二次探查再散列Hash表的C++实现

/***************************************************************************** *                                    student.h *****************************************************************************/#ifndef STUDENT_H#define STUDENT_H#include <iostream>#include <string>using namespace std;class Student{public:Student() : key(0), firstName("Ming"), lastName("Zhang"){ }Student( int number, const string &name1="Ming",const string &name2="Zhang" ){key = number;firstName = name1;lastName = name2;}~Student(){ }inline void operator=( const Student &stu ){key = stu.key;firstName = stu.firstName;lastName = stu.lastName;}inline bool operator<( const Student &stu ){   return key < stu.key;   }inline bool operator>( const Student &stu ){   return key > stu.key;   }inline bool operator==( const Student &stu ){   return key == stu.key;   }friend istream& operator>>( istream &in, Student &stu ){in >> stu.key >> stu.lastName >> stu.firstName;return in;}friend ostream& operator<<( ostream &out, Student &stu ){out << stu.key << "\t"<< stu.lastName << " " << stu.firstName << endl;return out;}int key;private:string firstName;string lastName;};// class Student#endif

 

/***************************************************************************** *                                    hashtable.h * * Hash table implemented by C++ template class. * * This class provides "search", "insert" and "remove" operations by using a * Hash Table. We use the quadratic probing method to prevent the element * number exceeding half of the total table size. * *****************************************************************************//*对于线性探测，让散列表近乎填满元素是个坏主意，因为此时表的性能会降低。对于平方探测，情况更糟：一旦表被填满超过一半，若表的大小不是素数，那么甚至在表被填满一半之前，就不能保证找到空的单元了。这是因为最多只有表的一半可以用做解决冲突的备选位置。  定理：如果使用平方探测，且表的大小是素数，那么当表至少有一半是空的时候，  总能够插入一个一个新的元素。*/#ifndef HASHTABLE_H#define HASHTABLE_H#include <iostream>#include <cstdlib>#include <string>using namespace std;template <typename Object, typename Key>class HashTable{public:explicit HashTable( int size = 7 );~HashTable();void makeEmpty();inline bool search( const Key k, Object &x ) const;bool insert( const Object &x );bool remove( const Key k, Object &x);enum EntryFlag { ACTIVE, EMPTY, DELETED };private:struct HashEntry{Object element;EntryFlag info;HashEntry( const Object &x=Object(), EntryFlag i = EMPTY ): element(x), info(i){}};HashEntry *array;int currentSize;int tableSize;inline bool isActive( int currentPos ) const;int findPos( const Key k ) const;void rehash();//再散列int myhash( const Key k ) const;};bool isPrime( int n );int nextPrime( int n );#include "hashtable_impl.h"#endif

 

实现文件：

 

/***************************************************************************** *                               hashtable_impl.h * * Implementation for Hashtable class. * *****************************************************************************/// constructors and deconstructortemplate <typename Object, typename Key>HashTable<Object, Key>::HashTable( int size ) : tableSize(size){array = new HashEntry[tableSize];if( array == NULL ){cout << "Out of memory!" << endl;exit(1);}makeEmpty();}template <typename Object, typename Key>HashTable<Object, Key>::~HashTable(){delete []array;}// make the table emptytemplate <typename Object, typename Key>void HashTable<Object, Key>::makeEmpty(){currentSize = 0;for( int i = 0; i < tableSize; ++i )array[i].info = EMPTY;}//searching an element with the "k" and the assign it to "x"template <typename Object, typename Key>inline bool HashTable<Object, Key>::search( const Key k, Object &x) const{int index = findPos( k );if( !isActive( index ) )return false;else{x = array[index].element;return true;}}//insert an element into the hashtable. If the number//is greater than half of the table size, then  make "re-hashing"template <typename Object, typename Key>bool HashTable<Object, Key>::insert( const Object &x) {int currentPos = findPos( x.key );if( isActive( currentPos ) )return false;array[currentPos] = HashEntry( x, ACTIVE );if( ++currentSize > tableSize/2 )rehash();return true;}//remove an element with key "k" and then assign it to "x"template <typename Object, typename Key>bool HashTable<Object, Key>::remove( const Key k, Object &x) {int currentPos = findPos(k);if( !isActive( currentPos ) )return false;else{x = array[currentPos].element;array[currentPos].info = DELETED;currentSize--;return true;}}// if the current position is active, return truetemplate <typename Object, typename Key>inline bool HashTable<Object, Key>::isActive( int currentPos ) const{return array[currentPos].info == ACTIVE;}//find the position of the element with key "k" int the hashtabletemplate <typename Object, typename Key>int HashTable<Object, Key>::findPos( const Key k ) const{int offset = 1;int currentPos = myhash( k );while( array[currentPos].info != EMPTY &&   array[currentPos].element.key != k ){currentPos += offset;offset += 2;if( currentPos >= tableSize )currentPos -= tableSize;}return currentPos;}//to ensure the number of elements is not greater //than half of the table size//对于使用平方探测的开放地址散列法，如果表的元素填的太满，那么操作的运行时间//将开始消耗过长，且插入操作可能失败。这可能发生在有太多的删除和插入混合的场合。//此时，一个解决方法是建立另外一个两倍大的表（而且使用一个相关的新散列函数），//扫描整个原始散列表，计算每个（未删除的）元素的新散列值并将其插入到新表中。//整个操作称为再散列（rehashing）。这是一种非常昂贵的操作；其运行时间为O(N)，因为有N//个元素要再散列而且表的大小约为2N，不过这并不经常发生，所以实际效果并没有这么差。//本程序中只要表满到一半就再散列。template <typename Object, typename Key>void HashTable<Object, Key>::rehash(){int oldTableSize = tableSize;HashEntry *oldArray = array;tableSize = nextPrime( 2*oldTableSize );array = new HashEntry[tableSize];if( array == NULL ){cerr << "Out of memory!" << endl << endl;exit(1);}for( int j=0; j<tableSize; ++j )array[j].info = EMPTY;currentSize = 0;for( int i=0; i<oldTableSize; ++i ){if( oldArray[i].info == ACTIVE )insert( oldArray[i].element );}delete []oldArray;}//hash mappingtemplate <typename Object, typename Key>int HashTable<Object, Key>::myhash( const Key k ) const{int hashValue = k%tableSize;if( hashValue < 0)hashValue +=tableSize;return hashValue;}//If n is a prime number, return truebool isPrime( int n ){if( n==2 || n==3 )return true;if( n==1 || n%2==0 )return false;for( int i=3; i*i<=n; i+=2 )if( n%i == 0 )return false;return true;}//find the next prime number larger than nint nextPrime( int n ){int i = n+1;while( isPrime(i)==false )i += 2;return i;}

 

测试文件：

 

/***************************************************************************** *                               hashtable_test.cpp * * Hash table class testing. * *****************************************************************************/#include <iostream>#include <string>#include "Student.h"#include "hashtable.h"using namespace std;const int N = 10;int main(){int x[N] = { 3, 2, 1, 4, 5, 6, 7, 10, 9, 8 };    int y[N] = { 3, 2, 1, 4, 5, 16, 17, 20, 19, 18 };Student stu;HashTable <Student, int> ht;for( int i=0; i<N; ++i ){stu.key = x[i];if( ht.insert( stu ) )cout << "Inserting success: " << stu;elsecout << "Inserting failure. " << endl;}cout << endl;for( int j=0; j<N; ++j ){if( ht.remove( y[j], stu ) )cout << "removing success: " << stu;elsecout << "Removing failure." << endl;}cout << endl;for( int k=0; k<N; ++k ){        if( ht.search( x[k], stu ) )            cout << "Searching success: " << stu;        else            cout << "Searching failure." << endl; }    cout << endl;return 0;}