Added question 236.

Author: luceCoding

leetcode/medium/236_lowest_common_ancestor_of_a_binary_tree.md

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+# 236. Lowest Common Ancestor of a Binary Tree
+
+## Recursive Solution
+
+- Runtime: O(N)
+- Space: O(H)
+- N = Number of nodes in tree
+- H = Height of tree
+
+From the perspective of a root node, there are only three options to consider.
+- The LCA exists on the left sub-tree.
+- The LCA exists on the right sub-tree.
+- The LCA is the root node.
+
+To figure out if an LCA exists would mean we need to find p and q in either sub-tree.
+If either are found, we have to let the parent know of their existence.
+
+The other question is when to evaluate these conditions.
+We generally don't want to traverse a sub-tree if the LCA is already found, so if the recursion function returns the LCA, we should instead return it back up the tree.
+Secondly, if LCA has not been found from either side, we need to know if either p or q were found.
+So a number would be returned to the parent node.
+With this number, we can check if our root is p or q and add it with the returned number found.
+If the number happens to be 2, we found the LCA.
+In summary, we need a post-order traversal recursion call.
+
+The worst case is that we have to traverse the entire tree to find p and q. However, we will never need more than height of the tree O(H) space to find p or q.
+
+```
+from collections import namedtuple
+
+LCA = namedtuple('LCA', ['n_found', 'lca'])
+
+class Solution:
+    def lowestCommonAncestor(self, root: 'TreeNode', p: 'TreeNode', q: 'TreeNode') -> 'TreeNode':
+
+        def LCA_helper(root):
+            if root is None:
+                return LCA(n_found=0, lca=None)
+            left = LCA_helper(root.left)
+            if left.n_found == 2:
+                return left
+            right = LCA_helper(root.right)
+            if right.n_found == 2:
+                return right
+            n_found = left.n_found + right.n_found + (1 if root is p or root is q else 0)
+            return LCA(n_found=n_found, lca=root if n_found == 2 else None)
+
+        return LCA_helper(root).lca
+```