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<Node*> 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<Node*> 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<Node*> 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;
}