Solution 2 for Scaler Topics Fortnightly Contest - 14

This article is part of the Scaler Topics Fortnightly Contest - 14

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Solution Approach

• The positive elements should be in the same subset to maximize the power. Instead of multiple negative elements in a single subset, they should be in different subsets.
• We can include some negative elements with the subset with positive ones. Including a greater negative part is more beneficial than including a smaller negative element.
• Sort the harmful elements in decreasing order. Brute force over them and pick the best possible power.
• Pseudocode: $l = len(pos)$ $x = sum(pos)$ $y = sum(neg)$ $ans = l * x + y$ $neg.sort(reverse=True)$ for i in neg: $l += 1$ $x += i$ $y -= i$ $ans = max(ans, l * x + y)$

Time Complexity- $O(N * log(N))$

Space Complexity- $O(N)$

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