LCABST.md

236. Lowest Common Ancestor of a Binary Tree

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

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).”

        _______3______
       /              \
    ___5__          ___1__
   /      \        /      \
   6      _2       0       8
         /  \
         7   4

For example, the lowest common ancestor (LCA) of nodes 5 and 1 is 3.

Another example is LCA of nodes 5 and 4 is 5, since a node can be a descendant of itself according to the LCA definition.

Java

public TreeNode lowestCommonAncestor(TreeNode root, TreeNode p, TreeNode q) {
    if (root == null || root == p || root == q) {
        return root;
    }
    TreeNode right = lowestCommonAncestor(root.right, p, q);
    TreeNode left = lowestCommonAncestor(root.left, p, q);
    if (left == null) {
        return right;
    } else if (right == null) {
        return left;
    } else {
        // both of them is not null
        return root;
    }
}

Objective-C

- (TreeNode *)lowestCommonAncestor:(TreeNode *)root withP:(TreeNode *)p withQ:(TreeNode *)q {
    if (root == nil || root == p || root == q) {
        return root;
    }

    TreeNode *left = [self lowestCommonAncestor:root.left withP:p withQ:q];
    TreeNode *right = [self lowestCommonAncestor:root.right withP:p withQ:q];

    if (left == nil) {
        return right;
    } else if (right == nil) {
        return left;
    } else {
        return root;
    }
}