Unique random number set computation

In one of Quarkslab's projects, we came across the issue of randomizing a large set of integers, described as a list of disjoint intervals. These intervals can be represented as a sorted list of integers couples, like this one: $[1, 4], [10, 15], [17, 19], \ldots$. The idea is to randomly and uniquely select numbers across these intervals, giving a shuffled list of numbers that belong to them. For instance, $[1,10,18,4,3,11,15,17,19,12,14,13,2]$ is a possible output. Moreover, each possible permutation of the integers set should have equal probability of appearance. If you're just interested in the final library that "do the job", go directly to the implementation section to download the leeloo C++ open-source library on Github !

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