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I am interesting to calculate the time between a first event and last event.

I calculate this in following way: The data looks as:

datesListEx = {"2014-12-08", "2014-01-14", "2014-05-30", "2014-11-13",
"2014-03-30", "2014-09-28", "2014-03-05", "2014-07-28", 
"2014-03-05", "2014-11-13", "2014-02-12", "2013-11-27", 
"2013-12-08", "2014-01-04", "2014-07-07", "2014-07-07", 
"2014-03-30", "2014-11-13", "2014-02-21", "2014-04-23", 
"2013-11-11", "2014-04-06", "2014-02-12", "2014-01-04", 
"2014-08-25", "2014-10-07", "2013-11-19", "2013-11-19", 
"2014-02-18", "2014-10-07", "2014-01-14", "2013-11-04", 
"2014-03-05", "2014-02-12", "2014-05-30", "2014-12-08", 
"2014-02-02", "2014-07-07", "2014-06-12"};

I sorted the data

datesListExSort = Sort@datesListEx;

And subtraction 

 DateDifference[First[datesListExSort], Last[datesListExSort]]

I repeat the action thousands of times (with different data), the subtraction between dates that takes a lot of time. Is there a way to speed up this action?

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    $\begingroup$ You can convert to integers with AbsoluteTime /@ datesListEx and do computations and finally convert back with DateString[#, {"Year", "-", "Month", "-", "Day"}] &. (Documentation says "AbsoluteTime[] gives the total number of seconds since the beginning of January 1, 1900, in your time zone.") $\endgroup$ – Henrik Schumacher May 12 '18 at 14:21
  • $\begingroup$ Thank you. The convert to integers take more time than using DateDifference In[266]:= AbsoluteTime /@ datesListEx; // AbsoluteTiming Out[266]= {0.0176399, Null} and DateDifference[First[datesListExSort], Last[datesListExSort]] // AbsoluteTiming Out[262]= {0.00331155, Quantity[399, "Days"]} $\endgroup$ – Kiril Danilchenko May 12 '18 at 14:33
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Edmund made a very good point. If your data strings are well-structured, you can load the data even faster with

dates2 = Map[
     DateObject[Join[#, {0, 0, 0}]] &,
     StringCases[datesListEx, s : DigitCharacter .. :> ToExpression[s]]
     ]; // RepeatedTiming // First

0.00048

Compared to Edmund's solution:

dates1 = Map[
     DateObject[{#, {"Year", "Month", "Day"}}] &,
     datesListEx
     ]; // RepeatedTiming // First

dates1 == dates2

0.00806

True

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If you are processing dates it is better to have them as DateObjects and use the functions in the Date & Time guide. Try converting to DateObjects when you import. Over a list of DateObjects named dates you will find DateDifference @@ DateBounds@dates to be very fast.

dates = DateObject[{#, {"Year", "Month", "Day"}}] & /@ datesListEx;

Then

RepeatedTiming[
 DateDifference @@ DateBounds@dates;
 ]

{0.00085, Null}

versus

RepeatedTiming[
 datesListExSort = Sort@datesListEx;
 DateDifference[First[datesListExSort], Last[datesListExSort]];
 ]

{0.0031, Null}

Hope this helps.

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