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how to get rid of timestamp and change column into date format R

I have a dataset with a date format that is below. I want to:

1. strip the time off the date column, so that it becomes 2/06/2020 or better yet 2Jun2020

2. then I want to make my column Date into date format, so that I can subset off it

> print(df$Date)
   [1] "2/06/2020 0:00"  "12/06/2020 0:00" "12/06/2020 0:00" "29/06/2020 0:00" "3/06/2020 0:00"  "25/06/2020 0:00" "25/06/2020 0:00"
   [8] "25/06/2020 0:00" "26/06/2020 0:00" "18/06/2020 0:00" "3/06/2020 0:00"  "4/06/2020 0:00"  "10/06/2020 0:00" "10/06/2020 0:00"

> summary(df$Date)
   Length     Class      Mode 
    16749 character character 

I tried this but it returned all NA's :

df$Date2 <- as.Date(df$Date, format = "%d-%m-%Y %H:%M")

Does this work:

d <- c("2/06/2020 0:00",  "12/06/2020 0:00", "12/06/2020 0:00", "29/06/2020 0:00")
as.Date(gsub('(.*)(\\s\\d:\\d{2})','\\1',d),format = '%d/%m/%Y')
[1] "2020-06-02" "2020-06-12" "2020-06-12" "2020-06-29"

If you want it in 02/06/2020 format:

format(as.Date(gsub('(.*)(\\s\\d:\\d{2})','\\1',d),format = '%d/%m/%Y'),'%d/%m/%Y')
[1] "02/06/2020" "12/06/2020" "12/06/2020" "29/06/2020"

building on previous answer:

d = "2/06/2020 0:00"
x = format(as.Date(gsub('(\\s\\0(\\d):\\0(\\d){2})','\\1',d),format = '%d/%m/%Y'),'%d/%m/%Y')
gsub("^0+(\\d)", "\\1", x)

# [1] "2/06/2020"

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