How do you solve Minimum Stability Factor of Array on LeetCode?

Minimum Stability Factor of Array (LeetCode #3605) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n log n) time complexity and O(1) space complexity. Key insight: Stable subarrays require HCF >= 2.

What is the time complexity of Minimum Stability Factor of Array?

The optimal solution for Minimum Stability Factor of Array runs in O(n log n) time and uses O(1) space. Binary search reduces the problem size logarithmically, while GCD checks are linear.

What is the brute force solution for Minimum Stability Factor of Array?

The brute force approach for Minimum Stability Factor of Array is Brute Force, with O(n²) time complexity and O(1) space complexity. Check all possible subarrays and calculate their HCF. Modify elements as needed to maximize the length of stable subarrays. The optimal Optimal Solution approach improves this to O(n log n).

What are the interview tips for Minimum Stability Factor of Array?

Clarify the definition of stability. Discuss potential edge cases. Explain your thought process clearly.

What are common mistakes when solving Minimum Stability Factor of Array?

Overlooking single-element stability. Miscalculating GCD for larger subarrays.

#3605

Minimum Stability Factor of Array

Hard

ArrayMathBinary SearchGreedySegment TreeNumber TheoryHash MapArray

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

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Intuition

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

Use binary search to find the maximum length of stable subarrays, leveraging fast GCD queries to determine stability efficiently.

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Algorithm

3 steps

1Step 1: Binary search for the maximum length of stable subarrays (k).
2Step 2: For each k, check if it's possible to achieve stability with at most maxC modifications using a sliding window approach.
3Step 3: Use a segment tree or similar structure to efficiently compute GCD over subarray ranges.

solution.py13 lines

1def min_stability_factor(nums, maxC):
2    def canAchieve(k):
3        count = 0
4        for i in range(len(nums) - k + 1):
5            if gcd(*nums[i:i+k]) < 2:
6                count += 1
7        return count <= maxC
8    left, right = 1, len(nums)
9    while left < right:
10        mid = (left + right) // 2
11        if canAchieve(mid): right = mid
12        else: left = mid + 1
13    return left

ℹ

Complexity note: Binary search reduces the problem size logarithmically, while GCD checks are linear.

1Stable subarrays require HCF >= 2.
2Modifications can strategically increase stability.

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