* dynamic programming
* tries
* depth/breadth first traversal of a graph
* combinatorics
* graph colouring
* prime generation techniques
These topics are almost guaranteed to crop up every year, and the people who do well in these programming competitions learn all these techniques off by heart. They have their own library and macros which do all this stuff, and when they read the question they instantly see which technique they need to use and boom they're done. You have to remember that these people have been practising this stuff from a very early age, and that in many cases, spending hours and hours becoming good at this is their only way out of a crappy life (Eastern Europeans). However, being good at competitive programming has very little correlation with being a good software engineer (I think there is some analysis done by the likes of Google or Microsoft which proves this, I will try to find the link later).