## Dijkstra in the NetworkProblem #84 |

*Note: to start work on this task you need to solve Graph Generator to generate input data.*

**Dijkstra's algorithms** solves very popular task - it allows to find the sortest paths from the given node of
a graph to all other nodes.

Of course this can find applications in logistics etc., but far more common usage is in communication networks.

For example, think of Zig-Bee network, consisting of `N`

modules. These small
devices are capable of determining the shortest route to destination extremely fast, notwithstanding that the
network geometry can change over time - some modules can go offline, some other could be installed on vehicles etc.
So most routers in almost every network technology utilize this method or some derivative
(like A*).

In this task you are to implement Dijkstra's algorithm - the details you can find in the corresponding Wikipedia article.

The simplest form (without min-priority queue) would be sufficient.

The graph is described the same way as in Graph Generator problem - by specifying the number of vertices and the seed for randomizer.

For example, if we use the same graph with `10`

nodes and initialize random generator with the same seed `0`

and will
run the Dijkstra's algorithm starting from node `1`

, we'll get the following paths to each of destinations:

```
dest. path length
1 1 0
2 1-2 1
3 1-2-3 2
4 1-2-4 2
5 1-2-4-5 5
6 1-2-4-6 9
7 1-2-4-8-7 4
8 1-2-4-8 3
9 1-2-4-6-9 16
10 1-10 3
```

The tree of these paths is marked with green lines in the picture above.

**Input data** will contain three numbers `N`

- the number of nodes, `X0`

- seed for random generator and `S`

the
index of starting vertex (from where we are to search for paths to others).

**Answer** should contain the route length to each vertex in the graph.

Example:

```
input data:
10 0 1
answer:
0 1 2 2 5 9 4 3 16 3
```

*Attention: the length of the answer will be several kilobytes long - not very much, so it would give you no problem
when copying and pasting it - but take care not to truncate it accidentally.*

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