Step Traversing a Tree
POI II Stage 3 Problem 2Step Traversing a TreeA graph is a pair (V, E), where V is a finite set of elements called vertices of the graph, and E is a subset of the set of all unordered pairs of distinct vertices. The elements of the set E are called edges of the graph. If for each pair of distinct vertices u, v there exists exactly one sequence of distinct vertices w0, w1, ..., wk, such that w0 = u, wk = v and the pairs {wi, wi + 1} are in E, for i = 0, ..., k - 1, then the graph is called a tree. We say that the distance between the vertices u and v in the tree is k. It is known that a tree of n vertices has exactly n - 1 edges. A tree T whose vertices are numbered from 1 to n can be unambiguously described by giving the number of its vertices n, and an appropriate sequence of n - 1 pairs of positive integers describing its edges. Any permutation of vertices - i.e. a sequence in which each vertex appears exactly once - is called a traversing order of a tree. If the distance of each two consecutive vertices in some order of the tree T is at most c, then we say that it is a traversing order of the tree with step c. It is known that for each tree its traversing order with step 3 can be found. ExampleThe picture shows a tree of 7 vertices. The vertices are represented by black dots, and edges by line segments joining the dots.
This tree can be traversed with step 3 by visiting its vertices in the following order: 7 2 3 5 6 4 1. TaskWrite a program that:
Input
OutputIn the successive lines of the file DRZ.OUT one should write the numbers of the successive vertices in a traversing order of the tree with step 3 - each number should be written in a separate line.ExampleThe following file DRZ.IN is a correct description of the tree presented in the picture:7 1 2 2 3 2 4 4 5 5 6 1 7The following file DRZ.OUT is a correct solution: 7 2 3 5 6 4 1SubmitStatistics |