How do I calculate Date Difference between row observations in R

Question

Here is the sample dataframe (Market_Test) Not sure of DataFrame comes out properly or not hence the image

Submarket   Market          Date            URL of test
Seattle_Sub1    Seattle         1/2/2016        Abc.com/test1
Seattle_Sub2    Seattle         1/3/2016        Abc.com/test2
Seattle_Sub1    Seattle         1/5/2016        Abc.com/test3
Portland_Sub1   Portland    1/15/2016   Abc.com/test4
Portland_Sub2   Portland    1/10/2016   Abc.com/test3
Portland_Sub2   Portland    1/11/2016   Abc.com/test2
Portland_Sub1   Portland    1/10/2016   Abc.com/test1

I need to calculate and pivot the data on the SubMarket Level and make it look like the following OutputData Frame Image-

Submarket   Market       No of Days Testing   Gap b/w test Days
Seattle_Sub1    Seattle           2                3
Seattle_Sub2    Seattle           1                0
Portland_Sub1   Portland      2                5
Portland_Sub2   Portland      2                1

There are around 300,000 observations so relatively big data set.

I am able to easily solve the No of Days Testing problem using sqldf and distinct count but hit a roadblock with Gap b/w Test Days calculation.

One thing I tried was using rank the original datframe and then calcualte the delta between 2 values of rank but in ddply but that takes very long, infact it never gets completed.

Inputdf <- mutate(Inputdf,Date_Rank = rank(Date)) 

Otheroption would have been to use lag/lead functions in sql but sqldf does not allow that.

Thanks much in advance.