Problem 1: Split and Sort Array

Description

You are given an array A of N integers. You can split the array into two non-empty parts, left and right, sort the elements in each part independently and join them back together.

For example, given array A = [1, 3, 2, 4], you can split it in the following three ways:

• left = [1], right = [3, 2, 4]. Sorting the elements and joining the parts back together results in the array:
  [1, 2, 3, 4].
• left = [1, 3], right = [2, 4].
  Resulting sorted and rejoined array:
  [1, 3, 2, 4].
• left = [1, 3, 2], right = [4].
  Resulting sorted and rejoined array:
  [1, 2, 3, 4].

Your task is to find the number of ways of splitting the array into two parts such that, after sorting the two parts and rejoining them into a single array, the resulting array will be sorted in non-decreasing order.

For the array shown above, the answer is 2: the first and third splits result in a sorted array.

Function Signature

class Solution {
    public int solution(int[] A);
}

Given an array A of length N, returns the number of different ways of obtaining a sorted array by applying the procedure described above.

Examples

1. Given A = [1, 3, 2, 4], the function should return 2, as explained above.
2. Given A = [3, 2, 10, 9], the function should return 1.
   The successful split is [3, 2], [10, 9]. After sorting and rejoining the parts you will receive [2, 3, 9, 10].
3. Given A = [5, 5, 5], the function should return 2.
   The splits that result in a sorted array are:
   • left = [5], right = [5, 5]
   • left = [5, 5], right = [5]
4. Given A = [3, 1, 2], the function should return 0.
   There are no splits that would result in a sorted array.

Constraints

• N is an integer within the range [2, 100,000]
• Each element of array A is an integer within the range [1, 1,000,000,000]

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Problem 2: Minimize Absolute Sum

Description

There is an array A consisting of N integers. Choose at most one element to multiply by -1 in order to obtain an array whose sum of elements is as close to 0 as possible. That is, find the sum with the minimum absolute value.

Function Signature

int solution(vector<int> &A);

Given an array A, returns the minimum absolute value of the sum of A that can be obtained.

Examples

1. For A = [1, 3, 2, 5], after multiplying the last element by -1, A will be equal to [1, 3, 2, -5].
   Its sum is 1. It is not possible to obtain any sum closer to 0. The function should return 1.
2. For A = [-4, 0, -3, -3], we can multiply -4 by -1 and therefore obtain A = [4, 0, -3, -3].
   Its sum is -2. The function should return 2.
3. Assume that A = [4, -3, 5, -7].
   Its sum is -1. There is no possible move that could improve this result.
   The function should return 1.
4. Assume that A = [-15, 18, -1, -1, 10, -22].
   It is optimal to change -1 to 1. The function should return 9.

Constraints

• N is an integer within the range [1..100,000]
• Each element of array A is an integer within the range [-1,000..1,000]

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