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<iostream>#include<stack>#include<queue>using namespace std;template<class T>struct BinaryTreeNode{    T _data;    BinaryTreeNode<T> *_pRight;    BinaryTreeNode<T> *_pLeft;    BinaryTreeNode(T data) : _data(data), _pRight(nullptr), _pLeft(nullptr)    {}};template<class T>class BinaryTree{private:    typedef BinaryTreeNode<T> 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<Node*> 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<Node *> 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<Node *> 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<Node *> 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");}