How do you solve Maximum Absolute Sum of Any Subarray on LeetCode?

Maximum Absolute Sum of Any Subarray (LeetCode #1749) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(1) space complexity. Key insight: The maximum absolute sum can be derived from both the maximum and minimum sums of subarrays.

What is the brute force solution for Maximum Absolute Sum of Any Subarray?

The brute force approach for Maximum Absolute Sum of Any Subarray is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach involves checking all possible subarrays and calculating their absolute sums. This is straightforward but inefficient for larger arrays. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Maximum Absolute Sum of Any Subarray?

Maximum Absolute Sum of Any Subarray uses the following concepts: Array, Dynamic Programming. The recommended patterns to study are: Kadane's Algorithm, Dynamic Programming.

What are the interview tips for Maximum Absolute Sum of Any Subarray?

Always clarify whether the problem allows for empty subarrays, as this can affect your approach. Discuss your thought process and the trade-offs of different approaches with the interviewer. Practice explaining your code clearly and concisely, as communication is key in interviews.

What are common mistakes when solving Maximum Absolute Sum of Any Subarray?

Forgetting to consider both maximum and minimum sums when calculating the absolute sum. Not handling empty subarrays correctly, which can lead to incorrect results.

#1749

Maximum Absolute Sum of Any Subarray

Medium

ArrayDynamic ProgrammingKadane's AlgorithmDynamic Programming

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

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Intuition

Time O(n)Space O(1)

The optimal solution leverages a modified version of Kadane's algorithm to find the maximum absolute sum efficiently. Instead of calculating the sum directly, we track both the maximum and minimum sums as we iterate through the array.

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Algorithm

4 steps

1Step 1: Initialize variables to track the maximum and minimum sums as well as the current sum.
2Step 2: Iterate through the array, updating the current sum by adding the current element.
3Step 3: Update the maximum and minimum sums based on the current sum.
4Step 4: The maximum absolute sum is the maximum of the absolute values of the maximum and minimum sums.

solution.py14 lines

1# Full working Python code
2
3def maxAbsoluteSum(nums):
4    max_sum = 0
5    min_sum = 0
6    current_sum = 0
7    for num in nums:
8        current_sum += num
9        max_sum = max(max_sum, current_sum)
10        min_sum = min(min_sum, current_sum)
11    return max(abs(max_sum), abs(min_sum))
12
13# Example usage
14print(maxAbsoluteSum([1, -3, 2, 3, -4]))  # Output: 5

ℹ

Complexity note: The time complexity is O(n) because we only make a single pass through the array. The space complexity is O(1) as we are using a constant amount of space.

1The maximum absolute sum can be derived from both the maximum and minimum sums of subarrays.
2Using a single pass through the array allows us to efficiently track necessary sums.

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