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How to change array elements?

Given an array of 'n' integers. We are allowed to apply sign change operation on all elements. How can we find the minimum possible non-negative array sum efficiently?

  • For example:  Consider this array A= { 2, 1, 3, 4, 2}. Since A can be changed to A' = { -2, -1, -3, 4, 2 },the minimum possible non-negative sum is zero for this array.

  • Answer:

    Same as problem of splitting the array into 2 subarrays such that the difference between the sum of 2 sub-arrays in minimum.

Anonymous at Quora Visit the source

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This is just the http://en.wikipedia.org/wiki/Partition_problem / http://en.wikipedia.org/wiki/Subset_sum_problem in disguise. You have to partition the given numbers (or, more precisely, their absolute values) into two piles that have sums as close to each other as possible. (In our case, the two piles are "numbers that will have the + sign" and "- sign".)

Michal Forišek

You can think about this problem  as two stacks and you try to minimize the difference of their height. This is the offline scheduling problem and it is solvable by a greedy algorithm. Sort the list (max to min) for each object, lay it on the stack with the lowest height code snippet:- http://stackoverflow.com/a/25255629 source:- http://stackoverflow.com/questions/14272380/given-one-can-change-the-sign-of-numbers-find-minimum-sum-of-array

Akib Khan

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