OpenAI OA - New Questions | HackerRank - 2 Questions + Thoughts

This time, I'm going to share a set of the newest ones that came out on October 6 OpenAI OA real questions, appearing on the HackerRank platform. There are two programming questions in the whole OA, the overall difficulty is between Medium ~ Hard, the first question is path optimization on tree, the second question is biased towards graph search + state compression.

Question 1: Optimal Path

Title Description

A distributed system of servers is represented as a tree with tree_nodes nodes, numbered from 1 to tree_nodes. Moving between directly connected servers takes 1 unit of time.

A process needs to.

• Start at the start_node server.
• Complete tasks at servers listed in an array task_nodes[] of size num_tasks (by visiting them in any order).
• End at the end_node server.

Find the minimum time required to complete all tasks and reach end_node.
Edges are bidirectional.

Constraints.

2 ≤ tree_nodes ≤ 2×10^5
1 ≤ num_tasks ≤ tree_nodes
1 ≤ start_node, end_node, task_nodes[i] ≤ tree_nodes

Example Inputs and Outputs

tree_nodes = 5
tree_from = [3, 2, 4, 1]
tree_to = [2, 5, 3, 2]
start_node = 1
end_node = 5
start_node = 1 end_node = 5 task_nodes = [4, 2]

Output:

6

Explanation:
The optimal path is 2 -> 3 -> 1(which under the tree mapping is equivalent to returning to the main path after visiting a task node).
A total of 6 units of time were spent.

Explanation of Ideas

This problem is a combination of "shortest path in tree + shortest set of necessary points".
The key idea is:

• The task nodes are in arbitrary order, so you can start by finding the set of necessary nodes that need to be accessed.
• These nodes include:
  • All task_nodes
  • start_node and end_node
  • and their nodes on the least common ancestor path in the tree

Then we just need to compute the minimum connected subtree covered by these nodes in the tree (also known as the "Steiner Tree"), the
Then use DFS or BFS to find the total path length.

Key findings

The shortest path length to visit all the task nodes in the tree and go from the start point to the end point is:

2 * (sum of edges in minimal subtree) - distance(start_node, end_node)

The explanation is as follows:

• Each edge needs to be traveled through twice (go + back), but that part of the start → end path does not need to be turned back;
• So subtract the distance from start to end once.

Question 2: Minimum Operations to Reach Target

Title Description

You are given a starting integer start, a target integer target, and an integer array operations[].

In each step, you can move from your current position X to (x + op) % 100000, where op is any element from the array operations.

Return the minimum number of operations required to reach target From start.
If it is impossible to reach target, return -1.

Example

start = 3
target = 30
operations = [2, 5, 7]

Output:

6

Explanation:
An optimal path is:

3 → 5 → 10 → 15 → 22 → 24 → 30

Total 6 steps.

Deconstructing Ideas

This question looks simple, but it is a typical BFS state search on a graph.

Each number (0 to 999999) is viewed as a node, the
slave node X This can be done by adding any op(and then modulo 100000) jumps to a new node.

The goal is to start with start until (a time) target Minimum number of steps --
Unprivileged graph shortest path → BFS template questions.

OpenAI OA Difficulty Summary

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