Find k-th recipient in command propagation order
Find k-th Recipient in Command Propagation Order
An organization's structure is represented as a rooted tree with n individuals (nodes), labeled 1 to n. You are provided with a parent array of size n+1 (1-indexed) that describes this tree:
parent[i] = -1indicates that personiis the root (the top leader).- Otherwise,
parent[i]is the direct manager (parent) of personi. - Each person can have zero or more direct reports (children).
Command Propagation Rule
When a person u issues a command, it is disseminated to all subordinates of u (i.e., all descendants of u). This propagation follows a strict, deterministic order:
- First, consider
u's direct children, sorted by their increasing person ID. - The command is sent to the child with the smallest ID first.
- Crucially, before the command is sent to the next direct child, it must be fully propagated throughout the entire subtree of the current child, following this same propagation rule recursively.
This process defines a unique traversal order for the descendants of u. It is equivalent to a Depth-First Search (DFS) preorder traversal of u's subtree (excluding u itself), where children are always visited in ascending order of their person IDs.
Task
Given the parent array, an issuer u, and a 1-indexed integer k, your task is to return the person ID of the k-th subordinate who receives the command according to the described propagation order.
If person u has fewer than k descendants, return -1.
Input/Output
- Input:
parent[](the tree structure),u(the issuer's ID),k(the 1-indexed recipient number). - Output: The person ID of the k-th recipient, or
-1if not found.
Notes and Assumptions
- The input
parentarray always forms a valid tree with exactly one root. kis 1-indexed and refers only to descendants; the issueruis not counted as a recipient.- The number of people
ncan be large (e.g., up to 2e5). Therefore, an efficient approach that avoids simulating the propagation step-by-step for each query is generally expected. If multiple queries are anticipated, consider how to optimize for that scenario.
AI interview prep
Core dilemma
Efficiently querying the k-th element in a specific, deterministic DFS traversal order of a tree, especially when dealing with large N and potential for multiple queries, balancing pre-computation costs against query performance.
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Unlock the interviewer X-Ray rubric, tradeoff matrix, stress tests, clarifying questions, and key concepts.
Find k-th recipient in command propagation order
Find k-th Recipient in Command Propagation Order
An organization's structure is represented as a rooted tree with n individuals (nodes), labeled 1 to n. You are provided with a parent array of size n+1 (1-indexed) that describes this tree:
parent[i] = -1indicates that personiis the root (the top leader).- Otherwise,
parent[i]is the direct manager (parent) of personi. - Each person can have zero or more direct reports (children).
Command Propagation Rule
When a person u issues a command, it is disseminated to all subordinates of u (i.e., all descendants of u). This propagation follows a strict, deterministic order:
- First, consider
u's direct children, sorted by their increasing person ID. - The command is sent to the child with the smallest ID first.
- Crucially, before the command is sent to the next direct child, it must be fully propagated throughout the entire subtree of the current child, following this same propagation rule recursively.
This process defines a unique traversal order for the descendants of u. It is equivalent to a Depth-First Search (DFS) preorder traversal of u's subtree (excluding u itself), where children are always visited in ascending order of their person IDs.
Task
Given the parent array, an issuer u, and a 1-indexed integer k, your task is to return the person ID of the k-th subordinate who receives the command according to the described propagation order.
If person u has fewer than k descendants, return -1.
Input/Output
- Input:
parent[](the tree structure),u(the issuer's ID),k(the 1-indexed recipient number). - Output: The person ID of the k-th recipient, or
-1if not found.
Notes and Assumptions
- The input
parentarray always forms a valid tree with exactly one root. kis 1-indexed and refers only to descendants; the issueruis not counted as a recipient.- The number of people
ncan be large (e.g., up to 2e5). Therefore, an efficient approach that avoids simulating the propagation step-by-step for each query is generally expected. If multiple queries are anticipated, consider how to optimize for that scenario.