After working on my program some more, i've encountered a logic error where the ouput should be $"$No Hamiltonian Cycle exists" but im getting $1.$ How do i change my code to account for if no hamiltonian cycle exists?

Here is the code:

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

$/*$ IMPLEMENT THIS FUNCTION $*/$

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

$//$ Iterate through all permutations of vertices

std::vector permutation$($n$\_$vertices$)$;

for $($vertex$\_$t i $=0$; i $<$ n$\_$vertices; $++$i$)$

permutation$[$i$]=$ i;

do $\{$

double cost $=0\mathrm{.}0$;

$//$ Calculate the cost of the current permutation

for $($size$\_$t i $=0$; i $<$ n$\_$vertices; $++$i$)\{$

vertex$\_$t src $=$ permutation$[$i$]$;

vertex$\_$t dst $=$ permutation$[($i $+1)\%$ n$\_$vertices$]$;

$//$ Find the corresponding edge and add its weight to the total cost

for $($const auto& edge : edges$)\{$

if $($std::get$<0>($edge$)==$ src && std::get$<1>($edge$)==$ dst$)\{$

cost $+=$ std::get$<2>($edge$)$;

break;

$\}$

$\}$

$\}$

$//$ Update the minimum cost if the current permutation has lower cost

if $($cost $<$ min$\_$cost$)$

min$\_$cost $=$ cost;

$\}$ while $($std::next$\_$permutation$($permutation$.$begin$(),$ permutation.end$()))$;

return min$\_$cost;

$\}$

For more context, this is the Traveling Salesman Problem. I think it would be a simple if statement, but I don't know what to check.