Leetcode235. Lowest Common Ancestor of a Binary Search Tree

Posted 2020-10-24 于淼

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.

Tips：找到一棵二叉查找树中两个结点的最低公共祖先。

解决方案：二叉查找树是一个已经排好序的二叉树，所有左子树结点都小于父结点，所有右子树结点都大于父节点，所以，只需要比较当前结点与p、q结点val的大小进行比较。若p、q的值都小于当前节点，那么最低公共祖先一定在当前节点的左子树上，相反则在右子树上。

方案一：使用循环：

 public TreeNode lowestCommonAncestor(TreeNode root, TreeNode p, TreeNode q) {
            while (true) {
                if (root.val > p.val && root.val > q.val)
                    root = root.left;
                else if (root.val < p.val && root.val < q.val)
                    root = root.right;
                else
                    return root;
            }
        }

方案二： 使用递归：

public TreeNode lowestCommonAncestor(TreeNode root, TreeNode p, TreeNode q) {
        TreeNode ans = root;
        if (root.val > p.val && root.val > q.val) {
            ans = lowestCommonAncestor(root.left, p, q);
        } else if (root.val < p.val && root.val < q.val) {
            ans = lowestCommonAncestor(root.right, p, q);
        } else {
            ans = root;
        }
        return ans;
    }