## 「CodeForces 1198C」 Matching vs Independent Set

You are given a graph with 3⋅𝑛 vertices and 𝑚 edges. You are to find a matching of 𝑛 edges, or an independent set of 𝑛 vertices.

A set of edges is called a matching if no two edges share an endpoint.

A set of vertices is called an independent set if no two vertices are connected with an edge.

## 「CodeForces 1277F」Beautiful Rectangle

You are given 𝑛 integers. You need to choose a subset and put the chosen numbers in a beautiful rectangle (rectangular matrix). Each chosen number should occupy one of its rectangle cells, each cell must be filled with exactly one chosen number. Some of the 𝑛 numbers may not be chosen.

## 「CodeForces1278D&E」Segment Tree & Tests for problem D

As the name of the task implies, you are asked to do some work with segments and trees.

Recall that a tree is a connected undirected graph such that there is exactly one simple path between every pair of its vertices.

You are given 𝑛 segments [𝑙1,𝑟1],[𝑙2,𝑟2],…,[𝑙𝑛,𝑟𝑛], 𝑙𝑖<𝑟𝑖 for every 𝑖. It is guaranteed that all segments' endpoints are integers, and all endpoints are unique — there is no pair of segments such that they start in the same point, end in the same point or one starts in the same point the other one ends.

## 「AtCoder 131E」 Friendships

Does there exist an undirected graph with N vertices satisfying the following conditions?