Yen's algorithm

K shortest path problem have three ideas:

• recurrence method
  based on P(i), recurrent resolve the P(i+1) shortest path.
• direct method
  direct find the shortest path, like delete method.
• synthetic method
  i have no idea yet.

Yen’s algorithm computes single-source K-shortest loopless paths for a graph with non-negative edge cost.
The algorithm was published by Jin Y. Yen in 1971 and employs any shortest path algorithm to find the best path,
then proceeds to find K − 1 deviations of the best path.

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Reference

http://www.coolee.me/yen-k-shortest-path.html
https://en.wikipedia.org/wiki/Yen%27s_algorithm