The IOITC is an informatics training camp in which qualifying candidates from the Indian Computing Olympiad participate. In this note, I will discuss the problems encountered by the participants.

The problems may not be all original, although the TST problems and the APIO problems, definitely are. Please do not be discouraged to solve the problems in your own way; my description of them may not be accurate and only serves an illustrative purpose.

Advanced Applications of Depth First Search

• Given a graph, check if there exists a pair of vertices connected by three vertex disjoint simple paths
• Given a graph, and two vertices on it, check if there exists a simple path connecting them consisting of an odd number of edges

Warmup Problems

• Homogeneous Maintain a multiset supporting fast checking if it contains multiple kinds of items or an item twice
• Password Dynamic Programming - Generating strings satisfying constraints

Practice Problems

• Circles Computational Geometry - Projecting overlapping circles into a discretized grid
• Hill Numbers Dynamic Programming - Enumerating numeric strings satisfying a certain constraint on their digits
• Caves and Mines Trees - Finding and adjusting the weight of a node to make sure all its children satisfy a certain constraint
• Electronic Pollution Determining if a set of simultaneous equations allow solving a given equation
• Nice Inversions Minimizing inversions on ordered pairs
• Racing Gems Maximum Increasing Subsequence - Finding a path that allows maximum accumulation of points along a grid
• Mind Craft Modified Dijkstra - Minimum Cost reaching a vertex based on a dependency list
• Lexicographic Toposort Add edges to a Directed Acyclic Graph to maximize an objective function regarding its topological sort
• Tree Orientation Centroid Decomposition - Direct a given tree to maximize the number of pairs of vertices which can be reached from one to the other

Asian Pacific Informatics Olympiad Problems

• Boats Dynamic Programming - Enumerating sequences satisfying constraints
• Fireworks Trees - Minimal Cost modification of edges of a tree to ensure that all paths from the root to the leaves are equal
• Gap Designing a function to find the maximum gap between consecutive elements of an array not directly accessible

Team Selection Test Problems