Problem Description
Alice and Bob are playing a game with piles of stones, where each stone has an associated integer value given in the array stoneValue. They take turns picking 1, 2, or 3 stones from the start of the row of stones. The player with the highest score at the end wins, assuming both play optimally. Your task is to determine if Alice will win, Bob will win, or if the game will end in a tie.
Key Insights
- Both players aim to maximize their scores while minimizing the opponent's score.
- Players can take 1 to 3 stones on their turn, leading to different strategic choices.
- Using a dynamic programming approach can help track the best possible outcomes for each player as stones are taken.
Space and Time Complexity
Time Complexity: O(n)
Space Complexity: O(n)
Solution
The solution to this problem involves using dynamic programming (DP) to keep track of the maximum score difference each player can achieve starting from each position in the stoneValue array. We will define a DP array where dp[i] represents the maximum score difference Alice can achieve over Bob starting from the i-th stone. The approach iteratively calculates the best possible outcome for Alice by considering taking 1, 2, or 3 stones and updating the DP array accordingly.