Define Overlapping Ranges - R

I have two data frames. One with purchases during the month, one with advertisements (announcements) that were widely presented this month. To understand if a purchase can be reliably linked to an ad, I want to understand how many of the purchase dates occur within 4 days of an ad. To do this, I created some (cumbersome) code based on expanding each line of the ad base to cover the corresponding 4 day period and then using a merge construct to see where the (lack of) overlap is. This seems like a very cumbersome way to do things. Ideally - I would like to do this in dplyr elegantly. let me know if anyone has any suggestions

library(dplyr)
library(lubridate)
require(data.table)

# set start and end dates to sample between
day.start <- "2007/01/01"
day.end <- "2007/01/30"

set.seed(1) # define a random date/time selection function
rand.day.time <- function(day.start,day.end,size) {
  dayseq <- seq.Date(as.Date(day.start),as.Date(day.end),by="day")
  dayselect <- sample(dayseq,size,replace=TRUE)
  as.POSIXlt(paste(dayselect) )
}

dateval=rand.day.time(day.start,day.end,size=20)

###create initial dataframes
action=rep(c("ad","purchase"),10)
id=rep(c(1,1,2,2),5)
df=data.frame(customer=id,date=dateval,action=action)
df_pur=filter(df,action=="purchase");(df_pur=df_pur[order(df_pur$date),])
df_ad=filter(df,action=="ad");(df_ad=df_ad[order(df_ad$date),])

#expand data-frame to include all the ranges for which the ad might trigger purchases
df_ad_exp = df_ad %>%
  group_by(customer,date) %>%
  summarize(start=min(date),end=min(date+days(4))) 
df_ad_exp=as.data.frame(df_ad_exp)
df_ad_exp2=setDT(df_ad_exp)[, list(customer=customer, range=seq(start,end,by="day")), by=1:nrow(df_ad_exp)]

###merge the dataframe, use NA values to identify those dates in which purchase was made but no ad was "active"
df_ad_exp2=as.data.frame(df_ad_exp2)
(df_ad_exp2=df_ad_exp2[,c("customer","range")])
df_ad_exp2$helpercol=0
(df_pur_m=merge(df_pur,df_ad_exp2,by.x=c("date","customer"),by.y=c("range","customer"),all.x=TRUE))

df_pur_m$ad_in_range=df_pur_m$helpercol;df_pur_m$helpercol=NULL
df_pur_m$ad_in_range[!is.na(df_pur_m$ad_in_range)]=1;df_pur_m$ad_in_range[is.na(df_pur_m$ad_in_range)]=0

#outcomes
df_pur
df_ad
df_pur_m

> df_ad
   customer       date action
3         1 2007-01-07     ad
6         2 2007-01-07     ad
1         1 2007-01-08     ad
10        2 2007-01-12     ad
2         2 2007-01-18     ad
5         1 2007-01-19     ad
7         1 2007-01-21     ad
9         1 2007-01-22     ad
8         2 2007-01-24     ad
4         2 2007-01-29     ad
> df_pur_m
         date customer   action ad_in_range
1  2007-01-02        1 purchase           0
2  2007-01-06        2 purchase           0
3  2007-01-12        1 purchase           1
4  2007-01-12        1 purchase           1
5  2007-01-15        2 purchase           1
6  2007-01-20        2 purchase           1
7  2007-01-24        2 purchase           1
8  2007-01-27        1 purchase           0
9  2007-01-28        2 purchase           1
10 2007-01-30        1 purchase           0