236 Lowest Common Ancestor of a Binary Tree
236. Lowest Common Ancestor of a Binary Tree
1. Question
Given a binary tree, find the lowest common ancestor (LCA) of two given nodes in the tree.
According to thedefinition 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).”
_______3______
/ \
___5__ ___1__
/ \ / \
6 _2 0 8
/ \
7 4
For example, the lowest common ancestor (LCA) of nodes5
and1
is3
. Another example is LCA of nodes5
and4
is5
, 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 == null || root == p || root == q) {
return root;
}
TreeNode left = lowestCommonAncestor(root.left, p, q);
TreeNode right = lowestCommonAncestor(root.right, p, q);
if (left != null && right != null) {
return root;
}
return left != null ? left : right;
}
}
(2) Iteration
class Solution {
public TreeNode lowestCommonAncestor(TreeNode root, TreeNode p, TreeNode q) {
Map<TreeNode, TreeNode> parent = new HashMap<>();
Stack<TreeNode> stack = new Stack<>();
parent.put(root, null);
stack.push(root);
while (!parent.containsKey(p) || !parent.containsKey(q)) {
TreeNode curNode = stack.pop();
if (curNode.left != null) {
parent.put(curNode.left, curNode);
stack.push(curNode.left);
}
if (curNode.right != null) {
parent.put(curNode.right, curNode);
stack.push(curNode.right);
}
}
Set<TreeNode> ancestor = new HashSet<>();
while (p != null) {
ancestor.add(p);
p = parent.get(p);
}
while (!ancestor.contains(q)) {
q = parent.get(q);
}
return q;
}
}
3. Time & Space Complexity
Recursion: 时间复杂度O(n), 空间复杂度O(h)
Iteration: 时间复杂度O(n), 空间复杂度O(h)
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