BST二叉树的二分查找

"""
Definition of TreeNode:
class TreeNode:
    def __init__(self, val):
        self.val = val
        self.left, self.right = None, None
"""

class Solution:
    """
    @param root: the given BST
    @param target: the given target
    @return: the value in the BST that is closest to the target
    """
    
    def closestValue(self, root, target):
        # write your code here
        """
        特别简单好理解的方法，非递归：
如果当前root值比target大，就暂且把这个root值当成上限，然后往左边走
如果当前root值比target小，就暂且把这个root值当成下限，然后往右边走
左右摇摆着走，知道发现两个最接近target的值，由于是inplace的更新上下限，而且不递归，所以没有额外的空间损耗
O(h) time and O(1) space
        """
        if not root:
            return None
        
        lower, upper = root, root
        node = root
        while node:
            if node.val < target:
                lower = node
                node = node.right
            elif node.val > target:
                upper = node
                node = node.left
            else:
                return node.val
        return lower.val if abs(upper.val-target) > abs(lower.val-target) else             upper.val