一、類型定義
在多叉樹中，後序遍歷迭代器有只讀、讀寫、只讀反轉、讀寫反轉4種，在mtree容器中的定義如下：
1 typedef post_iterator_impl<false,false> post_iterator;
2 typedef post_iterator_impl<false,true> reverse_post_iterator;
3 typedef post_iterator_impl<true,false> const_post_iterator;
4 typedef post_iterator_impl<true,true> const_reverse_post_iterator;
二、接口定義
對於二叉樹的後序遍歷，我們都很熟悉，類似地，多叉樹的後序遍歷與二叉樹一樣：先訪問它的左子樹（若存在），再訪問它的右子樹（若存在），然後訪問它的根結點，遞歸地，每顆子樹內部結點的訪問順序都遵循著上面的規律。下面代碼是後序遍歷迭代器的聲明：
1 template<bool is_const,bool is_reverse>
2 class post_iterator_impl : public iterator_base_impl<is_const>
3 {
4 friend class mtree<T,false>;
5 typedef iterator_base_impl<is_const> base_type;
6 typedef typename base_type::node_pointer_type node_pointer_type;
7 typedef typename base_type::tree_pointer_type tree_pointer_type;
8 using base_type::tree_;
9 using base_type::off_;
10 using base_type::root_;
11 using base_type::skip_progeny_;
12 public:
13 post_iterator_impl();
14 post_iterator_impl(const base_type& iter);
15 post_iterator_impl& operator++();
16 post_iterator_impl& operator--();
17 post_iterator_impl operator++(int);
18 post_iterator_impl operator--(int);
19 post_iterator_impl operator + (size_t off);
20 post_iterator_impl& operator += (size_t off);
21 post_iterator_impl operator - (size_t off);
22 post_iterator_impl& operator -= (size_t off);
23 post_iterator_impl begin() const;
24 post_iterator_impl end() const;
25 protected:
26 void first(no_reverse_tag);
27 void first(reverse_tag);
28 void last(no_reverse_tag);
29 void last(reverse_tag);
30 void increment(no_reverse_tag);
31 void increment(reverse_tag);
32 void decrement(no_reverse_tag);
33 void decrement(reverse_tag);
34 private:
35 void forward_first();
36 void forward_last();
37 void forward_next();
38 void forward_prev();
39 };
三、接口實現
下面重點講述後序遍歷中4種定位方法的具體實現，隨後列出其它所有方法的實現代碼。
（1）forward_first：求正向第一個結點，就是子樹最左側最深的那個結點，代碼如下：
1 template<typename T>
2 template<bool is_const,bool is_reverse>
3 inline void mtree<T,false>::post_iterator_impl<is_const,is_reverse>::forward_first()
4 {
5 off_ = root_; node_pointer_type p_node = &(*tree_)[off_];
6 while (p_node->first_child_)
7 {
8 off_ += p_node->first_child_;
9 p_node = &(*tree_)[off_];
10 }
11 }
（2）forward_next：求正向最後一個結點，就是子樹的根結點，代碼如下：
1 template<typename T>
2 template<bool is_const,bool is_reverse>
3 inline void mtree<T,false>::post_iterator_impl<is_const,is_reverse>::forward_last()
4 {
5 off_ = root_;
6 }
（3）forward_next：求正向下一個結點，步驟如下：a) 如果當前結點不是根結點且有右兄弟，那麼就是以它的右兄弟為根的子樹的最右側最深的那個結點，反之則轉到b)。b) 如果當前結點是根結點或父結點為空，那麼返回end，否則就是其父結點。代碼如下： 1 template<typename T>
2 template<bool is_const,bool is_reverse>
3 inline void mtree<T,false>::post_iterator_impl<is_const,is_reverse>::forward_next()
4 {
5 node_pointer_type p_node = &(*tree_)[off_];
6 if (off_!=root_&&p_node->next_sibling_)
7 {
8 off_ += p_node->next_sibling_;
9 p_node = &(*tree_)[off_];
10 while (p_node->first_child_)
11 {
12 off_ += p_node->first_child_;
13 p_node = &(*tree_)[off_];
14 }
15 }
16 else
17 {
18 if (off_==root_||!p_node->parent_)
19 off_ = tree_->size();
20 else
21 off_ -= p_node->parent_;
22 }
23 } （4）forward_prev：求正向前一個結點，步驟如下：a) 如果當前結點有孩子且不跳過後代，那麼就是最後一個孩子結點，反之則轉到b)。 b) 如果當前結點不是根結點且有左兄弟結點，那麼就是其左兄弟結點，否則轉到c)。 c) 一直向上回溯，直到碰到根結點或父結點為空或存在左兄弟結點時才結束，如果碰到根結點或父結點為空，那麼返回end，否則就是其左兄弟結點。代碼如下：
1 template<typename T>
2 template<bool is_const,bool is_reverse>
3 inline void mtree<T,false>::post_iterator_impl<is_const,is_reverse>::forward_prev()
4 {
5 node_pointer_type p_node = &(*tree_)[off_];
6 if (!skip_progeny_&&p_node->last_child_)
7 {
8 off_ += p_node->last_child_;
9 }
10 else if (off_!=root_&&p_node->prev_sibling_)
11 {
12 off_ -= p_node->prev_sibling_;
13 }
14 else
15 {
16 while (off_!=root_&&p_node->parent_&&!p_node->prev_sibling_)
17 {
18 off_ -= p_node->parent_;
19 p_node = &(*tree_)[off_];
20 }
21 if (off_==root_||!p_node->parent_)
22 off_ = tree_->size();
23 else
24 off_ -= p_node->prev_sibling_;
25 }
26 }
（5）構造函數的實現，代碼如下：
1 template<typename T>
2 template<bool is_const,bool is_reverse>
3 inline mtree<T,false>::post_iterator_impl<is_const,is_reverse>::post_iterator_impl()
4 :base_type()
5 {
6 root_ = 0;
7 }
8 template<typename T>
9 template<bool is_const,bool is_reverse>
10 inline mtree<T,false>::post_iterator_impl<is_const,is_reverse>::post_iterator_impl(const base_type& iter)
11 :base_type(iter)
12 {
13 root_ = off_;
14 }
（6）公有方法的實現，代碼如下：
1 template<typename T>
2 template<bool is_const,bool is_reverse>
3 inline typename mtree<T,false>::template post_iterator_impl<is_const,is_reverse>&
4 mtree<T,false>::post_iterator_impl<is_const,is_reverse>::operator++()
5 {
6 increment(typename reverse_trait<is_reverse>::type());
7 return *this;
8 }
9 template<typename T>
10 template<bool is_const,bool is_reverse>
11 inline typename mtree<T,false>::template post_iterator_impl<is_const,is_reverse>&
12 mtree<T,false>::post_iterator_impl<is_const,is_reverse>::operator--()
13 {
14 decrement(typename reverse_trait<is_reverse>::type());
15 return *this;
16 }
17 template<typename T>
18 template<bool is_const,bool is_reverse>
19 inline typename mtree<T,false>::template post_iterator_impl<is_const,is_reverse>
20 mtree<T,false>::post_iterator_impl<is_const,is_reverse>::operator++(int)
21 {
22 post_iterator_impl<is_const,is_reverse> iter(*this);
23 --(*this);
24 return iter;
25 }
26 template<typename T>
27 template<bool is_const,bool is_reverse>
28 inline typename mtree<T,false>::template post_iterator_impl<is_const,is_reverse>
29 mtree<T,false>::post_iterator_impl<is_const,is_reverse>::operator--(int)
30 {
31 post_iterator_impl<is_const,is_reverse> iter(*this);
32 --(*this);
33 return iter;
34 }
35 template<typename T>
36 template<bool is_const,bool is_reverse>
37 inline typename mtree<T,false>::template post_iterator_impl<is_const,is_reverse>
38 mtree<T,false>::post_iterator_impl<is_const,is_reverse>::operator + (size_t off)
39 {
40 post_iterator_impl<is_const,is_reverse> iter(*this);
41 iter += off;
42 return iter;
43 }
44 template<typename T>
45 template<bool is_const,bool is_reverse>
46 inline typename mtree<T,false>::template post_iterator_impl<is_const,is_reverse>&
47 mtree<T,false>::post_iterator_impl<is_const,is_reverse>::operator += (size_t off)
48 {
49 while (off)
50 {
51 if (base_type::is_null()) break;
52 ++(*this); --off;
53 }
54 return *this;
55 }
56 template<typename T>
57 template<bool is_const,bool is_reverse>
58 inline typename mtree<T,false>::template post_iterator_impl<is_const,is_reverse>
59 mtree<T,false>::post_iterator_impl<is_const,is_reverse>::operator - (size_t off)
60 {
61 post_iterator_impl<is_const,is_reverse> iter(*this);
62 iter -= off;
63 return iter;
64 }
65 template<typename T>
66 template<bool is_const,bool is_reverse>
67 inline typename mtree<T,false>::template post_iterator_impl<is_const,is_reverse>&
68 mtree<T,false>::post_iterator_impl<is_const,is_reverse>::operator -= (size_t off)
69 {
70 while (off)
71 {
72 if (base_type::is_null()) break;
73 --(*this); --off;
74 }
75 return *this;
76 }
77 template<typename T>
78 template<bool is_const,bool is_reverse>
79 inline typename mtree<T,false>::template post_iterator_impl<is_const,is_reverse>
80 mtree<T,false>::post_iterator_impl<is_const,is_reverse>::begin() const
81 {
82 post_iterator_impl<is_const,is_reverse> iter(*this);
83 iter.first(typename reverse_trait<is_reverse>::type());
84 return iter;
85 }
86 template<typename T>
87 template<bool is_const,bool is_reverse>
88 inline typename mtree<T,false>::template post_iterator_impl<is_const,is_reverse>
89 mtree<T,false>::post_iterator_impl<is_const,is_reverse>::end() const
90 {
91 post_iterator_impl<is_const,is_reverse> iter(*this);
92 if (tree_)
93 {
94 iter.off_ = tree_->size();
95 }
96 return iter;
97 }
（7）間隔層定位方法的實現，代碼如下：
1 template<typename T>
2 template<bool is_const,bool is_reverse>
3 inline void mtree<T,false>::post_iterator_impl<is_const,is_reverse>::first(no_reverse_tag)
4 {
5 assert(tree_&&root_<tree_->size());
6 forward_first();
7 }
8 template<typename T>
9 template<bool is_const,bool is_reverse>
10 inline void mtree<T,false>::post_iterator_impl<is_const,is_reverse>::first(reverse_tag)
11 {
12 assert(tree_&&root_<tree_->size());
13 forward_last();
14 }
15 template<typename T>
16 template<bool is_const,bool is_reverse>
17 inline void mtree<T,false>::post_iterator_impl<is_const,is_reverse>:: last(no_reverse_tag)
18 {
19 assert(tree_&&root_<tree_->size());
20 forward_last();
21 }
22 template<typename T>
23 template<bool is_const,bool is_reverse>
24 inline void mtree<T,false>::post_iterator_impl<is_const,is_reverse>:: last(reverse_tag)
25 {
26 assert(tree_&&root_<tree_->size());
27 forward_first();
28 }
29 template<typename T>
30 template<bool is_const,bool is_reverse>
31 inline void mtree<T,false>::post_iterator_impl<is_const,is_reverse>::increment(no_reverse_tag)
32 {
33 assert(tree_&&off_<=tree_->size());
34 off_!=tree_->size() ? forward_next() : first(no_reverse_tag());
35 }
36 template<typename T>
37 template<bool is_const,bool is_reverse>
38 inline void mtree<T,false>::post_iterator_impl<is_const,is_reverse>::increment(reverse_tag)
39 {
40 assert(tree_&&off_<=tree_->size());
41 off_!=tree_->size() ? forward_prev() : first(reverse_tag());
42 }
43 template<typename T>
44 template<bool is_const,bool is_reverse>
45 inline void mtree<T,false>::post_iterator_impl<is_const,is_reverse>::decrement(no_reverse_tag)
46 {
47 assert(tree_&&off_<=tree_->size());
48 off_ !=tree_->size() ? forward_prev() : last(no_reverse_tag());
49 }
50 template<typename T>
51 template<bool is_const,bool is_reverse>
52 inline void mtree<T,false>::post_iterator_impl<is_const,is_reverse>::decrement(reverse_tag)
53 {
54 assert(tree_&&off_<=tree_->size());
55 off_ !=tree_->size() ? forward_next() : last(reverse_tag());
56 }
四、使用示例
（1）正向遍歷整顆樹，代碼如下：
1 mtree<int,false> mt;
2 mtree<int,false>::iterator_base root = mt.get_root();
3 mtree<int,false>::post_iterator it = root;
4 mtree<int,false>::post_iterator last = --it.end();
5 for (it = it.begin();it!=it.end();++it)
6 {
7 cout << *it;
8 if (it!=last)
9 cout <<" ";
10 }
（2）反向遍歷整顆樹 ，代碼如下：
1 mtree<int,false> mt;
2 mtree<int,false>::iterator_base root = mt.get_root();
3 mtree<int,false>::reverse_post_iterator r_it = root;
4 mtree<int,false>::reverse_post_iterator r_last = --r_it.end();
5 for (r_it = r_it.begin();r_it!=r_it.end();++r_it)
6 {
7 cout << *r_it;
8 if (r_it!=r_last)
9 cout <<" ";
10 }
