What is the brute force solution for Minimize the Maximum Adjacent Element Difference?

The brute force approach for Minimize the Maximum Adjacent Element Difference is Brute Force, with O(n²) time complexity and O(1) space complexity. In the brute force approach, we try all possible pairs of positive integers (x, y) to replace the -1 values in the array. For each pair, we compute the maximum absolute difference between adjacent elements and keep track of the minimum of these maximum differences. The optimal Optimal Solution approach improves this to O(n log(maxValue)).

What algorithm or data structure is used to solve Minimize the Maximum Adjacent Element Difference?

Minimize the Maximum Adjacent Element Difference uses the following concepts: Array, Binary Search, Greedy. The recommended patterns to study are: Binary Search, Greedy Algorithms.

What are the interview tips for Minimize the Maximum Adjacent Element Difference?

Always start with a brute-force solution to understand the problem better before optimizing. Think about how you can use binary search to narrow down the possible answers efficiently. Be prepared to explain your thought process clearly, especially when transitioning from brute force to optimal solutions.

What are common mistakes when solving Minimize the Maximum Adjacent Element Difference?

Students often try to brute-force all possible values for x and y without realizing the potential of binary search. Not considering edge cases where all elements are -1 or where known values are very close together.

#3357

Minimize the Maximum Adjacent Element Difference

Hard

ArrayBinary SearchGreedyBinary SearchGreedy Algorithms

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

💡

Intuition

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

In the optimal approach, we leverage binary search to find the minimum possible maximum difference. We can use the known values in the array to guide our search for the best pair (x, y) to fill in the -1s, ensuring we minimize the maximum difference efficiently.

⚙️

Algorithm

4 steps

1Step 1: Identify all known values in the array and their minimum and maximum.
2Step 2: Use binary search on the possible maximum differences, checking if a valid (x, y) can be found for each mid value.
3Step 3: For a given mid value, determine if we can fill -1s with x or y such that no adjacent differences exceed mid.
4Step 4: Adjust the binary search bounds based on whether a valid configuration was found.

solution.py25 lines

1# Full working Python code
2def canPlace(nums, maxDiff):
3    last = None
4    for num in nums:
5        if num != -1:
6            if last is not None and abs(num - last) > maxDiff:
7                return False
8            last = num
9        else:
10            if last is not None:
11                # Fill with last + maxDiff or last - maxDiff
12                last = last + maxDiff
13    return True
14
15
16def minimizeMaxDiff(nums):
17    left, right = 0, 10**9
18    while left < right:
19        mid = (left + right) // 2
20        if canPlace(nums, mid):
21            right = mid
22        else:
23            left = mid + 1
24    return left
25

ℹ

Complexity note: The time complexity is O(n log(maxValue)) because we perform a binary search over the possible maximum differences (up to 10^9) and for each mid value, we check the array in O(n) time.

1Understanding how to replace missing values optimally can drastically reduce the maximum difference between adjacent elements.
2Binary search is a powerful technique for minimizing or maximizing a value under certain constraints.

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