235 Lowest Common Ancestor of a Binary Search Tree

235. Lowest Common Ancestor of a Binary Search Tree
1. 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).”
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        _______6______
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       /              \
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    ___2__          ___8__
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   /      \        /      \
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   0      _4       7       9
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         /  \
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         3   5
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For example, the lowest common ancestor (LCA) of nodes2and8is6. Another example is LCA of nodes2and4is2, since a node can be a descendant of itself according to the LCA definition.
2. Implementation
(1) Recursion
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class Solution {
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    public TreeNode lowestCommonAncestor(TreeNode root, TreeNode p, TreeNode q) {
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        if (root.val < Math.min(p.val, q.val)) {
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            return lowestCommonAncestor(root.right, p, q);
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        }
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        else if (root.val > Math.max(p.val, q.val)) {
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            return lowestCommonAncestor(root.left, p, q);
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        }
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        else {
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            return root;
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        }
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    }
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}
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(2) Iteration
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class Solution {
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    public TreeNode lowestCommonAncestor(TreeNode root, TreeNode p, TreeNode q) {
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        TreeNode curNode = root;
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        while (curNode != null) {
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            if (curNode.val < p.val && curNode.val < q.val) {
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                curNode = curNode.right;
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            }
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            else if (curNode.val > p.val && curNode.val > q.val) {
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                curNode = curNode.left;
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            }
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            else {
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                break;
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            }
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        }
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        return curNode;
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    }
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}
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3. Time & Space Complexity
Recursion: 时间复杂度: O(h), 空间复杂度: O(h)
Iteration: 时间复杂度:O(h) , 空间复杂度：O(1)

257 Binary Tree Paths

236 Lowest Common Ancestor of a Binary Tree

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Contents

235. Lowest Common Ancestor of a Binary Search Tree

1. Question

2. Implementation

3. Time & Space Complexity