I need help working on this C$++$ program revolving around the traveling salesman problem. I can't send the whole program so I'll send the part im supposed to work on$.$ We are only supposed to work on the TSP function.

double TSP$($const std::vector &edges, unsigned int n$\_$vertices$)\{$

$/*$ IMPLEMENT THIS FUNCTION $*/$

double min$\_$cost $=$ std::numeric$\_$limits::infinity$()$;

return min$\_$cost;

$\}$

vertex$\_$t get$\_$source$($const weighted$\_$edge$\_$t &edg$)\{$

return std::get$<0>($edg$)$;

$\}$

vertex$\_$t get$\_$destination$($const weighted$\_$edge$\_$t &edg$)\{$

return std::get$<1>($edg$)$;

$\}$

vertex$\_$t get$\_$weight$($const weighted$\_$edge$\_$t &edg$)\{$

return std::get$<2>($edg$)$;

$\}$

unsigned int get$\_$vertex$\_$count$($const std::vector &edges$)\{$

unsigned int n$\_$vertices $=0$;

if$(!$edges.empty$())\{$

std::set vertex$\_$set;

$/*$ add the source vertices to vertex$\_$set $*/$

std::transform$($

edges.begin$(),$

edges.end$(),$

std::inserter$($vertex$\_$set, vertex$\_$set.end$()),$

get$\_$source

$)$;

$/*$ add the destination vertices to vertex$\_$set $*/$

std::transform$($

edges.begin$(),$

edges.end$(),$

std::inserter$($vertex$\_$set, vertex$\_$set.end$()),$

get$\_$destination

$)$;

$/*$ get the largest vertex from vertex$\_$set and add $1*/$

n$\_$vertices $=*$std::max$\_$element$($vertex$\_$set.begin$(),$ vertex$\_$set.end$())+1$;

$\}$

return n$\_$vertices;

$\}$

std::vector read$\_$graph$($const std::string &filename$)\{$

std::vector edges;

std::ifstream file$($filename$)$;

if$($file$)\{$

$/*$ read edges into a set to remove duplicates $*/$

std::set edge$\_$set;

vertex$\_$t src$,$ dst;

double wt;

while$($file $>>$ src && file $>>$ dst && file $>>$ wt$)\{$

edge$\_$set.insert$($ weighted$\_$edge$\_$t$($src$,$dst$,$wt$))$;

$\}$

$/*$ check if there was an error reading in the file $*/$

if$($file$.$bad$())\{//$ i$/$o error

std::ostringstream oss;

oss $<<$ filename $<<"$: $"<<$ strerror$($errno$)$;

throw std::runtime$\_$error$($oss$.$str$())$;

$\}$

else if$(($file$.$fail$()$ && $!$file.eof$()))\{//$ conversion error

std::ostringstream oss;

oss $<<$ filename $<<"$: error reading file";

throw std::runtime$\_$error$($oss$.$str$())$;

$\}$

$/*$ copy the edges read to the edges vector $*/$

std::copy$($edge$\_$set.begin$(),$ edge$\_$set.end$(),$ std::back$\_$inserter$($edges$))$;

$\}$

else $\{//$ error opening file

std::ostringstream oss;

oss $<<$ filename $<<"$: $"<<$ strerror$($errno$)$;

throw std::runtime$\_$error$($oss$.$str$())$;

$\}$

if$($edges$.$empty$())\{$

std::ostringstream oss;

oss $<<$ filename $<<"$: file does not contain any edges";

throw std::runtime$\_$error$($oss$.$str$())$;

$\}$

return edges;

$\}$

void usage$($int argc, char $*$argv$[])\{$

if$($argc $!=2)\{$

std::cerr $<<$ "Invalid number of command line arguments." $<<$ std::endl $<<$ std::endl;

$\}$

std::cout $<<$ "usage: $"$;

std::cout $<<$ argv$[0]<<"$ infile" $<<$ std::endl;

std::cout $<<"$ infile $-$ file containing a list of edges" $<<$ std::endl $<<$ std::endl;

std::cout $<<"$It is assumed that each line of contains an edge of the" $<."<<$ std::endl;

$\}$

int main$($int argc, char $*$argv$[])\{$

if$($argc $!=2)\{$

usage$($argc$,$ argv$)$;

$\}$

else $\{$

try $\{$

std::vector edges $=$ read$\_$graph$($argv$[1])$;

unsigned int n$\_$vertices $=$ get$\_$vertex$\_$count$($edges$)$;

double min$\_$cost $=$ TSP$($edges$,$ n$\_$vertices$)$;

if$($min$\_$cost $==$ std::numeric$\_$limits::infinity$())\{$

std::cout $<<"$No Hamiltonian cycle exists." $<<$ std::endl;

$\}$

else $\{$

std::cout $<<$ min$\_$cost $<<$ std::endl;

$\}$

$\}$

catch $($std::exception &ex$)\{$

std::cerr $<<$ ex$.$what$()<<$ std::endl;

$\}$

$\}$

return $0$;

$\}$