# MattMSumner/Shortest-Path

The second of two coding challenges for a job I applied for.
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# Shortest-Path

This was the second of two coding challenges for a job I applied for.

Problem: Shortest Paths

Input File: data.dat

Given a directed graph $G=(V,;E)$, and a source vertex $v_0\inV$, please write a program to output the lengths of the shortest paths between $v_0$ and all other vertices in the graph $G$. We assume the edges in digraph $G$ can have negative costs, provided that the sum of the costs around any cycle in the digraph is positiv. The vertices are labeled from 1 to $n$, if $G$ has $n$ vertices. The data fromats of the input and the output of this problem are arranged as follows.

Input:

Your program must accept the following input data from input file data.dat

1. A positive integer $n$, it stands for the total number vertices of $G$.

2. A source vertex $v_0$ ($v_0\in V$, i.e., it could be any vertex in $G$.)

3. The cost matrix $W$ of $G$. It is arranged by row-wise order as follows.

the first row of cost matrix W (enter) the second row of cost matrix W (enter) ... the last row of cost matrix W (enter)

Output:

The lengths of the shortest paths from v0 to all other vertices $v_i$, the format is ($v_0$ -> $v_i$) = ?

Notes:

1. In the input, we arrange the input data $W(v_i,;v_j)$ = '-', if $(v_i,;v_j)$ is not an edge in $G$, $v_i\ne v_j$, and $W(v_i,;v_j)=0$, if $v_i=v_j$.

2. Your program must be able to accept the multiple set of input data.

Example:

Assume we have the following 5-vertex digraph $G$ and its cost matrix $W$.

If we let $v_0=1$, then your input data must be

5
1
0 2 - - 10
- 0 3 - 7
- - 0 4 -
- - - 0 5
- - 6 - 0


and the output would be

(1 -> 2) = 2
(1 -> 3) = 5
(1 -> 4) = 9
(1 -> 5) = 9