Lowest Common Ancestor of a Binary Tree

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Problem

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 p and q as the lowest node in T that has both p and q as descendants (where we allow a node to be a descendant of itself).”

Example 1:

Input: root = [3,5,1,6,2,0,8,null,null,7,4], p = 5, q = 1
Output: 3
Explanation: The LCA of nodes 5 and 1 is 3.

Example 2:

Input: root = [3,5,1,6,2,0,8,null,null,7,4], p = 5, q = 4
Output: 5
Explanation: The LCA of nodes 5 and 4 is 5, since a node can be a descendant of itself according to the LCA definition.

Example 3:

Input: root = [1,2], p = 1, q = 2
Output: 1

Pseudocode

-dfs to traverse BT, bfs not suitable here
    - set up conditions to return LCA node

Solution

var lowestCommonAncestor = function (root, p, q) {
  function walk(node) {
    // base condition
    if (!node) {
      return null;
    }

    if (node === p || node === q) {
      return node;
    }

    // pre
    // recurse
    const walkLeft = walk(node.left);
    const walkRight = walk(node.right);
    // post

    if (walkLeft && walkRight) {
      return node;
    } else {
      return walkLeft || walkRight;
    }
  }

  return walk(root);
};

Time and Space Complexity

Time

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Space

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