Determine winner in optimal-play card game
Problem Description
Given a row of N cards, each with an integer value (which can be positive, zero, or negative), two players take turns picking a card. In each turn, a player must choose either the leftmost or the rightmost available card. Both players play optimally, aiming to maximize their own total score.
Implement a function winner_score(cards: List[int]) -> int that calculates and returns the maximum possible score difference between the first player and the second player (i.e., first_player_score - second_player_score).
Requirements
- Explain the time and space complexity of your solution.
- Modify the function to also return one optimal sequence of picks (as a list of card indices).
Constraints
1 <= N <= 2000
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Core dilemma
The central engineering conflict is modeling optimal play in a two-player, zero-sum game with perfect information, where each player's decision directly impacts the other's optimal strategy. The challenge lies in formulating a recursive solution that avoids redundant computations and correctly applies the minimax principle to maximize the score difference.
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Determine winner in optimal-play card game
Problem Description
Given a row of N cards, each with an integer value (which can be positive, zero, or negative), two players take turns picking a card. In each turn, a player must choose either the leftmost or the rightmost available card. Both players play optimally, aiming to maximize their own total score.
Implement a function winner_score(cards: List[int]) -> int that calculates and returns the maximum possible score difference between the first player and the second player (i.e., first_player_score - second_player_score).
Requirements
- Explain the time and space complexity of your solution.
- Modify the function to also return one optimal sequence of picks (as a list of card indices).
Constraints
1 <= N <= 2000