Find nearest common manager for multiple employees
Problem: Find Nearest Common Manager for Multiple Employees
Given an organizational hierarchy, represented as a rooted tree, you are tasked with building this tree from a list of (employee, manager) pairs.
Your primary goal is to implement a function that, for a given set of k (where k ≥ 2) employees, efficiently returns their nearest common organizational node. This node is defined as the lowest common ancestor (LCA) for all k specified nodes within the hierarchy.
You must:
- Design and Implement APIs:
- An API to construct the organizational tree from the provided
(employee, manager)pairs. - An API to validate the input, specifically detecting cycles and disconnected components within the hierarchy, and handling such invalid inputs gracefully.
- An API to compute the LCA for a set of
kemployees efficiently.
- An API to construct the organizational tree from the provided
- Preprocessing: Discuss and implement suitable preprocessing approaches to optimize LCA queries. Consider techniques such as storing parent pointers with depths, binary lifting, or Euler tour with Range Minimum Query (RMQ).
- Complexity Analysis: Analyze the time and space complexity of your chosen construction, validation, and LCA computation methods.
- Unit Tests: Include clear unit tests covering typical scenarios and critical edge cases. These include:
- Employees located in different subtrees.
- One or more specified employees not found in the hierarchy.
- The root of the tree being the nearest common manager.
- All employees being the same or directly in the same path.
AI interview prep
Core dilemma
Balancing the time and space complexity of preprocessing the organizational hierarchy against the efficiency of subsequent k-LCA queries, especially for large N (number of employees) and varying k.
3 tradeoffs and 3 stress tests locked
Interview prep
Unlock the interviewer X-Ray rubric, tradeoff matrix, stress tests, clarifying questions, and key concepts.
Find nearest common manager for multiple employees
Problem: Find Nearest Common Manager for Multiple Employees
Given an organizational hierarchy, represented as a rooted tree, you are tasked with building this tree from a list of (employee, manager) pairs.
Your primary goal is to implement a function that, for a given set of k (where k ≥ 2) employees, efficiently returns their nearest common organizational node. This node is defined as the lowest common ancestor (LCA) for all k specified nodes within the hierarchy.
You must:
- Design and Implement APIs:
- An API to construct the organizational tree from the provided
(employee, manager)pairs. - An API to validate the input, specifically detecting cycles and disconnected components within the hierarchy, and handling such invalid inputs gracefully.
- An API to compute the LCA for a set of
kemployees efficiently.
- An API to construct the organizational tree from the provided
- Preprocessing: Discuss and implement suitable preprocessing approaches to optimize LCA queries. Consider techniques such as storing parent pointers with depths, binary lifting, or Euler tour with Range Minimum Query (RMQ).
- Complexity Analysis: Analyze the time and space complexity of your chosen construction, validation, and LCA computation methods.
- Unit Tests: Include clear unit tests covering typical scenarios and critical edge cases. These include:
- Employees located in different subtrees.
- One or more specified employees not found in the hierarchy.
- The root of the tree being the nearest common manager.
- All employees being the same or directly in the same path.