Question

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How can I find the common ancestor of two nodes in a binary tree?
first common ancestor of a binary tree

I have a binary tree as below. I need to find the least common ancestor (LCA). e.g LCA of 6 and 4 is 1, LCA of 4 and 5 is 2.

    1
   / \
  2   3
 / \ / \
4  5 6  7 

Can anyone please suggest how should I approach and solve this problem?

Answer 1

Start with an ordinary depth-first search algorithm:

public Node find(Node node, int target) {
    if(node == null || node.value == target) {
        return node;
    }
    if(node.value > target) {
        return find(node.left, target);
    } else {
        return find(node.right, target);
    }
}

Now, adapt this to take two “target” parameters, target1 and target2.

When the search for target1 takes you left, and the search for target2 takes you right, you’ve found the LCA.

This assumes that both targets actually do exist. If you need to assert that they do, you’ll need to continue the search after finding the potential LCA.

public Node findLca(Node node, int t1, int t2) {
    if(node == null) {
        return null;
    }
    if(node.value > t2 && node.value > t1) {
        // both targets are left
        return findLca(node.left, t1, t2);
    } else if (node.value < t2 && node.value < t1) {
        // both targets are right
        return findLca(node.right, t1, t2);
    } else {
        // either we are diverging or both targets are equal
        // in both cases so we've found the LCA
        // check for actual existence of targets here, if you like
        return node;
    }
}