Maximum Absolute Sum of Any Subarray - Practice Coding Problems

Maximum Absolute Sum of Any Subarray - Problem

Given an integer array nums, you need to find the maximum absolute sum of any subarray within it.

The absolute sum of a subarray is the absolute value of the sum of all elements in that subarray. For example, if a subarray sums to -15, its absolute sum is 15. If it sums to 8, its absolute sum is 8.

Your task: Return the maximum possible absolute sum among all possible subarrays (including empty subarrays with sum 0).

Key insight: The maximum absolute sum will be either the maximum positive sum or the absolute value of the minimum negative sum of any subarray.

Input & Output

example_1.py — Basic Case

$ Input: [1, -3, 2, 3, -4]

› Output: 5

💡 Note: The subarray [2, 3] has sum 5, which has the maximum absolute value among all subarrays.

example_2.py — All Negative

$ Input: [-2, -3, -1]

› Output: 1

💡 Note: The subarray [-1] has sum -1, and its absolute value 1 is the maximum absolute sum. We could also choose empty subarray with sum 0, but 1 > 0.

example_3.py — Single Element

$ Input: [2]

› Output: 2

💡 Note: The only non-empty subarray is [2] with sum 2, so the maximum absolute sum is 2.

Constraints

1 ≤ nums.length ≤ 10⁴
-10⁴ ≤ nums[i] ≤ 10⁴
Empty subarray is allowed with sum 0

Visualization

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Understanding the Visualization

Track Maximum Heat

Use Kadane's algorithm to find the period with maximum positive temperature change

Track Maximum Cold

Use Kadane's algorithm to find the period with maximum negative temperature change

Compare Extremes

The most extreme period is whichever has the larger absolute temperature change

Key Takeaway

🎯 Key Insight: The maximum absolute sum is either the largest positive sum or the largest negative sum (in absolute terms) - Kadane's algorithm finds both efficiently!

Asked in

a Amazon 45 G Google 38 ⊞ Microsoft 32 f Meta 28

The optimal solution uses Kadane's algorithm twice - once to find the maximum subarray sum and once to find the minimum subarray sum. The answer is the maximum absolute value between these two results. This approach runs in O(n) time and O(1) space, making it highly efficient for the given constraints.

Common Approaches

Approach	Time	Space	Notes
✓ Brute Force (Check All Subarrays)	O(n²)	O(1)	Generate all possible subarrays and find the one with maximum absolute sum
Two-Pass Kadane's Algorithm	O(n)	O(1)	Apply Kadane's algorithm twice - once for maximum sum, once for minimum sum

Brute Force (Check All Subarrays) — Algorithm Steps

Use outer loop for starting index i
Use inner loop for ending index j (from i to end)
Calculate sum of subarray from i to j
Update maximum absolute sum if current absolute sum is larger
Return the maximum absolute sum found

Visualization

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Step-by-Step Walkthrough

Start with first element

Begin checking subarrays starting from index 0

Extend subarray

Add next elements one by one, calculating running sum

Track maximum

Keep track of maximum absolute sum seen so far

Move to next start

Repeat process starting from next index

Code -

solution.c — C

#include <stdio.h>
#include <stdlib.h>
#include <string.h>

int abs_val(int x) {
    return x < 0 ? -x : x;
}

int max(int a, int b) {
    return a > b ? a : b;
}

int maxAbsoluteSum(int* nums, int numsSize) {
    int maxAbsSum = 0;
    
    for (int i = 0; i < numsSize; i++) {
        int currentSum = 0;
        for (int j = i; j < numsSize; j++) {
            currentSum += nums[j];
            maxAbsSum = max(maxAbsSum, abs_val(currentSum));
        }
    }
    
    return maxAbsSum;
}

int main() {
    char input[1000];
    fgets(input, sizeof(input), stdin);
    int nums[1000];
    int count = 0;
    char* token = strtok(input, "[],\n");
    while (token != NULL) {
        nums[count++] = atoi(token);
        token = strtok(NULL, "[],\n");
    }
    printf("%d\n", maxAbsoluteSum(nums, count));
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(n²)

Two nested loops iterate through all possible subarray combinations

⚠ Quadratic Growth

Space Complexity

O(1)

Only using constant extra space for variables

✓ Linear Space

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Smart Actions

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Input & Output

Constraints

Visualization

Related Problems

Common Approaches

Brute Force (Check All Subarrays) — Algorithm Steps

Visualization

Code -

Time & Space Complexity

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