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Just to comment a bit on the NP-Completeness suggested by anonymous:
- Marc Serra October 15, 2016You can define a graph where each node represents an array element, and a vertex between two nodes indicates that these two elements can be picked simultaneously. The solution of the problem is then the maximal set of nodes where each node in the set is connected to all other nodes in the set. Finding this set is called the maximum clique problem, which is NP-Complete for a general graph. However, if you follow the rules to determine compatible pairs of array elements the graph you obtain is a comparability graph (See wikipedia). This particular type of graph that has the property that there exists an ordering of the nodes for which, if there is a vertex between i and j and a vertex between j and k (i < j < k) then there is a vertex between i and k. For this specific type of graph the clique problem actually has an efficient solution, which can be calculated by a DFS search.