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overlapping ranges with priority

A customer of ours (a leading Italian consumer goods retailer) has asked us to solve the following problem, that occurs quite frequently and that is not trivial to solve efficiently – and that is very interesting to design and fun to blog about!
the problem
Prices of skus (i.e. goods) have validity ranges (time intervals) and can overlap; on an overlapping range, the strongest priority (lower number) wins.…