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Introduction:

In today’s blog post, we’ll dive into an intriguing array challenge that Alex, a bright student, is facing. He’s in a rush to solve this puzzle before heading to school, and he’s seeking our assistance. The challenge involves an array of integers, and Alex can perform a unique operation on it. Let’s explore the problem, understand the constraints, and find a solution together.

Problem Description:

Alex has been given an array, a1, a2, …, aN, of length N. He can perform a single operation in which he selects two indices, l and r, and reverses the signs of all the elements in the subarray [al, al+1, …, ar]. His goal is to maximize the sum of the array elements and determine the minimum number of operations required to achieve this maximum sum.

Input Format:

The input consists of two lines:

1. The first line contains an integer N, representing the length of the array.
2. The second line contains N space-separated integers, a1, a2, …, an, which are the array elements.

Constraints:

• 1 ≤ N ≤ 2 * 10^5
• -10^9 ≤ ai ≤ 10^9

Output Format:

Print two space-separated integers:

1. The maximum possible sum of integers in the array.
2. The minimum number of operations required to achieve this maximum sum.

Sample Problem and Solution:

Let’s take an example to understand the problem and solution better:

Sample Input:

4
-1 0 -2 -1

Sample Output:

4 1

Explanation:

To maximize the sum, we should select indices l = 0 and r = 3. After one operation, the array becomes: [1, 0, 2, 1]. The sum of the array elements is 1 + 0 + 2 + 1 = 4. Therefore, the maximum sum is 4, and the minimum number of operations required to achieve this sum is 1.

SOLUTION USING PYTHON:

n = int(input().strip())
arr = list(map(int, input().strip().split()))

# Initialize variables
max_sum = 0
operations = 0

for num in arr:
    max_sum += abs(num)  # Calculate the maximum sum

# Count the number of negative elements in the array
negative_count = sum(1 for num in arr if num < 0)

# If there are negative numbers, we need to perform operations to make them all positive
if negative_count % 2 != 0:
    # Find the minimum absolute value in the array
    min_abs = min(abs(num) for num in arr)
    # Subtract twice the minimum absolute value from the maximum sum
    max_sum -= 2 * min_abs

# Output the maximum sum and the number of operations
print(max_sum, 1 if negative_count % 2 != 0 else 0)

The above code passed only one Test cases.

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