Find smallest common organization for employees

You are given an organization structure and employee-to-organization membership. Define any reasonable data structures you need. ## Part 1 (base) Assume the org structure is a **tree** (each org has at most one parent). Each employee belongs to **exactly one** org node. Implement a function that returns the **smallest / lowest** organization that contains **both** employees (i.e., the lowest common ancestor org of their org nodes). - Input: `employeeAId`, `employeeBId` - Output: the org id/node representing the minimal common org - You may assume each org node can have a `parent` pointer. ## Part 2 (follow-up) Now assume an employee can belong to **multiple** orgs in the same org tree. Implement a function that returns the **minimal** org that contains both employees, meaning: - the returned org is an ancestor of **at least one** org of employee A, and - an ancestor of **at least one** org of employee B, - and among all such orgs, it is the “lowest/smallest” one (closest to the employees). Clarify how you break ties if there are multiple valid minimal orgs. ## Part 3 (follow-up) Now assume an org can belong to **multiple parent orgs** (i.e., the org structure is a **DAG**, not a tree). Employees may still belong to one or multiple orgs. Return the set of **minimal common org(s)** that satisfy the condition above. (There may be more than one minimal common org in a DAG.) - Define precisely what “minimal” means in a DAG (e.g., no descendant of that org is also a common org). ## Part 4 (follow-up / discussion) The membership edges (employee→org and org→org) can change over time. Discuss how you would support: - `add/remove` employee membership edges - `add/remove` org-to-org edges (while preventing cycles if you require a DAG) - repeated queries for minimal common org(s) State what time/space tradeoffs you would target and any constraints/assumptions (e.g., number of orgs, number of employees, query/update ratio).