##When N=5
nonlinearBFfive<-read.csv("/Users/uzma/Downloads/Nonlinearoutput/Bruteforce5items.csv",header=TRUE)
nonlinearEPCAfive<-read.csv("/Users/uzma/Downloads/Nonlinearoutput/EPCA5items.csv",header=TRUE)


## When N=10
nonlinearBFten<-read.csv("/Users/uzma/Downloads/Nonlinearoutput/Bruteforce10items.csv",header=TRUE)
nonlinearEPCAten<-read.csv("/Users/uzma/Downloads/Nonlinearoutput/EPCA10items.csv",header=TRUE)

## When N=15
nonlinearBFfifteen<-read.csv("/Users/uzma/Downloads/Nonlinearoutput/Bruteforce15items.csv",header=TRUE)
nonlinearEPCAfifteen<-read.csv("/Users/uzma/Downloads/Nonlinearoutput/EPCA15items.csv",header=TRUE)

## When N=18
nonlinearBFeighteen<-read.csv("/Users/uzma/Downloads/Nonlinearoutput/Bruteforce18items.csv",header=TRUE)
nonlinearEPCAeighteen<-read.csv("/Users/uzma/Downloads/Nonlinearoutput/EPCA18items.csv",header=TRUE)


##When N=5
x1<-nonlinearBFfive$X
l1<-nonlinearEPCAfive$System.Time.EPCA
l2<-nonlinearBFfive$System.Time.BF
#test.data10<-cbind(x,y1,y2)
boxplot(l1,l2,names=c("EPCA","Brute Force"),main="N=5")

##Difference in the mean of the two boxplots above
diffnmean5<-mean(l2)-mean(l1)
## The difference is positive Brute Force- Greedy
diffnmean5

## [1] -0.002431523

##When N=10
x2<-nonlinearBFten$X
l3<-nonlinearEPCAten$System.Time.EPCA
l4<-nonlinearBFten$System.Time.BF
boxplot(l3,l4,names=c("EPCA","Brute Force"),main="N=10")

##Difference in the mean of the two boxplots above
diffnmean10<-mean(l4)-mean(l3)
## The difference is positive Brute Force- Greedy
diffnmean10

## [1] 0.1166903

## When N=15
x3<-nonlinearBFfifteen$X
l5<-nonlinearEPCAfifteen$System.Time.EPCA
l6<-nonlinearBFfifteen$System.time
boxplot(l5,l6,names=c("EPCA","Brute Force"),main="N=15")

##Difference in the mean of the two boxplots above
diffnmean12<-mean(l6)-mean(l5)
## The difference is positive Brute Force- Greedy
diffnmean12

## [1] 155.843

## When N=18
x4<-nonlinearBFeighteen$X
l7<-nonlinearEPCAeighteen$System.Time.EPCA
l8<-nonlinearBFeighteen$System.time
boxplot(l7,l8,names=c("EPCA","Brute Force"),main="N=18")

##Difference in the mean of the two boxplots above
diffnmean14<-mean(l8)-mean(l7)
## The difference is positive Brute Force- Greedy
diffnmean14

## [1] 265.3828

## Final line plot

dfnplot<-c(diffnmean5,diffnmean10,diffnmean12,diffnmean14)
plot(dfnplot,type='l',xaxt = "n",xlab="Maximum number of items available", ylab="Time Difference in seconds", main="Time Difference: Brute Force - EPCA")
axis(1,at=1:4,labels=c(5,10,15,18))