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# Graphs
## Problem 1
`bipartite.cc` (C++17) takes an natural number `n` of edges and `n` lines
of pairs of connected vertices from stdin and print either `yes` or `no` to
stdout if the given graph is or is not bipartite respectively.
## Problem 2
`adjmat2edges.cc` takes an natural number `n` and a `n`-by-`n` adjacent matrix
of natural numbers from stdin and print triplets (`u`, `v`, `m`) separated by
spaces to stdout, where `u`, `v` are vertices and `m > 0` is the number of edges
connecting these two.
## Problem 3
`incidentmat2edges.cc` take 2 natural numbers `v`, `e` and a `v`-by-`e`
incidental matrix from stdin and print each edge along with number of its
appearance to stdout, e.g.
### Input
2 2
1 1
1 1
### Output
0 1 2
## Problem 4
`dijkstra.cc` (C++17) takes a natural number `n` of edges, 2 positive numbers
`s` and `e` (starting and ending of path), then `n` pairs of connected vertices
(both in `1..1023`) and the edge's weight. The output to stdout is the path
and the length, e.g.
### Input
9 1 6
1 2 4
1 3 2
2 3 1
2 4 5
3 5 10
3 4 8
4 5 2
4 6 6
5 6 3'
### Output
1 3 2 4 5 6 (length of 13)
## Problem 5
`connected.cc` (C++17) takes a natural number `n` and `n` pairs of connected
vertices from stdin and print the number of connected components of the given
undirected graph to stdout, e.g.
### Input
3
1 2
3 4
4 5
### Output
2
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