LeetCode 1690: Stone Game VII Solution

Master LeetCode problem 1690 (Stone Game VII), a medium challenge, with our optimized solutions in Java, C++, and Python. Explore detailed explanations, test your code in our interactive editor, and prepare for coding interviews.

1690. Stone Game VII

Medium

Array Math Dynamic Programming Game Theory

Problem Explanation

Explanation:

To solve this problem, we can use dynamic programming. We can define a dp array where dp[i][j] represents the maximum score difference between Alice and Bob when considering stones from index i to index j.

At each step, we need to consider two scenarios:

If Alice picks the left stone, the score difference will be the value of the left stone minus the score difference of the remaining stones after Bob's turn.
If Alice picks the right stone, the score difference will be the value of the right stone minus the score difference of the remaining stones after Bob's turn.

We fill the dp array from bottom-up, starting with stones of length 2 up to length n. Finally, the answer will be stored in dp[0][n-1].

Time Complexity:

The time complexity of this approach is O(n^2) where n is the number of stones.

Space Complexity:

The space complexity is O(n^2) for storing the dp array.

Solution Code

class Solution {
    public int stoneGameVII(int[] stones) {
        int n = stones.length;
        int[][] dp = new int[n][n];
        
        for (int len = 2; len <= n; len++) {
            for (int i = 0; i <= n - len; i++) {
                int j = i + len - 1;
                dp[i][j] = Math.max(stones[i] - dp[i + 1][j], stones[j] - dp[i][j - 1]);
            }
        }
        
        return dp[0][n - 1];
    }
}

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