What is your favorite algorithm and why?

My favorite data structure is the splay tree[1] and one of my favorite algorithms is the Boyer-Moore majority vote algorithm[2].

[1] https://en.wikipedia.org/wiki/Splay_tree

[2] http://www.cs.rug.nl/~wim/pub/whh348.pdf

I like Euclidean Algorithm. Solves metric crapton of problems in elementary number theory and basic abstract algebra.

Djikstra shortest path. it's a beautiful design.

BFS and DFS. Simple and quite useful!