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2708. Maximum Strength of a Group

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You are given a 0-indexed integer array nums representing the score of students in an exam. The teacher would like to form one non-empty group of students with maximal strength, where the strength of a group of students of indices i0, i1, i2, ... , ik is defined as nums[i0] * nums[i1] * nums[i2] * ... * nums[ik​].

Return the maximum strength of a group the teacher can create.

 

Example 1:

Input: nums = [3,-1,-5,2,5,-9]
Output: 1350
Explanation: One way to form a group of maximal strength is to group the students at indices [0,2,3,4,5]. Their strength is 3 * (-5) * 2 * 5 * (-9) = 1350, which we can show is optimal.

Example 2:

Input: nums = [-4,-5,-4]
Output: 20
Explanation: Group the students at indices [0, 1] . Then, we’ll have a resulting strength of 20. We cannot achieve greater strength.

 

Constraints:

  • 1 <= nums.length <= 13
  • -9 <= nums[i] <= 9
ArrayDynamic ProgrammingBacktrackingGreedyBit ManipulationSortingEnumeration

Hints

Hint 1
Try to generate all pairs of subsets and check which group provides maximal strength.
Hint 2
It can also be solved in O(NlogN) by sorting the array and using all positive integers.
Hint 3
Use negative integers only in pairs such that their product becomes positive.