How do you solve Minimum K to Reduce Array Within Limit on LeetCode?

Minimum K to Reduce Array Within Limit (LeetCode #3824) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n log(max(nums))) time complexity and O(1) space complexity. Key insight: Binary search optimizes the search for k.

What is the time complexity of Minimum K to Reduce Array Within Limit?

The optimal solution for Minimum K to Reduce Array Within Limit runs in O(n log(max(nums))) time and uses O(1) space. Binary search reduces the search space logarithmically while each check takes O(n).

What is the brute force solution for Minimum K to Reduce Array Within Limit?

The brute force approach for Minimum K to Reduce Array Within Limit is Brute Force, with O(n²) time complexity and O(1) space complexity. Try every possible value of k and calculate the number of operations needed for each. This is straightforward but inefficient. The optimal Optimal Solution approach improves this to O(n log(max(nums))).

What algorithm or data structure is used to solve Minimum K to Reduce Array Within Limit?

Minimum K to Reduce Array Within Limit uses the following concepts: Array, Binary Search. The recommended patterns to study are: Binary Search, Greedy.

What are the interview tips for Minimum K to Reduce Array Within Limit?

Explain your thought process clearly. Discuss time and space complexity. Practice binary search problems.

What are common mistakes when solving Minimum K to Reduce Array Within Limit?

Not considering edge cases for k. Miscalculating the number of operations.

#3824

Minimum K to Reduce Array Within Limit

Medium

ArrayBinary SearchBinary SearchGreedy

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

💡

Intuition

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

Use binary search to efficiently find the minimum k that satisfies the condition, leveraging the relationship between k and operations.

⚙️

Algorithm

3 steps

1Step 1: Set low to 1 and high to the maximum value in nums.
2Step 2: Perform binary search: calculate mid and check if nonPositive(nums, mid) <= mid * mid.
3Step 3: Adjust low or high based on the condition until low equals high, which gives the minimum k.

solution.py12 lines

1def nonPositive(nums, k):
2    return sum((num + k - 1) // k for num in nums)
3
4def minK(nums):
5    low, high = 1, max(nums)
6    while low < high:
7        mid = (low + high) // 2
8        if nonPositive(nums, mid) <= mid * mid:
9            high = mid
10        else:
11            low = mid + 1
12    return low

ℹ

Complexity note: Binary search reduces the search space logarithmically while each check takes O(n).

1Binary search optimizes the search for k.
2Understanding operations helps in calculating the required conditions.

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