Find a simple cycle in a weighted undirected graph whose length lies in a given user defined range?

This seems like a fundamentally algorithmic problem, rather than an implementation-specific one, so I have provided detailed, high-level pseudocode for the algorithm rather than actual code. Also, I don't know C++. Let me know if any of the syntax/logic is unclear, and I can clarify some more.

It essentially does a DFS, but doesn't stop when it finds the value: it continues searching, and reports all paths to the value (which meet the given distance criterion).

Depth first is fine. You have to abort when.

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