How do you solve Maximum Good Subarray Sum on LeetCode?

Maximum Good Subarray Sum (LeetCode #3026) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(n) space complexity. Key insight: Understanding the properties of prefix sums can significantly reduce the time complexity of subarray problems.

What is the brute force solution for Maximum Good Subarray Sum?

The brute force approach for Maximum Good Subarray Sum is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach involves checking every possible subarray to see if it meets the criteria of being 'good'. This means calculating the sum of each subarray and checking the absolute difference between the first and last elements. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Maximum Good Subarray Sum?

Maximum Good Subarray Sum uses the following concepts: Array, Hash Table, Prefix Sum. The recommended patterns to study are: Hash Map, Array.

What are the interview tips for Maximum Good Subarray Sum?

Always clarify the problem statement and constraints before jumping into coding. Think about different approaches and discuss them with the interviewer to show your thought process. Practice dry-running your code with sample inputs to catch potential errors before submitting.

What are common mistakes when solving Maximum Good Subarray Sum?

Not considering edge cases where no good subarray exists. Failing to update the maximum sum correctly when a good subarray is found.

#3026

Maximum Good Subarray Sum

Medium

ArrayHash TablePrefix SumHash 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)

The optimal approach uses a HashMap to store prefix sums, allowing us to quickly check for good subarrays by leveraging the properties of prefix sums and the required difference k.

⚙️

Algorithm

6 steps

1Step 1: Initialize a HashMap to store prefix sums and their corresponding indices.
2Step 2: Initialize a variable to keep track of the maximum sum found.
3Step 3: Iterate through the array, calculating the prefix sum as you go.
4Step 4: For each element, check if the prefix sum minus k or plus k exists in the HashMap.
5Step 5: If it exists, calculate the subarray sum and update the maximum sum if this sum is greater.
6Step 6: Store the current prefix sum in the HashMap.

solution.py12 lines

1def maxGoodSubarraySum(nums, k):
2    prefix_sum = 0
3    max_sum = 0
4    prefix_map = {}
5    for i in range(len(nums)):
6        prefix_sum += nums[i]
7        if (prefix_sum - k) in prefix_map:
8            max_sum = max(max_sum, prefix_sum - prefix_map[prefix_sum - k])
9        if (prefix_sum + k) in prefix_map:
10            max_sum = max(max_sum, prefix_sum - prefix_map[prefix_sum + k])
11        prefix_map[prefix_sum] = prefix_sum
12    return max_sum

ℹ

Complexity note: This complexity is achieved because we only traverse the array once and use a HashMap to store prefix sums, leading to linear time complexity.

1Understanding the properties of prefix sums can significantly reduce the time complexity of subarray problems.
2Using a HashMap allows for quick lookups, which is essential for optimizing the solution.

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