lowest-common-ancestor-of-a-binary-tree.js

/**
 * 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.
 */

/**
 * @param {TreeNode} root
 * @param {TreeNode} p
 * @param {TreeNode} q
 * @return {TreeNode}
 */
const lowestCommonAncestor = (root, p, q) => {
  if (!root || root === p || root === q) {
    return root;
  }

  const left = lowestCommonAncestor(root.left, p, q);
  const right = lowestCommonAncestor(root.right, p, q);

  if (left && right) {
    return root;
  }

  return left ? left : right;
};

export default lowestCommonAncestor;