Practice Mode • Trees & Graphs • medium

Support Escalation Hops

180 points

Measure the shortest escalation path in a support graph.

Problem

You are implementing measure the shortest escalation path in a support graph. The input is one JSON value. Return exactly the JSON or scalar result described by the examples, with stable ordering and no extra logging. Return the unweighted shortest-hop distance between two nodes. Explain your reasoning and complexity during interview review; the judge evaluates only the returned result.

Input contract

One UTF-8 JSON value matching the structures shown in the examples.

Output contract

One deterministic JSON value or scalar with no explanatory text.

Target complexity

O(V+E) time, O(V) space

Judge protocol

function-stdin-json-v1

Examples

Example 1

Input: {"edges":[["a","b"],["b","c"],["a","x3"]],"goal":"c","start":"a"}
Output: 2

This example demonstrates the core trees graphs invariant.

Example 2

Input: {"edges":[],"goal":"a","start":"a"}
Output: 0

This example covers the empty or minimum boundary.

Constraints

Input is valid UTF-8 JSON and is at most 64 KB.
Output must be deterministic for identical input.
Do not use network access, persistent filesystem writes, subprocesses, or environment secrets.
Handle the empty or minimum boundary shown in the examples.

Progressive hints

Integrity: hidden tests, editorial solutions, and assessment-only cases are never sent to the browser as answer keys. Final execution occurs only in the separately isolated runner.

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