CF545E Paths and Trees

Little girl Susie accidentally found her elder brother's notebook. She has many things to do, more important than solving problems, but she found this problem too interesting, so she wanted to know its solution and decided to ask you about it. So, the problem statement is as follows. Let's assume that we are given a connected weighted undirected graph $ G=(V,E) $ (here $ V $ is the set of vertices, $ E $ is the set of edges). The shortest-path tree from vertex $ u $ is such graph $ G_{1}=(V,E_{1}) $ that is a tree with the set of edges $ E_{1} $ that is the subset of the set of edges of the initial graph $ E $ , and the lengths of the shortest paths from $ u $ to any vertex to $ G $ and to $ G_{1} $ are the same. You are given a connected weighted undirected graph $ G $ and vertex $ u $ . Your task is to find the shortest-path tree of the given graph from vertex $ u $ , the total weight of whose edges is minimum possible.

N/A

N/A

In the first sample there are two possible shortest path trees: - with edges $ 1–3 $ and $ 2–3 $ (the total weight is $ 3 $ ); - with edges $ 1–2 $ and $ 2–3 $ (the total weight is $ 2 $ ); And, for example, a tree with edges $ 1–2 $ and $ 1–3 $ won't be a shortest path tree for vertex $ 3 $ , because the distance from vertex $ 3 $ to vertex $ 2 $ in this tree equals $ 3 $ , and in the original graph it is $ 1 $ .