Shortest path from source to every other node with skip some(W) edges

I have read one answer on Quora (https://www.quora.com/How-do-I-find-shortest-path-with-the-ability-to-skip-some-edges ) using modified Dijkstra algorithm but can't figure out how to code it in c++. Any help is appreciated.
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Have you already managed implementing the plain Dijkstra algorithm or need you help with that?
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