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).”
_______6______
/ \
___2__ ___8__
/ \ / \
0 _4 7 9
/ \
3 5
For example, the lowest common ancestor (LCA) of nodes2
and8
is6
. Another example is LCA of nodes2
and4
is2
, since a node can be a descendant of itself according to the LCA definition.
2. Implementation
(1) Recursion
class Solution {
public TreeNode lowestCommonAncestor(TreeNode root, TreeNode p, TreeNode q) {
if (root.val < Math.min(p.val, q.val)) {
return lowestCommonAncestor(root.right, p, q);
}
else if (root.val > Math.max(p.val, q.val)) {
return lowestCommonAncestor(root.left, p, q);
}
else {
return root;
}
}
}
(2) Iteration
class Solution {
public TreeNode lowestCommonAncestor(TreeNode root, TreeNode p, TreeNode q) {
TreeNode curNode = root;
while (curNode != null) {
if (curNode.val < p.val && curNode.val < q.val) {
curNode = curNode.right;
}
else if (curNode.val > p.val && curNode.val > q.val) {
curNode = curNode.left;
}
else {
break;
}
}
return curNode;
}
}
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)
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