Implement an iterator over a binary search tree (BST). Your iterator will be initialized with the root node of a BST.

Calling next() will return the next smallest number in the BST.

Note: next() and hasNext() should run in average O(1) time and uses O(h) memory, where h is the height of the tree.

Credits:
Special thanks to @ts for adding this problem and creating all test cases.

/**
 * Definition for binary tree
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode(int x) : val(x), left(NULL), right(NULL) {}
 * };
 */
class BSTIterator {
private:
    TreeNode *it;
    TreeNode *last;
    void toList(TreeNode *root){
        if(!root)
             return;
        //save
        TreeNode *cur=root;
        
        if(cur->left)
            toList(cur->left);
            
        cur->left=last;
        if(last)
            last->right=cur;
        last=cur;
        
        if(cur->right)
            toList(cur->right);
    }
public:
    BSTIterator(TreeNode *root) {
        last=NULL;
        toList(root);
        
        it=last;
        while(it&&it->left){
            it=it->left;
        }
    }

    /** @return whether we have a next smallest number */
    bool hasNext() {
        return (it!=NULL);
    }

    /** @return the next smallest number */
    int next() {
        int val= it->val;
        it=it->right;
        return val;
    }
};

/**
 * Your BSTIterator will be called like this:
 * BSTIterator i = BSTIterator(root);
 * while (i.hasNext()) cout << i.next();
 */

/**
 * Definition for binary tree
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode(int x) : val(x), left(NULL), right(NULL) {}
 * };
 */
class BSTIterator {
private:
    stack<TreeNode*> s;
    void toStack(TreeNode *root){
        if(root){
            TreeNode *p=root;
            while(p){
                s.push(p);
                p=p->left;
            }
        }
    }
public:
    BSTIterator(TreeNode *root) {
        toStack(root);
    }
    

    /** @return whether we have a next smallest number */
    bool hasNext() {
        return !s.empty();
    }

    /** @return the next smallest number */
    int next() {
        TreeNode* n= s.top();
        s.pop();
        toStack(n->right);
        return n->val;
    }
};

/**
 * Your BSTIterator will be called like this:
 * BSTIterator i = BSTIterator(root);
 * while (i.hasNext()) cout << i.next();
 */

Binary Search Tree Iterator