基本資料結構（5） —— 有序表

1 有序線性表

有序線性表是最基本的可搜尋容器，其提供除了可搜尋容器的操作，還有自己的一些基本操作。那麼什麼是可搜尋容器呢，可搜尋容器定義如下：

class SearchableContainer : public virtual Container{public:virtual bool IsMember (Object const&) const = 0;virtual void Insert (Object&) = 0;virtual void Withdraw (Object&) = 0;virtual Object& Find (Object const&) const = 0;};

 

也就是說，具有IsMember（判斷是否含有某對象）、Insert（插入某對象）、Withdraw（刪除某對象）和Find（尋找某對象）這四個基本操作的抽象容器就是可搜尋容器。

 

那麼什麼是有序線性表呢？定義如下：

class Position : public Iterator{};class List : public virtual SearchableContainer{public:    virtual Object& operator [] (unsigned int) const = 0;    virtual Object& operator [] (Position const&) const = 0;    virtual Position& FindPosition (Object const&) const = 0;    virtual void Withdraw (Position const&) = 0;};class OrderedList : public virtual List{public:    virtual void InsertAfter (Position const&, Object&) = 0;    virtual void InsertBefore (Position const&, Object&) = 0;};

 

我們看到有序線性表OrderedList除了具備可搜尋容器的基本特性，同時還具有以下操作：

    virtual Object& operator []
：存取表中某一給定位置上的對象。

    virtual Position& FindPosition：尋找對象在表中的位置。

    virtual void Withdraw (Position)：刪除表中某一給定位置上的對象。

    virtual void InsertAfter：把一個對象插在某一給定對象位置之後。

    virtual void InsertBefore：把一個對象插在某一給定對象位置之前。

 

有序線性表的數組標記法：

class ListAsArray : public virtual OrderedList{protected:    Array<Object*> array;    class Pos;public:    ListAsArray (unsigned int);    // ...    friend class Pos;};ListAsArray::ListAsArray (unsigned int size) :    array (size)    {}void ListAsArray::Insert (Object& object){    if (count == array.Length ())throw domain_error ("list is full");    array [count] = &object;    ++count;}Object& ListAsArray::operator [] (unsigned int offset) const{    if (offset >= count)throw out_of_range ("invalid offset");    return *array [offset];}bool ListAsArray::IsMember (Object const& object) const{    for (unsigned int i = 0; i < count; ++i)if (array [i] == &object)    return true;    return false;}Object& ListAsArray::Find (Object const& object) const{    for (unsigned int i = 0; i < count; ++i)if (*array [i] == object)    return *array [i];    return NullObject::Instance ();}void ListAsArray::Withdraw (Object& object){    if (count == 0)throw domain_error ("list is empty");    unsigned int i = 0;    while (i < count && array [i] != &object)++i;    if (i == count)throw invalid_argument ("object not found");    for ( ; i < count - 1U; ++i)array [i] = array [i + 1];    --count;}class ListAsArray::Pos : public Position{protected:    ListAsArray const& list;    unsigned int offset;public:    // ...    friend class ListAsArray;    friend class SortedListAsArray;};Position& ListAsArray::FindPosition (Object const& object) const{    unsigned int i = 0;    while (i < count && *array [i] != object)++i;    return *new Pos (*this, i);}Object& ListAsArray::operator [] (Position const& arg) const{    Pos const& position = dynamic_cast<Pos const&> (arg);    if (&position.list != this || position.offset >= count)throw invalid_argument ("invalid position");    return *array [position.offset];}void ListAsArray::InsertAfter (    Position const& arg, Object& object){    Pos const& position = dynamic_cast<Pos const&> (arg);    if (count == array.Length ())throw domain_error ("list is full");    if (&position.list != this || position.offset >= count)throw invalid_argument ("invalid position");    unsigned int const insertPosition = position.offset + 1;    for (unsigned int i = count; i > insertPosition; --i)array [i] = array [i - 1U];    array [insertPosition] = &object;    ++count;}void ListAsArray::Withdraw (Position const& arg){    Pos const& position = dynamic_cast<Pos const&> (arg);    if (count == 0)throw domain_error ("list is empty");    if (&position.list != this || position.offset >= count)throw invalid_argument ("invalid position");    for (unsigned int i = position.offset; i < count-1U; ++i)array [i] = array [i + 1];    --count;}

 

有序表也可以通過鏈表來實現，有興趣的可以自己去研究一下，不再贅述。

2 排序表

排序表是另一種很有用的可搜尋容器，它跟有序線性表的區別在於，不提供前插和後插的操作，當插入元素後，表中所有的元素應保持有序狀態，來看實現：

class SortedList : public virtual List{};

 

這可能是全文中最簡單的一個抽象類別實現了，其就是一個廣義表。來看排序表的數組標記法：

class SortedListAsArray :    public virtual SortedList, public virtual ListAsArray{    unsigned int FindOffset (Object const&) const;public:    SortedListAsArray (unsigned int);    // ...};void SortedListAsArray::Insert (Object& object){    if (count == array.Length ())throw domain_error ("list is full");    unsigned int i = count;    while (i > 0 && *array [i - 1U] > object)    {array [i] = array [i - 1U];--i;    }    array [i] = &object;    ++count;}unsigned int SortedListAsArray::FindOffset (    Object const& object) const{    int left = 0;    int right = count - 1;    while (left <= right)    {int const middle = (left + right) / 2;if (object > *array [middle])    left = middle + 1;else if (object < *array [middle])    right = middle - 1;else    return middle;    }    return count;}Object& SortedListAsArray::Find (Object const& object) const{    unsigned int const offset = FindOffset (object);    if (offset < count)return *array [offset];    elsereturn NullObject::Instance ();}Position& SortedListAsArray::FindPosition (    Object const& object) const{    Pos& result = *new Pos (*this);    result.offset = FindOffset (object);    return result;}void SortedListAsArray::Withdraw (Object& object){    if (count == 0)throw domain_error ("list is empty");    unsigned int const offset = FindOffset (object);    if (offset == count)throw invalid_argument ("object not found");    for (unsigned int i = offset; i < count - 1U; ++i)array [i] = array [i + 1];    --count;}

同樣，我們也不再贅述鏈表的實現方案了。