Jumped straight to simulating all three starting choices and got something working, but it was O(N^2) and they asked me to do better.
First, clarify the rules and edge cases (e.g., tie elimination, winner stays) to ensure correct understanding. Then, model the process as a state machine where the current opponent is determined by simulating matches, and use dynamic programming to compute the minimum hand changes needed to defeat the current opponent and all subsequent players. Finally, discuss time and space complexity and potential optimizations.
Pro tip: Mention that you would test with small cases and edge cases (e.g., all ties, no ties) to validate the DP transitions, and emphasize that the key is to track the minimum changes up to each player while considering the current hand.
Ask questions to confirm: ties eliminate both players and the next pair starts fresh; winner stays and faces the next player; you can change hand only between matches; you need to defeat the player who reaches you and all after them.
Define DP state as the minimum hand changes needed to defeat the current opponent and all subsequent players, given the current hand. Simulate the queue to determine who the current opponent is based on previous outcomes.
For each possible hand (rock, paper, scissors), compute the outcome against the current opponent. If you win, you stay and face the next player; if you lose, you are eliminated and the next player faces the opponent. Use DP to minimize changes.
Implement the DP iteratively from the end of the queue backwards, or use memoization. Optimize by noting that only three hands are possible, so state space is small. Discuss time and space complexity.
Walk through small examples (e.g., N=1, N=2) and edge cases (e.g., all ties, no ties) to ensure the DP correctly handles tie eliminations and winner progression.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.