首先先來看一下樹的結構：
樹是n（n>=0）個有限個數據的元素集合，形狀像一顆倒過來的樹。
650) this.width=650;" src="/e/u261/themes/default/images/spacer.gif" style="background:url("/e/u261/lang/zh-cn/images/localimage.png") no-repeat center;border:1px solid #ddd;" alt="spacer.gif" />
而二叉樹就是樹的一種特殊結構：
下面我就實現一下二叉鏈的這種結構：
首先是它的節點的結構：
template <typename T>
struct BinaryTreeNode
{
public:
BinaryTreeNode(const T &data)//構造函數
:_left(NULL)
,_right(NULL)
,_data(data)
{}
public:
BinaryTreeNode<T> * _left;//左子樹
BinaryTreeNode<T> * _right;//右子樹
T _data;//數據項
};然後是它的基本成員函數：
template <typename T>
class BinaryTree
{
typedef BinaryTreeNode<T> Node;//重命名struct結構
public:
BinaryTree()//無參的構造函數
:_root(NULL)
{}
BinaryTree(const T* a, size_t size, const T& invalid)//有參構造函數
:_root(NULL)
{
size_t index = 0;
_root = _CreatBinaryTree(a, size, invalid, index);
}
BinaryTree(const BinaryTree<T> & t)//拷貝構造
:_root(NULL)
{
_root = _Copy(t._root);
}
BinaryTree<T>& operator=(BinaryTree<T> t)//賦值運算符的重載
{
if (this != &t)//防止自賦值
{
swap(_root, t._root);
}
return *this;
}
~BinaryTree()//析構函數
{
if (_root)
{
_Delete(_root);
}
}
void PrevOrder()//前序遍歷
{
_PrevOrder(_root);
cout << "over"<<endl;
}
void InOrder()//中序遍歷
{
_InOrder(_root);
cout << "over" << endl;
}
void PostOrder()//後序遍歷
{
_PostOrder(_root);
cout << "over" << endl;
}
void LevelOredr()//層次遍歷
{
_LevelOrder(_root);
cout << "over" << endl;
}
size_t Size()//節點數
{
return _Size(_root);
}
size_t Depth()//深度
{
return _Depth(_root);
}
size_t LeafSize()//葉子節點數
{
return _LeafSize(_root);
}
protected:
//創建二叉樹
Node* _CreatBinaryTree(const T *a, size_t size, const T& invalid,size_t& index)
{
Node * cur = NULL;
if (index < size&&a[index] != invalid)//不能越界
{
cur = new Node(a[index]);//開闢節點
cur->_left = _CreatBinaryTree(a, size, invalid, ++index);//遞歸創建左子樹
cur->_right = _CreatBinaryTree(a, size, invalid, ++index);//遞歸創建右子樹
}
return cur;
}
//複製二叉樹
Node* _Copy(Node * root)
{
Node * cur = NULL;
if (root == NULL)
{
return NULL;
}
cur = new Node(root->_data);//創建該節點
cur->_left = _Copy(root->_left);
cur->_right = _Copy(root->_right);
return cur;
}
//刪除
void _Delete(Node * &root)
{
if (root == NULL)
{
return;
}
if (root->_left == NULL && root->_right == NULL)//該節點沒有左右孩子
{
delete root;//釋放該節點
root = NULL;
return;
}
_Delete(root->_left);
_Delete(root->_right);
}
//前序遍歷：根節點--左子樹--右子樹
void _PrevOrder(Node * root)
{
if (root == NULL)
{
return;
}
cout << root->_data << "->";
_PrevOrder(root->_left);
_PrevOrder(root->_right);
}
//中序遍歷：左子樹--根節點--右子樹
void _InOrder(Node * root)
{
if (root == NULL)
{
return;
}
_PrevOrder(root->_left);
cout << root->_data << "->";
_PrevOrder(root->_right);
}
//後序遍歷：左子樹--右子樹--根節點
void _PostOrder(Node * root)
{
if (root == NULL)
{
return;
}
_PrevOrder(root->_left);
_PrevOrder(root->_right);
cout << root->_data << "->";
}
//層次遍歷
void _LevelOrder(Node* root)
{
queue<Node*> q;
if (root == NULL)
{
return;
}
q.push(root);
while (!q.empty())
{
if (q.front()->_left != NULL)
{
q.push(q.front()->_left);
}
if (q.front()->_right != NULL)
{
q.push(q.front()->_right);
}
cout << q.front()->_data << "->";
q.pop();
}
}
//節點個數
size_t _Size(Node * root)
{
if (root == NULL)
{
return 0;
}
return _Size(root->_left) + _Size(root->_right) + 1;//當左子樹或者右子樹不爲空時，該節點有數據
}
//二叉樹的深度
size_t _Depth(Node * root)
{
if (root==NULL)
{
return 0;
}
size_t leftDepth = _Depth(root->_left);
size_t rightDepth = _Depth(root->_right);
/*if (leftDepth >= rightDepth)
{
return leftDepth + 1;
}
else
return rightDepth + 1;*/
return leftDepth > rightDepth?leftDepth + 1 : rightDepth+1;
}
//葉子節點個數
size_t _LeafSize(Node * root)
{
size_t size = 0;
if (root == NULL)
{
return size;
}
if (root->_left == NULL&&root->_right == NULL)
{
size++;
return size;
}
return _LeafSize(root->_left)+_LeafSize(root->_right);
}
private:
Node * _root;//根節點
};測試用例以及結果如下：
void Test()
{
int array1[10] = { 1, 2, 3, '#', '#', 4, '#' , '#', 5, 6 };
BinaryTree<int> b1(array1, 10, '#');
cout << "前序遍歷：";
b1.PrevOrder();
cout << "中序遍歷：";
b1.InOrder();
cout << "後序遍歷：";
b1.PostOrder();
cout << "層次遍歷：";
b1.LevelOredr();
cout << endl;
cout << "節點數：" << b1.Size() << endl;
cout << "深度：" << b1.Depth() << endl;
cout << "葉子節點數：" << b1.LeafSize() << endl;
cout << endl;
BinaryTree<int> b2(b1);
cout << "前序遍歷：";
b2.PrevOrder();
cout << "中序遍歷：";
b2.InOrder();
cout << "後序遍歷：";
b2.PostOrder();
cout << "層次遍歷：";
b2.LevelOredr();
cout << endl;
cout << "節點數：" << b2.Size() << endl;
cout << "深度：" << b2.Depth() << endl;
cout << "葉子節點數：" << b2.LeafSize() << endl;
cout << endl;
BinaryTree<int> b3;
b3 = b1;
cout << "前序遍歷：";
b3.PrevOrder();
cout << "中序遍歷：";
b3.InOrder();
cout << "後序遍歷：";
b3.PostOrder();
cout << "層次遍歷：";
b3.LevelOredr();
cout << endl;
cout << "節點數：" << b3.Size() << endl;
cout << "深度：" << b3.Depth() << endl;
cout << "葉子節點數：" << b3.LeafSize() << endl;
}
本文出自 “不斷進步的空間” 博客，請務必保留此出處http://10824050.blog.51cto.com/10814050/1766978