CF1242B 0-1 MST

Ujan has a lot of useless stuff in his drawers, a considerable part of which are his math notebooks: it is time to sort them out. This time he found an old dusty graph theory notebook with a description of a graph. It is an undirected weighted graph on $ n $ vertices. It is a complete graph: each pair of vertices is connected by an edge. The weight of each edge is either $ 0 $ or $ 1 $ ; exactly $ m $ edges have weight $ 1 $ , and all others have weight $ 0 $ . Since Ujan doesn't really want to organize his notes, he decided to find the weight of the minimum spanning tree of the graph. (The weight of a spanning tree is the sum of all its edges.) Can you find the answer for Ujan so he stops procrastinating?

N/A

N/A

The graph from the first sample is shown below. Dashed edges have weight $ 0 $ , other edges have weight $ 1 $ . One of the minimum spanning trees is highlighted in orange and has total weight $ 2 $ . In the second sample, all edges have weight $ 0 $ so any spanning tree has total weight $ 0 $ .