LeetCode 3449: Maximize the Minimum Game Score Solution

Master LeetCode problem 3449 (Maximize the Minimum Game Score), a hard 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.

3449. Maximize the Minimum Game Score

Hard

Array Binary Search Greedy

Problem Explanation

Explanation

To maximize the minimum game score, we need to find the optimal strategy for making at most m moves to either increase or decrease the index by 1 at each step. The idea is to use binary search to find the maximum possible minimum value in the game score. We can simulate the process of choosing the minimum value for the game score and check if it is possible to achieve that score within m moves.

Define a helper function to check if a given minimum value can be achieved within m moves.
Use binary search to find the maximum possible minimum value that can be achieved.
While performing the binary search, simulate the process of choosing the minimum value and check if it is possible within m moves.

Time complexity: O(n * log(max_score) * log(n)) Space complexity: O(n)

Solution Code

class Solution {
    public int maximizeGameScore(int[] points, int m) {
        int left = 1;
        int right = (int)1e9;
        
        while (left < right) {
            int mid = left + (right - left) / 2;
            if (canAchieveScore(points, m, mid)) {
                left = mid + 1;
            } else {
                right = mid;
            }
        }
        
        return left - 1;
    }
    
    private boolean canAchieveScore(int[] points, int m, int minScore) {
        int n = points.length;
        int moves = 0;
        int sum = 0;
        
        for (int i = 0; i < n; i++) {
            sum += points[i];
            if (sum >= minScore) {
                sum = 0;
                moves++;
            }
        }
        
        return moves >= m;
    }
}

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