下搜索，直到找到和目标元素同一行但是列数小于目标元素的元素ak-1，然后决定下一步的行为插入一个新项Term作为ak并将已有元素向后移位，还是修改已存在的项ak。以此原理编写了Store和Retrieve函数，并扩展编写了Input函数和Output函数。对问题四，仿照课本例子编写了有序链表类SortedChain、开放寻址的散列表类HashTable、基于有序链表链接的散列表类ChainHashTabl

5、e，并对这三个类分别扩展编写了Output函数。3. 测试结果（测试输入，测试输出）问题一：问题二：上图显示了输入不符合下三角方阵约束时，抛出异常并退出程序。上图是正常运行的结果。问题三：普通的输入和输出操作如下：矩阵相加：矩阵转置：问题四：以上图的数据为例。从346就应该在链表链接的散列表上看到开放寻址解决冲突的例子。返回开放寻址的输出段，可以看到符合预期的结果：4.实现源代码（程序风格清晰易理解，有充分的注释）/* * TridiagonalMatrix.h * * Created on: Nov 22, 2015 * Author: xudp */#ifndef TRIDIAGONALM

6、ATRIX_H_#define TRIDIAGONALMATRIX_H_#include <iostream>using namespace std;template<class T>class TridiagonalMatrix public:/ 1、创建三对角矩阵类,采用按列映射方式,提供 store 和 retrieve 方法。TridiagonalMatrix(int size = 10);TridiagonalMatrix();/ row>0, column>0TridiagonalMatrix<T>& Store(int ro

7、w, int column, const T& value);T Retrieve(int row, int column);void Input(istream& in, ostream& out);void Output(ostream& out) const;friend ostream& operator<< (ostream& out, const TridiagonalMatrix<T>& matrix)matrix.Output(out);return out;friend istream&

8、operator>> (istream& in, TridiagonalMatrix<T>& matrix)matrix.Input(in, cout);return in;private:T* e;/ Store all elementsint size;template class TridiagonalMatrix<double>#endif /* TRIDIAGONALMATRIX_H_ */* * TridiagonalMatrix.cpp * * Created on: Nov 22, 2015 * Author: xudp */

9、#include "TridiagonalMatrix.h"#include "Exceptions.h"template<class T>TridiagonalMatrix<T>:TridiagonalMatrix(int size) if (size < 1)throw InvalidParameterValue();e = new T3 * size - 2;this->size = size;template<class T>TridiagonalMatrix<T>:Tridiagona

10、lMatrix() delete e;template<class T>TridiagonalMatrix<T>& TridiagonalMatrix<T>:Store(int row, int column,const T& value) if (row < 1 | row > size | column < 1 | column > size| (row - column) > 1 | (row - column) < -1)throw InvalidParameterValue();e2 * colu

11、mn + row - 3 = value;return *this;template<class T>T TridiagonalMatrix<T>:Retrieve(int row, int column) if (row < 1 | row > size | column < 1 | column > size| (row - column) > 1 | (row - column) < -1)throw InvalidParameterValue();return e2 * column + row - 3;template<

12、;class T>void TridiagonalMatrix<T>:Input(istream& in, ostream& out) out << "请按行主顺序依次输入元素，" << endl;out << "元素个数必须恰好是" << (3 * size - 2) << "个: "<< endl;for (int i = 0; i < size; i+) for (int j = i - 1; j <= i +

13、1; j+) if (i = 0 && j = -1)continue;if (i = size - 1 && j = size)continue;T element;in >> element;Store(i + 1, j + 1, element);out << "操作成功完成. " << endl;template<class T>void TridiagonalMatrix<T>:Output(ostream& out) const for (int i = 0; i

14、 < size; i+) for (int j = 0; j < size; j+)if (i - j) > 1 | (i - j) < -1)out << "0t"else out << e2 * j + i << "t"out << endl;/* * SparseMatrix.h * * Created on: Oct 20, 2015 * Author: xudp */#ifndef SPARSEMATRIX_H_#define SPARSEMATRIX_H_#include

15、 <iostream>using namespace std;template<class T> class SparseMatrix;template<class T>class Term friend SparseMatrix<T> ;private:int row, col;T value;template<class T>class SparseMatrix public:/* 3、创建稀疏矩阵类,采用行主顺序把稀疏矩阵映射到一维数组中,实现稀 * 疏矩阵的转置和两个稀疏矩阵的加法操作。 */SparseMatrix(int

16、maxTerms = 10);SparseMatrix(const SparseMatrix<T>& spm);SparseMatrix() delete a;void Transpose(SparseMatrix<T> &b) const;void Add(const SparseMatrix<T> &b, SparseMatrix<T> &c) const;/* * Write the store and retrieve functions for a sparse matrix stored in * ro

17、w-major order in a one-dimensional array. */SparseMatrix<T>& Store(const T& x, int i, int j);T Retrieve(int i, int j) const;void Input(istream& in, ostream& out);void Output(ostream& out) const;friend ostream& operator<<(ostream& out, const SparseMatrix<T&g

18、t;& matrix) matrix.Output(out);return out;friend istream& operator>>(istream& in, SparseMatrix<T>& matrix) matrix.Input(in, cout);return in;int GetMaxSize()return MaxTerms;private:void Append(const Term<T>& t);int rows, cols; / matrix dimensionsint terms; / curr

19、ent number of nonzero termsTerm<T> * a; / term arrayint MaxTerms; / size of array a;template class SparseMatrix<double> ;#endif /* SPARSEMATRIX_H_ */* * SparseMatrix.cpp * * Created on: Oct 20, 2015 * Author: xudp */#include "SparseMatrix.h"#include "Exceptions.h"temp

20、late<class T>SparseMatrix<T>:SparseMatrix(int maxTerms) / Sparse matrix constructor.if (maxTerms < 1)throw BadInitializers();MaxTerms = maxTerms;a = new Term<T> MaxTerms;terms = cols = rows = 0;template<class T>SparseMatrix<T>& SparseMatrix<T>:Store(const T

21、& theVal, int theRow,int theCol) if (theRow < 1 | theCol < 1 | theRow > rows | theCol > cols)throw OutOfBounds();int cursor = -1;do cursor+;if (cursor = terms) Term<T> t;t.row = theRow;t.col = theCol;t.value = theVal;Append(t);return *this; while (acursor.row < theRow| (acur

22、sor.row = theRow && acursor.col < theCol);if (acursor.row = theRow && acursor.col = theCol) / (theRow,theCol) is already existent.acursor.value = theVal;else if (terms >= MaxTerms)throw NoMem();for (int k = terms - 1; k >= cursor; k-) ak + 1 = ak;acursor.row = theRow;acursor

23、.col = theCol;acursor.value = theVal;terms+;return *this;template<class T>T SparseMatrix<T>:Retrieve(int theRow, int theCol) const if (theRow < 1 | theCol < 1 | theRow > rows | theCol > cols)throw OutOfBounds();int cursor = 0;while (acursor.row < theRow| (acursor.row = the

24、Row && acursor.col < theCol) cursor+;if (cursor = terms) / not in the sparse matrixreturn 0;if (acursor.row = theRow && acursor.col = theCol) / (theRow,theCol) is already existent.return acursor.value;elsereturn 0;template<class T>void SparseMatrix<T>:Output(ostream&am

25、p; out) const out << "最大容许行数：" << rows << " 最大容许列数：" << cols << " 非零元素数：" << terms<< endl;/ put terms, one per linefor (int i = 0; i < terms; i+)out << "a(" << ai.row << ',' << ai.col

26、 << ") = " << ai.value<< endl;template<class T>void SparseMatrix<T>:Input(istream& in, ostream& out) out << "分别输入行数最大值，列数最大值，以及本次输入的元素组数："int theTerms;in >> rows >> cols >> theTerms;if (theTerms > MaxTerms)throw NoM

27、em();/ input termsint theRow, theCol;T theVal;for (int i = 0; i < theTerms; i+) out << "依次输入第" << (i + 1) << "项的所在的行、列，以及它对应的数值"in >> theRow >> theCol >> theVal;Store(theVal, theRow, theCol);template<class T>void SparseMatrix<T>:

28、Transpose(SparseMatrix<T> &b) const / Return transpose of *this in b./ make sure b has enough spaceif (terms > b.MaxTerms)throw NoMem();/ set transpose characteristicsb.cols = rows;b.rows = cols;b.terms = terms;/ initialize to compute transposeint *ColSize, *RowNext;ColSize = new intcol

29、s + 1;RowNext = new introws + 1;/ find number of entries in each column of *thisfor (int i = 1; i <= cols; i+) / initializeColSizei = 0;for (int i = 0; i < terms; i+)ColSizeai.col+;/ find the starting point of each row of bRowNext1 = 0;for (int i = 2; i <= cols; i+)RowNexti = RowNexti - 1 +

30、 ColSizei - 1;/ perform the transpose copying from *this to bfor (int i = 0; i < terms; i+) int j = RowNextai.col+; / position in bb.aj.row = ai.col;b.aj.col = ai.row;b.aj.value = ai.value;template<class T>void SparseMatrix<T>:Add(const SparseMatrix<T> &b, SparseMatrix<T&

31、gt; &c) const / Compute c = (*this) + b./ 矩阵规模匹配if (rows != b.rows | cols != b.cols)throw SizeMismatch();c.cols = cols;c.rows = rows;/ 重新初始化稀疏矩阵cdelete c.a;int newMaxTerms = b.terms + terms;c.MaxTerms = (newMaxTerms > c.MaxTerms) ? newMaxTerms : c.MaxTerms;c.a = new Term<T> c.MaxTerms;/

32、 Not the best way.bool* hasMatched_b = new boolb.terms;for (int i = 0; i < b.terms; i+)hasMatched_bi = false;int curIndex = 0;for (int i = 0; i < terms; i+) bool isMatched = false;for (int j = 0; j < b.terms; j+) if (ai.row = b.aj.row && ai.col = b.aj.col) isMatched = true;hasMatche

33、d_bj = true;c.acurIndex.row = ai.row;c.acurIndex.col = ai.col;c.acurIndex.value = ai.value + b.aj .value;break;if (!isMatched) c.acurIndex.row = ai.row;c.acurIndex.col = ai.col;c.acurIndex.value = ai.value;curIndex+;for (int i = 0; i < b.terms; i+) if (!hasMatched_bi) c.acurIndex.row = b.ai.row;c

34、.acurIndex.col = b.ai.col;c.acurIndex.value = b.ai.value;curIndex+;/ When writing this function by myself, I forgot the following:c.terms = curIndex;delete hasMatched_b;template<class T>void SparseMatrix<T>:Append(const Term<T>& t) / Append a nonzero term t to *thisif (terms &g

35、t;= MaxTerms)throw NoMem();aterms = t;terms+;/* * SortedChain.h * * Created on: Nov 9, 2015 * Author: xudp */#ifndef SORTEDCHAIN_H_#define SORTEDCHAIN_H_#include <iostream>using namespace std;/* template note: E denotes the data type of the chain elements, and K * that of the keys on which the

36、 chain is sorted. */template<class E, class K> class SortedChain;template<class E, class K>class SortedChainNode friend class SortedChain<E, K> ;private:E data;SortedChainNode<E, K> *link;template<class E, class K>class SortedChain public:SortedChain() first = 0;SortedC

37、hain();bool IsEmpty() const return first = 0;int Length() const;bool Search(const K& k, E& e) const;SortedChain<E, K>& Delete(const K& k, E& e);SortedChain<E, K>& Insert(const E& e);SortedChain<E, K>& DistinctInsert(const E& e);void Output(ostrea

38、m& out) const;friend ostream& operator<< (ostream& out, const SortedChain<E,K>& sc)sc.Output(out);return out;private:SortedChainNode<E, K> *first;template class SortedChainNode<long, long> ;template class SortedChain<long, long> ;#endif /* SORTEDCHAIN_H_

39、 */* * SortedChain.cpp * * Created on: Nov 9, 2015 * Author: xudp */#include "SortedChain.h"#include "Exceptions.h"template<class E, class K>SortedChain<E, K>:SortedChain() SortedChainNode<E, K>* p = first;SortedChainNode<E, K>* tmp;while (p) tmp = p;p = p

40、->link;delete tmp;template<class E, class K>int SortedChain<E, K>:Length() const SortedChainNode<E, K> *p = first;int ret = 0;while (p) ret+;p = p->link;return ret;template<class E, class K>bool SortedChain<E, K>:Search(const K& k, E& e) const / Put elemen

41、t that matches k in e./ Return false if no match.SortedChainNode<E, K> *p = first;/ search for match with kfor (; p && p->data < k; p = p->link);/ verify matchif (p && p->data = k) / yes, found matche = p->data;return true;return false;template<class E, class

42、K>SortedChain<E, K>& SortedChain<E, K>:Delete(const K& k, E& e) / Delete element that matches k./ Put deleted element in e./ Throw BadInput exception if no match.SortedChainNode<E, K> *p = first, *tp = 0; / trail p/ search for match with kfor (; p && p->da

43、ta < k; tp = p, p = p->link);/ verify matchif (p && p->data = k) / found a matche = p->data; / save data/ remove p from chainif (tp)tp->link = p->link;elsefirst = p->link; / p is first node.delete p;return *this;throw BadInput(); / no matchtemplate<class E, class K>

44、;SortedChain<E, K>& SortedChain<E, K>:Insert(const E& e) SortedChainNode<E, K>* p;if (!first | first->data >= e) p = new SortedChainNode<E, K>();p->data = e;p->link = first;first = p; else p = first;while (p->link) if (p->link->data < e) p = p-

45、>link; else SortedChainNode<E, K>* ncn = new SortedChainNode<E, K>();ncn->data = e;ncn->link = p->link;p->link = ncn;break;if (!p->link) p->link = new SortedChainNode<E, K>();p = p->link;p->link = 0;p->data = e;return *this;template<class E, class K

46、>SortedChain<E, K>& SortedChain<E, K>:DistinctInsert(const E& e) / Insert e only if no element with same key/ currently in list./ Throw BadInput exception if duplicate.SortedChainNode<E, K> *p = first, *tp = 0; / trail p/ move tp so that e can be inserted after tpfor (;

47、p && p->data < e; tp = p, p = p->link);/ check if duplicateif (p && p->data = e)throw BadInput();/ not duplicate, set up node for eSortedChainNode<E, K> *q = new SortedChainNode<E, K>q->data = e;/ insert node just after tpq->link = p;if (tp)tp->link =

48、 q;elsefirst = q;return *this;template<class E, class K>void SortedChain<E, K>:Output(ostream& out) constSortedChainNode<E, K> *p = first;if (!first)out << "(Empty chain.)"elsewhile(p)out << p->data << "t"p = p->link;out << endl

49、;/* * LowerTriangularMatrix.h * * Created on: Nov 22, 2015 * Author: xudp */#ifndef LOWERTRIANGULARMATRIX_H_#define LOWERTRIANGULARMATRIX_H_#include <iostream>using namespace std;template<class T>class LowerTriangularMatrix public:/ 2、创建下三角矩阵类,采用按列映射方式,提供 store 和 retrieve 方法。LowerTriangu

50、larMatrix(int size = 10);LowerTriangularMatrix();/ row>0, column>0LowerTriangularMatrix<T>& Store(int row, int column, const T& value);T Retrieve(int row, int column);void Input(istream& in, ostream& out);void Output(ostream& out) const;friend ostream& operator<

51、;<(ostream& out,const LowerTriangularMatrix<T>& matrix) matrix.Output(out);return out;friend istream& operator>>(istream& in, LowerTriangularMatrix<T>& matrix) matrix.Input(in, cout);return in;private:T* e;/ Store all elementsint size;template class LowerTria

52、ngularMatrix<double> ;#endif /* LOWERTRIANGULARMATRIX_H_ */* * LowerTriangularMatrix.cpp * * Created on: Nov 22, 2015 * Author: xudp */#include "LowerTriangularMatrix.h"#include "Exceptions.h"template<class T>LowerTriangularMatrix<T>:LowerTriangularMatrix(int si

53、ze) if (size < 1)throw InvalidParameterValue();e = new Tsize * (size + 1) / 2;this->size = size;template<class T>LowerTriangularMatrix<T>:LowerTriangularMatrix() delete e;template<class T>LowerTriangularMatrix<T>& LowerTriangularMatrix<T>:Store(int row, int co

54、lumn,const T& value) if (row < 1 | row < column | column < 1)throw InvalidParameterValue();esize * (column - 1) - 1 + row + column * (1 - column) / 2 = value;return *this;template<class T>T LowerTriangularMatrix<T>:Retrieve(int row, int column) if (row < 1 | row > size

55、 | column < 1 | column > size| (row - column) > 1 | (row - column) < -1)throw InvalidParameterValue();return esize * (column - 1) - 1 + row + column * (1 - column) / 2;template<class T>void LowerTriangularMatrix<T>:Input(istream& in, ostream& out)out << "请按

56、行主顺序依次输入元素，" << endl;out << "元素个数必须恰好是" << (size * (size + 1) / 2) << "个: "<< endl;for (int i = 0; i < size; i+) for (int j = 0; j <= i; j+) T element;in >> element;Store(i + 1, j + 1, element);out << "操作成功完成. " <&

57、lt; endl;template<class T>void LowerTriangularMatrix<T>:Output(ostream& out) const for (int i = 0; i < size; i+) for (int j = 0; j < size; j+)if (j > i)out << "0t"else out << esize * j + i - j * (j + 1) / 2 << "t"out << endl;/* * HashTable.h * * Created on: Nov 23, 2015 * Author: xudp */#ifndef HASHTABLE_H_#define HASHTABLE_H_#include <iostream>using namespace std;template<class E, class K>class HashTable /* * 4、使用散列表设计实现一个字典,假设关键字为整数且 D 为 961,在字典 * 中插入随机产生的 500 个不同的整数,实现字典的建立和搜索操作。