1749. Maximum Absolute Sum of Any Subarray

Description

You are given an integer array nums. The absolute sum of a subarray [numsl, numsl+1, ..., numsr-1, numsr] is abs(numsl + numsl+1 + ... + numsr-1 + numsr).

Return the maximum absolute sum of any (possibly empty) subarray of nums.

Note that abs(x) is defined as follows:

• If x is a negative integer, then abs(x) = -x.
• If x is a non-negative integer, then abs(x) = x.

 

Example 1:

Input: nums = [1,-3,2,3,-4]
Output: 5
Explanation: The subarray [2,3] has absolute sum = abs(2+3) = abs(5) = 5.

Example 2:

Input: nums = [2,-5,1,-4,3,-2]
Output: 8
Explanation: The subarray [-5,1,-4] has absolute sum = abs(-5+1-4) = abs(-8) = 8.

 

Constraints:

• 1 <= nums.length <= 105
• -104 <= nums[i] <= 104

 

Solutions

Solution: Dynamic Programming

• Time complexity: O(n)
• Space complexity: O(1)

 

JavaScript

/**
 * @param {number[]} nums
 * @return {number}
 */
const maxAbsoluteSum = function (nums) {
  let maxSum = Number.MIN_SAFE_INTEGER;
  let minSum = Number.MAX_SAFE_INTEGER;
  let result = 0;

  for (const num of nums) {
    maxSum = Math.max(maxSum + num, num);
    minSum = Math.min(minSum + num, num);
    result = Math.max(result, maxSum, Math.abs(minSum));
  }

  return result;
};