You are to write a program that receives an unweighted undirected graph and writes all its vertices in
order of increasing distance from given vertex S.
Distance between vertices A and B is the length of the shortest path from A to B.
If there are several vertices such that their distances to S are equal,
they may be printed in arbitrary order.
Input file format
Input file contains three integers N, M and S, where M is the number of edges,
S is the starting vertex.
Vertices are numbered with integer numbers from 1 to N.
Each of next M lines contains a pair of integers — numbers of vertices connected by an edge.
Output file format
Output file must contain sequence of vertex numbers sorted by increasing distance from S.
If some vertex is not reachable from S, output a single number −1.
You are to write a program that performs a topological sorting of a directed graph.
Graph contains N vertices, numbered with integers from 1 to N, and M edges.
In other words, given a partial order on numbers from 1 to N,
your program must produce some linear order on these numbers
which does not conflict with the given partial order.
Input file format
Input file contains two integers N and M, followed by M pairs of integers.
Integers in each pair are different, and represent starting and ending vertex of a graph edge.
These pairs may also be considered comparisons where the first number precedes
the second one.
Output file format
Output file must contain a permutation of integers from 1 to N —
numbers of vertices sorted in topological order.
(That is, representing a linear order.)
If ordering is not possible, output file must contain a single number −1.
You are to write a program that receives a connected undirected graph and finds
all its articulation points, which are the vertices that, if removed,
leave disconnected graph.
Input file format
Input file contains two integers N and M.
Vertices are numbered with integer numbers from 1 to N.
M is the number of edges.
Each of next M lines contain pair of integers — numbers of vertices
connected by an edge. There are no pairs of equal numbers.
Output file format
Output file must contain integer representing a quantity of articulation
points, followed by numbers of corresponding vertices in arbitrary order.
You are to write a program that receives a weighted directed graph and finds
distances from source vertex S to all other vertices. Distance from S to
some vertex W is the minimal length of path going from S to W.
Length of path is the sum of weights of its edges.
Vertices are numbered with integers from 1 to N.
Input file format
First line of input file contains three integers NM and S,
where M is the number of edges. Next M lines contain three
integers each —
starting vertex number, ending vertex number and weight of some edge respectively.
All weights are positive.
There is at most one edge connecting two vertices in every direction.
Output file format
Output file must contain N integers — distances from
source vertex to all vertices.
If some vertices are not reachable from S, corresponding numbers must be −1.
Constraints
1 ≤ N ≤ 1000.
All weights are less or equal than 1000.
You are to write a program that finds shortest distances from vertex S
to all other vertices in a given directed weighted graph.
Graph consists of N vertices, numbered from 1 to N, and M edges.
Input file format
Input file contains two integers NMS, followed my M triplets of integers
ui vi wi — starting vertex, ending vertex and weight or the edge.
There is at most one edge connecting any two vertices in every direction. There are no cycles of negative weight.
Output file format
Output file must contain a vector of N integers — distances from vertex S to other vertices.
The distance from any vertex to itself is considered to be 0.
If some vertex is not reachable from S, corresponding cell of the vector must contain empty space.
Constraints
0 ≤ N, M ≤ 1000.
All weights are less than 1000 by absolute value.
You are to write a program that finds shortest distances between all pairs
of vertices in a directed weighted graph.
Graph consists of N vertices, numbered from 1 to N, and M edges.
Input file format
Input file contains two integers N and M, followed my M triplets of integers
ui vi wi — starting vertex, ending vertex and weight or the edge.
There is at most one edge connecting two vertices in every direction. There are no cycles of negative weight.
Output file format
Output file must contain a matrix of size NxN.
Element in the j-th column of i-th row mush be the shortest distance between
vertices i and j.
The distance from the vertex to itself is considered to be 0.
If some vertex is not reachable from some other,
there must be empty space in corresponding cell of matrix.
Constraints
0 ≤ N ≤ 100.
All weights are less than 1000 by absolute value.
You are to write a program that receives a weighted directed graph and finds
all distances from fixed vertex S to all other vertices. Distance from S to
some vertex W is the minimal length of path going from S to W. Length of path
is the sum of weights of its arcs.
Input file format
Input file contains two integers N, M and S.
Vertices are numbered with integer numbers from 1 to N. S is the number of
source vertex. M is the number of arcs. Each of next M lines contain three
integers — numbers of starting and ending vertices of some arc and its weight
respectively. All weights are positive. There is at most one arc connecting
two vertices in every direction.
Output file format
Output file must contain N numbers. Each I-th number is the distance from
vertex S to vertex I. If some vertices are not reachable from S, corresponding
numbers must be −1.
Constraints
1 ≤ N, M ≤ 100000
All weights are less or equal 1000.
You are to write a program that receives an undirected connected graph and finds its Eulerian cycle.
Input file format
Input file contains two integers N, M.
Vertices are numbered with integer numbers from 1 to N. M is the number of edges. Each of following M lines contains a pair of
vertex numbers, connected by some edge. There is at most one edge connecting two vertices.
Output file format
Output file must contain a sequence of vertex numbers in order of traversal in an Eiler cycle.
If there does not exist any Eiler cycle, output file must contain −1.
You are to write a program that receives a weighted undirected graph and finds length of its shortest spanning tree.
Input file format
Input file contains two integers N, M.
Vertices are numbered with integer numbers from 1 to N. M is the number of edges. Each of next M lines contain three
integers describing an edge — numbers of vertices, connected by an edge and its weight respectively. All weights are
positive. There is at most one edge connecting two vertices.
Output file format
Output file must contain a signle integer number — length of the SST. If it is impossible to construct spanning tree,
output file must contain −1.
You are to write a program that receives a weighted undirected graph and finds length of its shortest spanning tree.
Input file format
Input file contains two integers N, M.
Vertices are numbered with integer numbers from 1 to N. M is the number of edges. Each of next M lines contain three
integers describing an edge — numbers of vertices, connected by an edge and its weight respectively. All weights are
positive. There is at most one edge connecting two vertices.
Output file format
Output file must contain a signle integer number — length of the SST. If it is impossible to construct spanning tree,
output file must contain −1.
Constraints
1 ≤ N, M ≤ 100000
All weights are less or equal 1000.
You are to write a program that receives a directed unweighted graph and finds all vertices of its strong-connected
component, containing given vertex S.
Input file format
Input file contains two integers N, M and S.
Vertices are numbered with integer numbers from 1 to N. M is the number of arcs.
Each of next M lines contain pair of integers — starting and ending vertices of some arc respectively.
There is at most one arc connecting two vertices in every direction.
Output file format
Output file must contain integer number T — amount of vertices in strong-connected component. After that, there must
be T integer numbers in ascending order — vertices of compontent themselves.
For a given undirected graph with N vertices and M edges
you need to figure out whether the graph is bipartite or no.
NOTE. A graph is called bipartite if it's possible
to split its vertices into two non-empty sets so that there is no edges
between any two vertices from the same set.
Input file format
Input file contains integers NM, then M
pairs of integers aibi describing the edges of the graph.
Output file format
Output BIPARTITE if the graph is bipartite or NO if it is not.
