Sum of minutes between multiple date ranges

Question

The scenario is users specify when they are available, these specified times can overlap each other. I'm trying to get the total time they are available for. Example with SQL Fiddle:

--Available--
ID  userID  availStart          availEnd
1   456     '2012-11-19 16:00'  '2012-11-19 17:00'
2   456     '2012-11-19 16:00'  '2012-11-19 16:50'
3   456     '2012-11-19 18:00'  '2012-11-19 18:30'
4   456     '2012-11-19 17:30'  '2012-11-19 18:10'
5   456     '2012-11-19 16:00'  '2012-11-19 17:10'
6   456     '2012-11-19 16:00'  '2012-11-19 16:50'

The output should be 130 minutes:

1: 60
2: 0 as falls inside 1
3: 30
4: 30 as the last 10 mins is covered by 3
5: 10 as first 60 mins is covered by 1
6: 0 as falls inside 1

I can get the total overlapping minutes, however this is more than the SUM of the available minutes:

SQL Fiddle

Any ideas how I can achieve this?

EDIT 21st Nov 12: Thanks so far for everyone's solutions - in a way I'm happy to see this wasn't an 'easy' query to write.

EDIT 23rd Nov 12: This is all great work. Internally here we're thinking it might be best to ensure users cannot enter overlapping times (eg forcing them to amend an existing entry)!

Answer 1

Gordon Linoff has a CTE based answer

I've done some performance analysis on all the working algorithms Blank values mean it took too long. This is tested on a single Core i7 X920 @2GHz chip, backed by a couple of SSDs. The only index created was a cluster on UserID, AvailStart. If you think you can improve any of the performance, let me know.

This CTE version was worse than linear, SQL Server can't do the RN = RN + 1 join in an efficient way. I rectified this with a hybrid approach below, where I save and index the first CTE into a table variable. This still takes ten times as much IO as the cursor based approach.

With OrderedRanges as (
  Select
    Row_Number() Over (Partition By UserID Order By AvailStart) AS RN,
    AvailStart,
    AvailEnd
  From
    dbo.Available
  Where
    UserID = 456
),
AccumulateMinutes (RN, Accum, CurStart, CurEnd) as (
  Select
    RN, 0, AvailStart, AvailEnd
  From
    OrderedRanges
  Where 
    RN = 1
  Union All
  Select
    o.RN, 
    a.Accum + Case When o.AvailStart <= a.CurEnd Then
        0
      Else 
        DateDiff(Minute, a.CurStart, a.CurEnd)
      End,
    Case When o.AvailStart <= a.CurEnd Then 
        a.CurStart
      Else
        o.AvailStart
      End,
    Case When o.AvailStart <= a.CurEnd Then
        Case When a.CurEnd > o.AvailEnd Then a.CurEnd Else o.AvailEnd End
      Else
        o.AvailEnd
      End
  From
    AccumulateMinutes a
        Inner Join 
    OrderedRanges o On 
        a.RN = o.RN - 1
)

Select Max(Accum + datediff(Minute, CurStart, CurEnd)) From AccumulateMinutes 

http://sqlfiddle.com/#!6/ac021/2

After doing some performance analysis, here's a hybrid CTE/table variable version that performs better than anything except the cursor based approach

Create Function dbo.AvailMinutesHybrid(@UserID int) Returns Int As
Begin

Declare @UserRanges Table (
  RN int not null primary key, 
  AvailStart datetime, 
  AvailEnd datetime
)
Declare @Ret int = Null

;With OrderedRanges as (
  Select
    Row_Number() Over (Partition By UserID Order By AvailStart) AS RN,
    AvailStart,
    AvailEnd
  From
    dbo.Available
  Where
    UserID = @UserID
)
Insert Into @UserRanges Select * From OrderedRanges


;With AccumulateMinutes (RN,Accum, CurStart, CurEnd) as (
  Select
    RN, 0, AvailStart, AvailEnd
  From
    @UserRanges
  Where 
    RN = 1
  Union All
  Select
    o.RN, 
    a.Accum + Case When o.AvailStart <= a.CurEnd Then
        0
      Else 
        DateDiff(Minute, a.CurStart, a.CurEnd)
      End,
    Case When o.AvailStart <= a.CurEnd Then 
        a.CurStart
      Else
        o.AvailStart
      End,
    Case When o.AvailStart <= a.CurEnd Then
        Case When a.CurEnd > o.AvailEnd Then a.CurEnd Else o.AvailEnd End
      Else
        o.AvailEnd
      End
  From
    AccumulateMinutes a
        Inner Join 
    @UserRanges o On 
        a.RN + 1 = o.RN
)

Select 
  @Ret = Max(Accum + datediff(Minute, CurStart, CurEnd)) 
From 
  AccumulateMinutes 
Option
  (MaxRecursion 0)

Return @Ret

End

http://sqlfiddle.com/#!6/bfd94