HashTable-散列表/哈希表,是根據關鍵字(key)而直接訪問在內存存儲位置的數據結構。
它通過一個關鍵值的函數將所需的數據映射到表中的位置來訪問數據,這個映射函數叫做散列函數,存放記錄的數組叫做散列表。
直接定址法--取關鍵字的某個線性函數爲散列地址,Hash(Key)= Key 或 Hash(Key)= A*Key + B,A、B爲常數。
除留餘數法--取關鍵值被某個不大於散列表長m的數p除後的所得的餘數爲散列地址。Hash(Key)= Key % P。
平方取中法
摺疊法
隨機數法
數學分析法
線性探測
程序1.0
#include<iostream> using namespace std; enum State { EMPTY, DELETE, EXITS, }; template<class T> class HashTable { public: HashTable(size_t capacity = 10) : _capacity(capacity) ,_tables(new T[_capacity]) , _states(new State[_capacity]) , _size(0) { //將狀態表置空 for (size_t i = 0; i < _capacity; i++) { _states[i] = EMPTY; } //注意:不能用memset,因爲這個函數是“置位”的,它將每一位置成設置的值 } HashTable(const HashTable<T>&h) :_tables(new T[h._capacity]) , _states(new State[h._capacity]) , _size(h._size) , _capacity(h._capacity) { for (size_t i = 0; i < _capacity; i++) { _tables[i] = h._tables[i]; _states[i] = h._states[i]; } } HashTable<T>&operator=(HashTable<T> h) { if (this != &h) { swap(_tables, h._tables); swap(_states, h._states); swap(_size, h._size); swap(_capacity, h._capacity); } return *this; } ~HashTable() { if (_tables != NULL) { delete[] _tables; _tables = NULL; } if (_states != NULL) { delete[] _states; _states = NULL; } } public: bool Insert(const T&key)//插入 { if (_size == _capacity) { cout << "hashtable is full"; return false; } size_t index = _HashFunc(key); //線性探測 while (_states[index] ==EXITS) { if (_tables[index] == key) { return false; } ++index; if (index == _capacity)//若找到尾還未找到空位則從表頭繼續找 { index = 0; } } _tables[index] = key; _states[index] = EXITS; _size++; } bool Find(const T&key)//查找 { size_t index = _HashFunc(key); size_t start = index;//保存起始位置,若從這個位置找了一圈還沒找到則元素不存在 while (_tables[index] != EMPTY) { if (_tables[index] == key) { if (_states[index] != DELETE) return true; else { cout << "fail"; return false; } } ++index; if (index == _capacity) index = 0;//找到尾還未找到則從頭繼續找 if (index == start) { cout << "fail"; return false; } } cout << "fail"; return false; } bool Remove(const T&key) { size_t index = _HashFunc(key); size_t start = index; while (_states[index] != EMPTY) { if (_tables[index] == key) { _states[index]=DELETE; _size--; return true; } ++index; if (index == _capacity) index = 0; if (index == start) return false; } return false; } void Print() { if (_tables == NULL || _states == NULL) cout << "EMPTY"; for (size_t i = 0; i < _capacity; i++) { printf("(%d-%d:%d) ",i, _states[i], _tables[i]); } cout << endl; } private: size_t _HashFunc(const T&key)//安排在哈希表中的位置 { return key%_capacity; } private: size_t _capacity;//容量 T* _tables;//哈希表 State* _states;//狀態表 size_t _size;//存儲元素個數 };
哈希衝突:
不同的Key值經過哈希函數Hash(Key)處理以後可能產生相同的值哈希地址,我們稱這種情況爲哈希衝突。任意的散列函數都不能避免產生衝突。
散列表的荷載因子:α=填入表的元素個數/散列表長度
填入表的元素個數越多,產生衝突的可能性越大,反之,越小
荷載因子應嚴格限制在0.7~0.8以下,超過0.8則會導致cpu的緩存不命中率上升
故以下方法爲檢查容量,若荷載因子過大則進行擴容
程序2.0:
#include<iostream> using namespace std; enum State { EMPTY, DELETE, EXITS, }; template<class T> class HashTable { public: HashTable(size_t capacity = 10) : _capacity(capacity) ,_tables(new T[_capacity]) , _states(new State[_capacity]) , _size(0) { //將狀態表置空 for (size_t i = 0; i < _capacity; i++) { _states[i] = EMPTY; } //注意:不能用memset,因爲這個函數是“置位”的,它將每一位置成設置的值 } HashTable(const HashTable<T>&h) :_tables(new T[h._capacity]) , _states(new State[h._capacity]) , _size(h._size) , _capacity(h._capacity) { for (size_t i = 0; i < _capacity; i++) { _tables[i] = h._tables[i]; _states[i] = h._states[i]; } } HashTable<T>&operator=(HashTable<T> h) { if (this != &h) { swap(_tables, h._tables); swap(_states, h._states); swap(_size, h._size); swap(_capacity, h._capacity); } return *this; } ~HashTable() { if (_tables != NULL) { delete[] _tables; _tables = NULL; } if (_states != NULL) { delete[] _states; _states = NULL; } } public: bool Insert(const T&key)//插入 { /*if (_size == _capacity) { cout << "hashtable is full"; return false; }*/ Checkcapacity(); size_t index = _HashFunc(key); //線性探測 while (_states[index] ==EXITS) { if (_tables[index] == key) { return false; } ++index; if (index == _capacity)//若找到尾還未找到空位則從表頭繼續找 { index = 0; } } _tables[index] = key; _states[index] = EXITS; _size++; } bool Find(const T&key)//查找 { size_t index = _HashFunc(key); size_t start = index;//保存起始位置,若從這個位置找了一圈還沒找到則元素不存在 while (_tables[index] != EMPTY) { if (_tables[index] == key) { if (_states[index] != DELETE) return true; else { cout << "fail"; return false; } } ++index; if (index == _capacity) index = 0;//找到尾還未找到則從頭繼續找 if (index == start) { cout << "fail"; return false; } } cout << "fail"; return false; } bool Remove(const T&key) { size_t index = _HashFunc(key); size_t start = index; while (_states[index] != EMPTY) { if (_tables[index] == key) { _states[index]=DELETE; _size--; return true; } ++index; if (index == _capacity) index = 0; if (index == start) return false; } return false; } void Print() { if (_tables == NULL || _states == NULL) cout << "EMPTY"; for (size_t i = 0; i < _capacity; i++) { printf("(%d-%d:%d) ",i, _states[i], _tables[i]); } cout << endl; } private: void Checkcapacity() { if (_size * 10 / _capacity == 7) { HashTable<T>tmp(2 * _capacity); for (size_t i = 0; i < _capacity; i++) { if (_states[i] == EXITS) { tmp.Insert(_tables[i]); } } this->_swap(tmp); } } void _swap(HashTable<T>&h) { swap(_tables, h._tables); swap(_states, h._states); swap(_capacity, h._capacity); swap(_size, h._size); } size_t _HashFunc(const T&key)//安排在哈希表中的位置 { return key%_capacity; } private: size_t _capacity;//容量 T* _tables;//哈希表 State* _states;//狀態表 size_t _size;//存儲元素個數 };
程序3,0
解決哈希衝突的另一個方法就是哈希桶,用鏈表來將同一位置上的數據鏈接在一起
#include<iostream> #include<vector> using namespace std; template<class K,class V> struct HashTableNode//結點結構 { V _value; K _key; HashTableNode<K, V>*_next; HashTableNode(const K&key, const V&value) :_value(value) , _key(key) , _next(NULL) {} }; template<class K,class V> class HashTable { public: HashTable() :_size(0) { _table.resize(_GetPrimeSize()); } HashTable(const HashTable<K,V>&h) :_size(0) { _table.resize(h._table.size()); _size = h._size; for (size_t i = 0; i < h._table.size(); i++) { HashTableNode<K, V>*cur = h._table[i]; while (cur) { Insert(cur->_key, cur->_value); cur = cur->_next; } } } HashTable<K, V>&operator=(HashTable<K, V> h) { _table.swap(h._table); swap(_size, h._size); return *this; } ~HashTable() { for (size_t i = 0; i < _table.size(); i++) { HashTableNode<K, V>*cur = _table[i]; while (cur) { HashTableNode<K, V>*del = cur; cur = cur->_next; delete del; } _table[i] = NULL; } } public: bool Insert(const K&key,const V&value) { _CheckCapacity(); size_t index = _HashFunc(key, _table.size()); HashTableNode<K, V>*cur = _table[index]; while (cur)//檢查是否存在 { if (cur->_value == value) return false; cur = cur->_next; } HashTableNode<K, V>*tmp = new HashTableNode<K, V>(key, value); tmp->_next = _table[index]; _table[index] = tmp; _size++; } HashTableNode<K, V>*Find(const K&key) { size_t index = _HashFunc(key,_table.size()); HashTableNode<K, V>*cur = _table[index]; while (cur) { if (cur->_key = key) return cur; else cur = cur->_next; } } bool Remove(const K&key) { size_t index = _HashFunc(key,_table.size()); HashTableNode<K, V>*cur = _table[index]; if (cur->_key == key) { _table[index] = cur->_next; delete cur; cur = NULL; _size--; return true; } HashTableNode<K, V>*prev = cur; cur = cur->_next; while (cur) { if (cur->_key == key) { prev->_next = cur->_next; delete cur; cur = NULL; _size--; return true; } prev = cur; cur = cur->_next; } return false; } void print() { size_t i = 0; for ( ; i < _table.size(); i++) { HashTableNode<K, V>*cur = _table[i]; if (cur) { while (cur) { printf("%d-[%d:%d]", i, cur->_key, cur->_value); cur = cur->_next; } } else { printf("%d-[NULL:NULL]", i); } cout << endl; } } protected: size_t _HashFunc(K key,size_t capacity) { return key % capacity; } void _CheckCapacity() { if (_size == _table.size()) { size_t _PrimeSize = _GetPrimeSize(); vector<HashTableNode<K, V>*>newTables; newTables.resize(_PrimeSize); for (size_t i = 0; i < _table.size(); i++) { HashTableNode<K, V>*cur = _table[i]; while (cur) { HashTableNode<K, V>*tmp = cur; cur = cur->_next; //頭插 size_t index = _HashFunc(tmp->_key, newTables.size()); tmp->_next = newTables[index]; newTables[index] = tmp; } _table[i] = NULL; } _table.swap(newTables); } } unsigned long _GetPrimeSize()//使哈希衝突最小化 { const int _PrimeSize = 28; static const unsigned long _PrimeList[_PrimeSize] = { 53ul, 97ul, 193ul, 389ul, 769ul, 1543ul, 3079ul, 6151ul, 12289ul, 24593ul, 49157ul, 98317ul, 196613ul, 393241ul, 786433ul, 1572869ul, 3145739ul, 6291469ul, 12582917ul, 25165843ul, 50331653ul, 100663319ul, 201326611ul, 402653189ul, 805306457ul, 1610612741ul, 3221225473ul, 4294967291ul }; size_t i = 0; for ( i = 0; i < _PrimeSize; i++) { if (_table.size() < _PrimeList[i]) return _PrimeList[i]; } return _PrimeList[_PrimeSize]; } private: vector<HashTableNode<K, V>*>_table;//順序表內保存結點 size_t _size;//元素個數 };