This is a blog on the $$$k$$$ shortest paths problem, and a neat algorithm by David Eppstein that can solve it very fast. You can find the original paper "Finding the $$$k$$$ Shortest Paths" here.
Given an edge-weighted directed graph $$$G$$$, the problem asks us to find the lengths of the $$$k$$$ shortest paths from a fixed vertex $$$s$$$ to a fixed vertex $$$t$$$.
This a very specific problem, and unlikely to show up in any programming contest. However, the ideas used to solve this may be useful in solving other problems.