Maybe you should say that the partition must have size greater than ceil(log2(x)/2)), since you test this at the test suite. The total number of partitions that a number has may be huge, even if we consider only unique sets (ignoring the order): a sum of binomial coefficients from 1 to the number-1 (where there is only one possible set of ones).
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Next lexicographic - permutation
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Reduce - Map-Reduce
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