給定一個二叉樹，判斷它是否是合法的二叉查詢樹(BST)

一棵BST定義為：

• 節點的左子樹中的值要嚴格小於該節點的值。
• 節點的右子樹中的值要嚴格大於該節點的值。
• 左右子樹也必須是二叉查詢樹。
• 一個節點的樹也是二叉查詢樹。

樣例

一個例子：

  2
 / \
1   4
   / \
  3   5

上述這棵二叉樹序列化為 {2,1,4,#,#,3,5}.

解題思路1：

二叉查詢樹有一個重要的性質：即中序遍歷遞增（不存在兩個節點值相等），根據此，中序遍歷完成後，檢視序列是否有序即可知道是否是二叉查詢樹。

/**
 * Definition of TreeNode:
 * class TreeNode {
 * public:
 *     int val;
 *     TreeNode *left, *right;
 *     TreeNode(int val) {
 *         this->val = val;
 *         this->left = this->right = NULL;
 *     }
 * }
 */

class Solution {
public:
    /**
     * @param root: The root of binary tree.
     * @return: True if the binary tree is BST, or false
     */
    bool isValidBST(TreeNode * root) 
    {
        // write your code here
        if(root == NULL)
            return true;
        
        vector<int> vec;   
        Inorder(root , vec);
        
        for(int i = 0;i < vec.size()-1;i++)
            if(vec[i] >= vec[i+1])
                return false;
        
        return true;
    }
    
private:
    void Inorder(TreeNode * root , vector<int> & vec)
    {
        if(root == NULL)
            return;
        
        Inorder(root->left , vec);
        vec.push_back(root->val);
        Inorder(root->right , vec);
    }
};
 

JAVA程式碼：

/**
 * Definition of TreeNode:
 * public class TreeNode {
 *     public int val;
 *     public TreeNode left, right;
 *     public TreeNode(int val) {
 *         this.val = val;
 *         this.left = this.right = null;
 *     }
 * }
 */

public class Solution {
    /**
     * @param root: The root of binary tree.
     * @return: True if the binary tree is BST, or false
     */
    public boolean isValidBST(TreeNode root) {
        // write your code here
        List<Integer> list = new ArrayList<>();
        
        isValidBST(root, list);
        
        return isOrder(list);
    }
    
    private void isValidBST(TreeNode root, List<Integer> list){
        if(root == null)
            return;
            
        isValidBST(root.left, list);
        list.add(root.val);
        isValidBST(root.right, list);
    }
    
    private boolean isOrder(List<Integer> list){
        for(int i=1 ; i<list.size() ; i++)
            if(list.get(i) <= list.get(i-1))
                return false;
        
        return true;
    }
}
 

JAVA程式碼2：非遞迴方法，類似非遞迴的中序遍歷

/**
 * Definition of TreeNode:
 * public class TreeNode {
 *     public int val;
 *     public TreeNode left, right;
 *     public TreeNode(int val) {
 *         this.val = val;
 *         this.left = this.right = null;
 *     }
 * }
 */

public class Solution {
    /**
     * @param root: The root of binary tree.
     * @return: True if the binary tree is BST, or false
     */
    public boolean isValidBST(TreeNode root) {
        // write your code here
        Stack<TreeNode> stack = new Stack<>();
        TreeNode pre = null;
        
        while(root!=null || !stack.isEmpty()){
            while(root != null){
                stack.push(root);
                root = root.left;
            }
            
            root = stack.pop();
            
            if(pre!=null && pre.val>=root.val)
                return false;
            pre = root;
            
            root = root.right;
        }
        
        return true;
    }
    
}