question

Given a binary search tree (BST), find the lowest common ancestor (LCA) of two given nodes in the BST.

According to the definition of LCA on Wikipedia: “The lowest common ancestor is defined between two nodes v and w as the lowest node in T that has both v and w as descendants (where we allow a node to be a descendant of itself).”

     _______6______
    /              \
 ___2__           ___8__
/      \         /      \
0      _4        7       9
      /  \
     3   5

For example, the lowest common ancestor (LCA) of nodes 2 and 8 is 6. Another example is LCA of nodes 2 and 4 is 2, since a node can be a descendant of itself according to the LCA definition.

explaination

节点p、q和根节点的关系有三种情况

（1）p、q在根节点的左结点

（2）p、q在根节点的右结点

（3）p、q分别在根节点的左右结点

由于是二叉查找树，所以在左结点比根结点小右结点比根结点大，可以根据这个性质进行判断

solution

public TreeNode lowestCommonAncestor(TreeNode root, TreeNode p, TreeNode q) {

    while((root.val-p.val)*(root.val-q.val) > 0)
    {
        root= root.val>p.val?root.left : root.right;
    }

    return root;
}