算法精粹(algorithm-essentials)

感谢soulmachine@github提供内容
## Binary Search Tree Iterator


### 描述

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.


### 分析

考察非递归的中序遍历。这道题本质上是写一个二叉树的中序遍历的迭代器。内部设置一个栈,初始化的时候,存储从根节点到最左叶子节点的路径。在遍历的过程中,每次从栈中弹出一个元素,作为当前的返回结果,同时探测一下当前节点是否存在右孩子,如果有,则进入右孩子,并把从该右孩子到最左叶子节点的所有节点入栈。


### 代码

{% if book.java %}
```java
// Binary Search Tree Iterator
public class BSTIterator {
public BSTIterator(TreeNode root) {
stack = new Stack<>();
while (root != null) {
stack.push(root);
root = root.left;
}
}

/** @return whether we have a next smallest number */
public boolean hasNext() {
return !stack.isEmpty();
}

/** @return the next smallest number */
public int next() {
final TreeNode node = stack.pop();
if (node.right != null) {
TreeNode p = node.right;
while (p != null) {
stack.push(p);
p = p.left;
}

}
return node.val;
}
private Stack stack;
}
```
{% endif %}