二叉树的面试题总结

1. 二叉树的创建
2. 二叉树的高度
3. 二叉树某层节点的个数
4. 二叉树的镜像
5. 二叉树最远两个节点的距离
6. 二叉树的前中后层序递归非递归遍历
7. 判断二叉树是否是完全二叉树
8. 二叉树叶子节点的个数

#include
#include
#include
using namespace std;
template<class T>
struct BinaryTreeNode
{
    T _data;
    BinaryTreeNode *_pRight;
    BinaryTreeNode *_pLeft;
    BinaryTreeNode(T data) : _data(data), _pRight(nullptr), _pLeft(nullptr)
    {}
};
template<class T>
class BinaryTree
{
private:
    typedef BinaryTreeNode Node;
public:
    BinaryTree() :_pRoot(nullptr)
    {}
    //创建二叉树
    BinaryTree(const T *arr, const size_t size, const T invalid)
    {
        size_t index = 0;
        _CreateTree(_pRoot, arr, size, index, invalid);
    }
    void PreOrder()
    {
        cout << "前序遍历递归版" << endl;
        _PreOrder(_pRoot);
        cout << endl;
    }
    void PreOrder_Nor()
    {
        cout << "前序遍历栈版" << endl;
        _PreOrder_Nor(_pRoot);
        cout << endl;
    }
    void PostOrder()
    {
        cout << "后续遍历递归版" << endl;
        _PostOrder(_pRoot);
        cout << endl;
    }
    void PostOrder_Nor()
    {
        cout << "后序遍历栈版" << endl;
        _PostOrder_Nor(_pRoot);
        cout << endl;
    }
    ~BinaryTree()
    {
        _DestroyTree(_pRoot);
    }
    //判断是否是完全二叉树
    bool IsCompleteBinaryTree()
    {
        return _IsCompleteBinaryTree(_pRoot);
    }
    //获取二叉树的镜像
    void GetBinaryMirror()
    {
        return _GetBinaryMirror(_pRoot);
    }
    //获取二叉树的高度
    size_t Height()
    {
        return _Height(_pRoot);
    }
    //得到二叉树叶子节点的个数
    size_t GetLeefNode()
    {
        return _GetLeefNode(_pRoot);
    }

    //得到二叉树第K层的节点数目
    size_t GetKLevelNode(size_t k)
    {
        cout << "树的第K层有多少节点" << endl;
        return _GetKLevelNode(_pRoot, k);
    }
    //得到二叉树中距离最远的两个结点之间的距离  
    int GetFarthestDistance()  
    {
        int distance = 0;
        _GetFarthestDistance(_pRoot, distance);
        return distance;
    }
private:
    //index记得给引用
    void _CreateTree(Node *&pRoot, const T *arr, const size_t size, size_t &index, T invalid)
    {
        if ((index < size) && (arr[index] != invalid))
        {
            pRoot = new Node(arr[index]);
            _CreateTree(pRoot->_pLeft, arr, size, ++index, invalid);
            _CreateTree(pRoot->_pRight, arr, size, ++index, invalid);
        }
    }
    void _PreOrder(Node *pRoot)
    {
        if (pRoot)
        {
            cout << pRoot->_data << " ";
            _PreOrder(pRoot->_pLeft);
            _PreOrder(pRoot->_pRight);
        }
    }
    void _PreOrder_Nor(Node *pRoot)
    {
        stack st;
        Node *pCur = pRoot;
        while (pCur || !st.empty())
        {
            while (pCur)
            {
                cout << pCur->_data << " ";
                st.push(pCur);
                pCur = pCur->_pLeft;
            }
            Node *pTop = st.top();
            st.pop();
            pCur = pTop->_pRight;
        }
        cout << endl;
    }
    void _PostOrder(Node *pRoot)
    {
        if (pRoot)
        {
            _PostOrder(pRoot->_pLeft);
            _PostOrder(pRoot->_pRight);
            cout << pRoot->_data << " ";
        }
    }
    void _PostOrder_Nor(Node *pRoot)
    {
        stack st;
        Node *pCur = pRoot;
        Node *pFlag = nullptr;
        while (pCur || !st.empty())
        {
            while (pCur)
            {
                st.push(pCur);
                pCur = pCur->_pLeft;
            }
            pCur = st.top();

            if ((nullptr == pCur->_pRight) || (pFlag == pCur->_pRight))
            {
                st.pop();
                cout << pCur->_data << " ";
                pFlag = pCur;
                pCur = nullptr;
            }
            else if (pCur->_pRight)
            {
                pCur = pCur->_pRight;
            }
        }
    }
    void _DestroyTree(Node *pRoot)
    {
        if (pRoot)
        {
            _DestroyTree(pRoot->_pLeft);
            _DestroyTree(pRoot->_pRight);
            delete pRoot;
            pRoot = nullptr;
        }
    }
    /*
    1. 层序遍历找到第一个度不为2的节点，把flag设置为true
    2. 若该节点只有左孩子没有右孩子继续遍历，若继续遍历的节点度不为0返回false
    3. 若该节点只有右孩子没有左孩子返回false
    4. 若栈为空返回true
    */
    bool _IsCompleteBinaryTree(Node *pRoot)
    {
        queue q;
        q.push(pRoot);
        if (NULL == pRoot->_pLeft&&NULL == pRoot->_pRight)
        {
            return true;
        }
        bool flag = false;
        while (!q.empty())
        {
            Node *pTop = q.front();
            if (flag && ((pTop->_pLeft) || (pTop->_pRight)))
                return false;
            if (pTop->_pLeft)
                q.push(pTop->_pLeft);
            if (pTop->_pRight && (NULL == pTop->_pLeft))
                return false;
            if (pTop->_pRight)
                q.push(pTop->_pRight);
            else
                flag = true;
            q.pop();
        }
        return true;
    }
    //找到二叉树中距离最远的两个节点
    int _GetFarthestDistance(Node* pRoot, int& distance)
    {
        if (NULL == pRoot)
            return  0;
        int left = _GetFarthestDistance(pRoot->_pLeft,distance);
        int right = _GetFarthestDistance(pRoot->_pRight, distance);
        if (left + right > distance)
            distance = left + right;
        return left > right ? left + 1 : right + 1;
    }
    //得到二叉树的镜像
    //层序或者前序后序遍历节点交换左右孩子
    void _GetBinaryMirror(Node *pRoot)
    {
        queue q;
        q.push(pRoot);
        while (!q.empty())
        {
            Node *pTop = q.front();
            if (pTop)
            {
                swap(pTop->_pLeft, pTop->_pRight);
            }
            if (pTop->_pLeft)
                q.push(pTop->_pLeft);
            if (pTop->_pRight)
                q.push(pTop->_pRight);
            q.pop();
        }
    }
    size_t _Height(Node *pRoot)
    {
        if (NULL == pRoot)
            return 0;
        size_t highLeft = 1 + _Height(pRoot->_pLeft);
        size_t highRight = 1 + _Height(pRoot->_pRight);
        return highLeft > highRight ? highLeft : highRight;
    }
    size_t _GetLeefNode(Node *pRoot)
    {
        if (pRoot == NULL)
            return 0;
        if (NULL == pRoot->_pLeft&&NULL == pRoot->_pRight)
            return 1;
        return _GetLeefNode(pRoot->_pLeft) + _GetLeefNode(pRoot->_pRight);
    }
    size_t _GetKLevelNode(Node *pRoot, size_t k)
    {
        if (k<1 || k>_Height(pRoot) || NULL == pRoot)
            return 0;
        if (k == 1 || NULL == pRoot->_pLeft || NULL == pRoot->_pRight)
            return 1;
        return _GetKLevelNode(pRoot->_pRight, k - 1) + _GetKLevelNode(pRoot->_pLeft, k - 1);
    }

private:
    Node *_pRoot;

};
void test()
{
    char arr[] = { '1', '2', '4', '#', '#', '#', '3', '5', '#', '#', '6' };
    char arr2[] = { '1', '2', '4', '#', '#', '9', '#', '#', '3', '5', '#', '#', '6' };
    size_t sz = sizeof(arr) / sizeof(arr[0]);
    BinaryTree<char> b(arr, sz, '#');
    size_t sz2 = sizeof(arr2) / sizeof(arr2[0]);
    BinaryTree<char> w(arr2, sz2, '#');
    cout << b.GetFarthestDistance() << endl;
    b.PreOrder();
    cout << "得到镜像" << endl;
    b.GetBinaryMirror();
    b.PreOrder_Nor();
    b.PostOrder();
    b.PostOrder_Nor();
    cout << w.GetKLevelNode(3) << endl;
    cout << "b是否是完全二叉树" << endl << b.IsCompleteBinaryTree() << endl;
    w.PostOrder_Nor();
    cout << "w的距离最大" << endl;
    cout << w.GetFarthestDistance() << endl;
    cout << "树的高度是：" << endl << b.Height() << endl;
    cout << "w是否是完全二叉树" << endl << w.IsCompleteBinaryTree() << endl;
    system("pause");
}
int main()
{
    test();
    system("pause");
}