What is the time complexity of Longest Arithmetic Sequence After Changing At Most One Element?

The optimal solution for Longest Arithmetic Sequence After Changing At Most One Element runs in O(n) time and uses O(n) space. Single pass to compute L and R arrays, leading to linear time complexity.

What is the brute force solution for Longest Arithmetic Sequence After Changing At Most One Element?

The brute force approach for Longest Arithmetic Sequence After Changing At Most One Element is Brute Force, with O(n²) time complexity and O(1) space complexity. Check every possible subarray and see if it can be made arithmetic by changing one element. This is straightforward but inefficient. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Longest Arithmetic Sequence After Changing At Most One Element?

Longest Arithmetic Sequence After Changing At Most One Element uses the following concepts: Array, Enumeration. The recommended patterns to study are: Hash Map, Array.

What are the interview tips for Longest Arithmetic Sequence After Changing At Most One Element?

Explain your thought process clearly. Use examples to illustrate your approach. Be prepared to discuss time and space complexities.

What are common mistakes when solving Longest Arithmetic Sequence After Changing At Most One Element?

Not considering edge cases where no change is needed. Overlooking the impact of changing different elements.

#3872

Longest Arithmetic Sequence After Changing At Most One Element

Medium

ArrayEnumerationHash MapArray

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

💡

Intuition

Time O(n)Space O(n)

Use dynamic programming to track the longest arithmetic subsequence lengths while allowing one change. This reduces the need for nested loops.

⚙️

Algorithm

3 steps

1Step 1: Create two arrays L and R to store lengths of arithmetic sequences ending and starting at each index.
2Step 2: Populate L by checking differences and counting lengths, then populate R similarly.
3Step 3: Combine L and R to find the maximum length by considering changing one element.

solution.py13 lines

1def longestArithSeqLength(nums):
2    n = len(nums)
3    L = [2] * n
4    R = [2] * n
5    for i in range(1, n):
6        for j in range(i):
7            if nums[i] - nums[j] == nums[j] - nums[j-1]:
8                L[i] = L[j] + 1
9    for i in range(n-2, -1, -1):
10        for j in range(i+1, n):
11            if nums[j] - nums[i] == nums[i+1] - nums[i]:
12                R[i] = R[j] + 1
13    return max(max(L), max(R))

ℹ

Complexity note: Single pass to compute L and R arrays, leading to linear time complexity.

1Changing one element can create a longer arithmetic sequence.
2Dynamic programming can efficiently track subarray lengths.

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