How do you solve Maximize the Minimum Game Score on LeetCode?

Maximize the Minimum Game Score (LeetCode #3449) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n log(max(points))) time complexity and O(1) space complexity. Key insight: Binary search helps efficiently narrow down possible scores.

What is the time complexity of Maximize the Minimum Game Score?

The optimal solution for Maximize the Minimum Game Score runs in O(n log(max(points))) time and uses O(1) space. The binary search runs in O(log(max(points))) and for each mid, we check the scores in O(n), leading to the overall complexity.

What is the brute force solution for Maximize the Minimum Game Score?

The brute force approach for Maximize the Minimum Game Score is Brute Force, with O(n²) time complexity and O(1) space complexity. Explore all possible moves to calculate game scores and find the minimum score for each configuration. This approach checks every combination, which is inefficient. The optimal Optimal Solution approach improves this to O(n log(max(points))).

What algorithm or data structure is used to solve Maximize the Minimum Game Score?

Maximize the Minimum Game Score uses the following concepts: Array, Binary Search, Greedy. The recommended patterns to study are: Binary Search, Greedy.

What are the interview tips for Maximize the Minimum Game Score?

Explain your thought process clearly. Discuss time and space complexities upfront. Practice similar problems to build confidence.

What are common mistakes when solving Maximize the Minimum Game Score?

Not considering edge cases where m is very small. Overlooking the bounds of the array during index adjustments.

#3449

Maximize the Minimum Game Score

Hard

ArrayBinary SearchGreedyBinary SearchGreedy

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n log(max(points)))
Space	O(1)	O(1)

💡

Intuition

Time O(n log(max(points)))Space O(1)

Use binary search to find the maximum possible minimum score. Fix a score x and check if it's achievable with m moves using a greedy approach.

⚙️

Algorithm

3 steps

1Step 1: Set low = 0 and high = max(points).
2Step 2: Perform binary search: for mid = (low + high) / 2, check if we can achieve mid as the minimum score.
3Step 3: Adjust low or high based on whether mid is achievable, until low meets high.

solution.py18 lines

1def canAchieve(points, m, x):
2    moves = 0
3    for p in points:
4        if p < x:
5            moves += x - p
6        if moves > m:
7            return False
8    return True
9
10def maxMinScore(points, m):
11    low, high = 0, max(points)
12    while low < high:
13        mid = (low + high + 1) // 2
14        if canAchieve(points, m, mid):
15            low = mid
16        else:
17            high = mid - 1
18    return low

ℹ

Complexity note: The binary search runs in O(log(max(points))) and for each mid, we check the scores in O(n), leading to the overall complexity.

1Binary search helps efficiently narrow down possible scores.
2Greedy checking ensures we validate achievable scores.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.