How should I practice Maximize the Chance of Selecting the Best Candidate?

Start by reading the full statement, solve the visible examples, then compare the pattern against related Google onsite interview problems in FastPrep.

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Maximize the Chance of Selecting the Best Candidate

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Problem statement

A ranking service returns the topCount best candidates, but not their internal order. You may choose any subset of at least two returned candidates and call a second service once; it identifies the worst candidate in that subset.

After discarding the identified worst candidate, choose one of the remaining subset members uniformly at random. Return the maximum possible probability of selecting the overall best candidate as a reduced fraction [numerator, denominator].

Function

maxSuccessFraction(topCount: int) → int[]

Examples

Example 1

topCount = 4return = [1,2]

Choose any two candidates. The best candidate is in that pair with probability 2/4, and the worst-selector then leaves it as the only choice.

Example 2

topCount = 5return = [2,5]

A two-candidate subset succeeds with probability 2/5.

Constraints

2 <= topCount <= 1000000000.
All returned candidates are distinct and have a strict total ranking.
The subset is chosen without knowing the internal ranking.

Source note: Author-written prompt excerpt retained for source fidelity.