UVa 12532: Interval Product involves a clever application of segment trees. Abridged problem statement: You are given a list of integers and a number of queries. Each query can either change one integer in the list, or ask for the sign of the product between a range of indicies. Print out a string with the answers to all the queries concatenated together.
UVa 793: Network Connections is a good UFDS implementation practice problem.
UVa 11503: Virtual Friends simplified problem statement: Several people are friending each other on social media. Every time two people become friends, print out the current size of their social network.
UVa 10507: Waking up brain simplified problem statement: There are several areas of the brain, each of which is connected to other areas of the brain. All the regions but 3 are “asleep”, but if a region is connected to 3 awake regions for a year, that region wakes up. Given the connections between various parts of the brain and the 3 regions that are initially awake, determine how long the entire brain takes to wake up.