leetcode_Kth Smallest Element in a BST

描述：

Given a binary search tree, write a function kthSmallest to find the kth smallest element in it.
Note:
You may assume k is always valid, 1 ≤ k ≤ BST's total elements.
Follow up:
What if the BST is modified (insert/delete operations) often and you need to find the kth smallest frequently? How would you optimize the kthSmallest routine?
Hint:
Try to utilize the property of a BST.Show More Hint

思路：

1.一般涉及到树的问题用树的遍历方式来解决的可能性比较大，或者就是递归了

2.对于本题，一种很朴素的解决方式就是不是二叉查找树么，中序遍历时不就是一个有序的序列么，直接上中序遍历，遍历到第K个数即是本题要求的Kth Smallest Element in a BST 

代码：

public int kthSmallest(TreeNode root, int k) {
		 int count=0;
	     Stack<TreeNode>st=new Stack<TreeNode>();
	     st.push(root);
	     TreeNode top=null;
	     while(!st.empty())
	     {
	    	 top=st.peek();
	    	 while(top.left!=null)
	    	 {
	    		 st.push(top.left);
	    		 top=top.left;
	    	 }
	    	 while(top.right==null)
	    	 {
	    		 count++;
	    		 if(count==k)
	    		    return top.val;
	    		 st.pop();
	    		 if(!st.empty())
	    			 top=st.peek();
	    		 else
	    			 break;
	    	 }
	    	 if(!st.empty())
	    	 {
	    		 count++;
	    		 if(count==k)
	    		    return top.val;
		    	 st.pop();
		    	 st.push(top.right);
	    	 }
	    	 
	     }
	     return -1;
    }