1.判断二叉树是否平衡

//求树的高度int TreeDepth(Node* t){    int hl,hr,h;    if(t != NULL)    {        hl = TreeDepth(t->left);        hr = TreeDepth(t->right);        h = hl>hr? hl:hr;        return h+1;    }    return 0;}//判断二叉树是否平衡int isBalanced(Node* t)  {     if(t==NULL) return 1;     int leftDepth = TreeDepth(t->left);     int rightDepth = TreeDepth(t->right);     if(abs(leftDepth-rightDepth) > 1)         return 0;     else         return isBalanced(t->left) && isBalanced(t->right); }

2.判断二叉树是否相同

//判断两棵二叉树是否相同int CompTree(Node* tree1, Node* tree2){    if(tree1 == NULL && tree2 == NULL)        return 1;    else if(tree1 == NULL || tree2 == NULL)        return 0;    if(tree1->data != tree2->data)        return 0;    if(CompTree(tree1->left,tree2->left)==1 && CompTree(tree1->right,tree2->right)==1)        return 1;    //反转二叉树也可能相同    if(CompTree(tree1->left,tree2->right)==1 && CompTree(tree1->right,tree2->left)==1)        return 1;    return 0;}

//拷贝二叉树   void CopyTree(Node* s,Node* & d)  {      if(s==NULL) d = NULL;      Node* temp = new Node;      temp->data = s->data;      if(d==NULL) d = temp;      if(s->left) CopyTree(s->left,d->left);      if(s->right) CopyTree(s->right,d->right);  }

3.判断二叉树是否完全二叉树

判断二叉树是否是完全二叉树：层次遍历二叉树，遍历的左右节点入队列。若出队列的结点为空，则以后出队列的结点都为空，则为完全二叉树，否则不是

int ComplateTree(Node* bt){    Node* p=bt;    queue
     
       q;    int tag=0;    if(p==NULL) return 1;    q.push(p);    while(!q.empty())    {         p=q.front(); q.pop();          if(p->left && !tag) q.push(p->left);         else if(p->left)  return 0;         else tag=1;         if(p->right && !tag) q.push(p->right);         else if(p->right)  return 0;         else tag=1;    }    return 1;}
     

4.判断二叉树是否二叉排序树

判断二叉树是否是二叉排序树（BST）：根据中序遍历序列是否升序来判断

bool IsBinarySortTree(Node* bt){    stack
     
       s;    Node* p = bt;    Node* pre = NULL;   // pre保持为p的中序前驱    while(p || !s.empty())    {        if(p)        {            s.push(p);            p = p->left;        }        else        {            p = s.top(); s.pop();            if( pre && (p->data <= pre->data) )  return false;  // 不是二叉排序树            pre = p;   // 记下前驱结点            p = p->right;        }    }    return true;  // 二叉排序树}
     

判断二叉树是否是二叉排序树（BST）：层次遍历二叉树，若出队列的结点小于左结点的值，或者是大于右结点的值，则不是BST，否则是BST

bool IsBST(Node* T){    queue
     
       q;    Node* p;    if(T == NULL) return true;    q.push(T);    while(!q.empty())    {        p = q.front(); q.pop();        if(p->left)          if(p->data < p->left->data)             return false;          else q.push(p->left);        if(p->right)          if(p->data > p->right->data)             return false;          else q.push(p->right);    }    return true;}