IOI 2013

Given an image (2D grid of RGB pixels), classify it into one of four categories: Class 1: Modern/abstract art (few colors, large uniform regions) Class 2: Paintings with distinct objects (moderate variation) Class 3:...

There is a cave with N doors (numbered 0 to N-1) and N switches (numbered 0 to N-1). Each switch controls exactly one door (a permutation), and each switch has a correct position (0 or 1) that opens its corresponding...

Given a forest (collection of trees) with N nodes and M edges (each with a weight), you can add edges of weight L to connect the trees into a single tree. Minimize the diameter (longest shortest path between any two n...

Given a 2D grid of size R C (up to 10^9 10^9), support two operations: Update (r, c, v): Set the value at cell (r, c) to v. Query (r_1, c_1, r_2, c_2): Return the GCD of all values in the rectangle [r_1, r_2] [c_1, c_...

There are A ``weak'' robots (each with a weight limit X_i) and B ``small'' robots (each with a size limit Y_j). There are T toys, each with weight W_k and size S_k. A weak robot i can pick up toy k if W_k < X_i. A sma...

Given a grid of R rows and C columns (R 5000, C 200), with horizontal edges (within each row) and vertical edges (between consecutive rows), each having a non-negative weight. Support two operations: changeH (r, c, w)...