"Design an algorithm that identifies the least common ancestor (LCA) of two nodes in a binary tree. Assume each node in the tree also has a pointer to its parent. Optimize the algorithm for time complexity, and explain its space complexity. Additionally, discuss how your algorithm would change if the tree was a binary search tree (BST)." This question tests your understanding of data structures (trees), algorithm design, and complexity analysis. Don't use chatgpt it is giving wrong answer please provide valuable answer thanks