Could you please run the following codes and interpret the results in R programme by giving some numeric examples $?$ # Define a function to implement the Minimum Violators Algorithm minimum$\_$violators$\_$algorithm $<-$ function$($components$,$ roots, Ts$,$ K$,$ g$)\{$ # Step $1$: Create a singleton cluster for each component clusters $<-$ lapply$($components$,$ function$($comp$)$ list$($components $=$ comp$))$

# Initialize set Q with roots of all clusters except the one containing the final product Q $<-$ setdiff$($roots$,$ tail$($roots$,1))$

# Initialize set r with the root of the final product cluster r $<-$ tail$($roots$,1)$

while $($length$($Q$)>0)\{$ # Step $2$: Find a cluster i in Q with minimal K$($Ci$)/$ g$($Ci$)$ min$\_$ratio $<-$ Inf min$\_$cluster $<-$ NULL

for $($i in Q$)\{$ Ci $<-$ clusters$[[$i$]]$ ratio $<-$ K$($Ci$)/$ g$($Ci$)$

if $($ratio $<$ min$\_$ratio $||($ratio $==$ min$\_$ratio && length$($Ci$components$)<$ length$($min$\_$cluster$components$)))\{$ min$\_$ratio $<-$ ratio min$\_$cluster $<-$ Ci $\}\}$

# Step $3$: Remove i from Q Q $<-$ setdiff$($Q$,$ which$($roots $==$ min$\_$cluster$components$[[1]]))$

# Check the condition K$($Ci$\text{'})/$ g$($Ci$\text{'})>=$ K$($Ci$)/$ g$($Ci$)$ if $($K$($min$\_$cluster$)/$ g$($min$\_$cluster$)>=$ K$($clusters$[[$r$]])/$ g$($clusters$[[$r$]]))\{$ # Add i to r r $<-$ c$($r$,$ min$\_$cluster$components$[[1]])\}$ else $\{$ # Collapse cluster i into cluster r clusters$[[$r$]]$$components $<-$ c$($clusters$[[$r$]]$$components, min$\_$cluster$components$)\}\}$

# Output the optimal clusters optimal$\_$clusters $<-$ lapply$($r$,$ function$($root$)$ clusters$[[$root$]])$ return$($optimal$\_$clusters$)\}$