citations - How to cite the original source of an algorithm and a secondary source that provides a clearer description of the algorithm?

I had a situation where for a particular algorithm, it first shows up in a paper [1]. This makes [1] a primary source. I found [1] a bit hard reading when it came to describing the implementation and fine details of the algorithm. But it was good at describing why the algorithm was needed.

I found another work, which was a masters thesis [2]. It included a step by step mathematical working from what was in [1] (and [2] cited [1] appropriately). It helped me a lot. I could have done the mathematical working myself, but didn't.

So I am writing a brief summery of the Algorithm:

The {{Foo}} algorithm allows the {{Bar}} problem to be solved [1]. It is based on the fact that {{Equation}} holds under {{Conditions}} [2]. {{My own explanation of {{Foo}} here}}

Is this correct?

Answer

This is correct only if the source of the first sentence is exclusively [1] and the source of your second sentence is exclusively [2].

That is, if you learn "The {{Foo}} algorithm allows the {{Bar}} problem to be solved" from [1] without having read [2], and "It is based on the fact that {{Equation}} holds under {{Conditions}}" is an original contribution of [2] that is not in [1], then your citation is correct.

Otherwise, you may have to cite [1,2] for the first and/or second sentence as appropriate.