Card Flipping Game
What is this problem about?
The Card Flipping Game interview question involves a set of cards, each with a number on the front and a number on the back. You can flip any card. You want to pick a card such that the number on its front does not appear on the back of any card. The goal is to find the minimum such number. This Card Flipping Game coding problem is a logic puzzle involving sets and exclusions.
Why is this asked in interviews?
Google uses this to test a candidate's ability to simplify conditions. It sounds like a game-tree or backtracking problem, but it's actually much simpler. It evaluates if you can identify that any number which appears on both the front and back of the same card can never be the answer, regardless of flips.
Algorithmic pattern used
This problem utilizes the Array, Hash Table interview pattern.
- Identify all "forbidden" numbers: any number x where a card has front == back == x. Store these in a Hash Set.
- Any other number that appears on either the front or back of any card could potentially be on the front while not being on any back (by flipping the other cards appropriately).
- Iterate through all numbers on all cards. If a number is not in the "forbidden" set, it's a candidate.
- Return the minimum candidate.
Example explanation
Cards: Front [1, 2, 4], Back [1, 3, 4]
- Card 0: (1, 1). Number 1 is forbidden.
- Card 1: (2, 3). Numbers 2 and 3 are candidates.
- Card 2: (4, 4). Number 4 is forbidden.
Candidates: {2, 3}. Minimum: 2.
Common mistakes candidates make
- Over-flipping: Trying to simulate all 2^N ways to flip cards.
- Ignoring the back: Only checking if a front number appears on other backs.
- Misunderstanding the rule: Thinking a number is disqualified if it appears on the back of any card. Actually, if it's on the back of a different card, you could just flip that card to make it a front number. Only if it's on both sides of the same card is it truly impossible to hide.
Interview preparation tip
In problems where you can "flip" or "toggle" items to satisfy a condition, look for the "invariants"—things that cannot be changed no matter what you do. Identifying what is impossible often reveals the simple path to the solution.
