You are given a directed graph G $=($V$,$ E$)$ with positive edge lengths. Please

develop an efficient algorithm by using Dikstra$$s algorithm to return the length of the shortest cycle in the

graph $($if the graph is acyclic, it should say so$)$ and implement it$.$ Your algorithm implementation should

take time at most O$(|$V $|3).$

Your input will be a graph described in a file, e$.$g$.,$testcase$-1.$txt$.$ The format will be as follows.

source vertex : list of destination vertices

v$1$ : dest$1$ wt$11$ dest$2$ wt$12...$

v$2$ : dest$3$ wt$23$ dest$7$ w$27...$

$...$

vN : destN$-1$ wtNN$-1$ destN$-2$ wtNN$-2...$

Your program should be able to accept any input file using a command$-$line argument as follows.

your program.py $$input input graph f ile

Your program should output, $$The length of the shortest cycle is: $val$,$ where val is the length. It

will be $0$ when there are no cycles.

For example, if my input file is as follows.

$0$: $1124$

$1$: $32$

$2$: $31$

$3$: $03$

The output is$,$The length of the shortest cycle is: $6,$ corresponding to the cycle $01$

$->12$

$->33$

$->0.$

For example, if my input file is as follows.

$0$: $11$

$1$: $22$

$2$: $33$

$3$: $1405$

The output is$,$The length of the shortest cycle is: $9,$ corresponding to the cycle $12$

$->23$

$->34$

$->1.$

For example, if my input file is as follows.

$0$: $11$

$1$: $22$

$2$: $33$

The output is$,$The length of the shortest cycle is: $0,$ since the graph is acyclic.

You must submit the following to receive full credit.

$(1)$ Python or Java script or C$++$ file with comments and structure.

$(2)$ Testcase$($s$)$ on which you validated your program. Each testcase must be a testcase$-$i$.$txt file where

i $=1,2,...,$ n are indices to your testcase files. You MUST include at least one testcase file.

$(3)$ Please make sure you handle corner cases, and gracefully error out when you are provided with in$-$

correct inputs, etc. Program crashes or errors or no outputs will be penalized.

Give the correct answer according to the above requirements and also verify whether it is satisfying all the requirements and testcases