1749. Maximum Absolute Sum of Any Subarray

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 (Ruby)

1. Prefix Sum

# @param {Integer[]} nums
# @return {Integer}
def max_absolute_sum(nums)
  sum = 0
  max_sum = 0
  min_sum = 0
  ret = 0

  nums.each do |x|
    sum += x
    max_sum = [max_sum, sum].max
    min_sum = [min_sum, sum].min
    ret = [ret, (sum - max_sum).abs, (sum - min_sum).abs].max
  end

  ret
end

Solutions (Rust)

1. Prefix Sum

impl Solution {
    pub fn max_absolute_sum(nums: Vec<i32>) -> i32 {
        let mut sum = 0;
        let mut max_sum = 0;
        let mut min_sum = 0;
        let mut ret = 0;

        for x in nums {
            sum += x;
            max_sum = max_sum.max(sum);
            min_sum = min_sum.min(sum);
            ret = ret.max((sum - max_sum).abs()).max((sum - min_sum).abs());
        }

        ret
    }
}