Determine Whether Two Date Ranges Overlap

Question

Given two date ranges  what is the simplest or most efficient way to determine whether the two date ranges overlap   As an example  suppose we have ranges denoted by DateTime variables StartDate1 to EndDate1 and StartDate2 to EndDate2

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a compact formula that works for me  class ValidityRuleRange           private final Date from          private final Date to              private boolean isOverlap ValidityRuleRange vrr            int c1   from compareTo vrr getTo             int c2   to compareTo vrr getFrom             return c1    0    c2    0    c1   c2    0

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The mathematical solution given by  Bretana is good but neglects two specific details    aspect of closed or half-open intervals empty intervals     About the closed or open state of interval boundaries  the solution of  Bretana valid for closed intervals       StartA  lt   EndB   and   EndA    StartB    can be rewritten for half-open intervals to       StartA  lt  EndB  and  EndA   StartB    This correction is necessary because an open interval boundary does not belong to the value range of an interval by definition     And about empty intervals  well  here the relationship shown above does NOT hold  Empty intervals which do not contain any valid value by definition must be handled as special case  I demonstrate it by my Java time library Time4J via this example   MomentInterval a   MomentInterval between Instant now    Instant now   plusSeconds 2    MomentInterval b   a collapse       make b an empty interval out of a  System out println a       2017-04-10T05 28 11 909000000Z 2017-04-10T05 28 13 909000000Z  System out println b       2017-04-10T05 28 11 909000000Z 2017-04-10T05 28 11 909000000Z    The leading square bracket     indicates a closed start while the last bracket     indicates an open end   System out println         startA  lt  endB      a getStartAsInstant   isBefore b getEndAsInstant         false System out println         endA  gt  startB      a getEndAsInstant   isAfter b getStartAsInstant         true  System out println  a overlaps b      a intersects b       a overlaps b  false   As shown above  empty intervals violate the overlap condition above  especially startA  lt  endB   so Time4J  and other libraries  too  has to handle it as special edge case in order to guarantee that the overlap of any arbitrary interval with an empty interval does not exist  Of course  date intervals  which are closed by default in Time4J but can be half-open  too  like empty date intervals  are handled in a similar way

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Short answer using momentjs   function isOverlapping startDate1  endDate1  startDate2  endDate2        return moment startDate1  isSameOrBefore endDate2   amp  amp       moment startDate2  isSameOrBefore endDate1       the answer is based on above answers  but its shortened

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For reasoning about temporal relations  or any other interval relations  come to that   consider Allen s Interval Algebra   It describes the 13 possible relations that two intervals can have with respect to each other   You can find other references      Allen Interval  seems to be an operative search term   You can also find information about these operations in Snodgrass s Developing Time-Oriented Applications in SQL  PDF available online at URL   and in Date  Darwen and Lorentzos Temporal Data and the Relational Model  2002  or  Time and Relational Theory  Temporal Databases in the Relational Model and SQL  2014  effectively the second edition of TD amp RM      The short ish  answer is  given two date intervals A and B with components  start and  end and the constraint  start  lt    end  then two intervals overlap if   A end  gt   B start AND A start  lt   B end   You can tune the use of  gt   vs  gt  and  lt   vs  lt  to meet your requirements for degree of overlap     ErikE comments      You can only get 13 if you count things funny    I can get  15 possible relations that two intervals can have  when I go crazy with it  By sensible counting  I get only six  and if you throw out caring whether A or B comes first  I get only three  no intersect  partially intersect  one wholly within other   15 goes like this   before before  start  within  end  after    start start  within  end  after    within within  end  after    end end  after    after after      I think that you cannot count the two entries  before before  and  after after    I could see 7 entries if you equate some relations with their inverses  see the diagram in the referenced Wikipedia URL  it has 7 entries  6 of which have a different inverse  with equals not having a distinct inverse    And whether three is sensible depends on your requirements   ---------------------- -------A------- ----------------------      ----B1----              ----B2----                  ----B3----                  ----------B4----------                  ----------------B5----------------                         ----B6----  ---------------------- -------A------- ----------------------                        ------B7-------                         ----------B8-----------                            ----B9----                            ----B10-----                            --------B11--------                                         ----B12----                                            ----B13----  ---------------------- -------A------- ----------------------

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Here s my solution in Java  which works on unbounded intervals too    private Boolean overlap  Timestamp startA  Timestamp endA                           Timestamp startB  Timestamp endB        return  endB    null    startA    null     startA after endB            amp  amp   endA    null    startB    null     endA before startB

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I found another quite simple approach  If start and end date of daterange1 falls before start date of daterange2 or start and end date of daterange1 falls after end date of daterange2 this means they don t intersect with each other  public boolean doesIntersect DateRangeModel daterange1  DateRangeModel  daterange2        return                 daterange1 getStartDate   isBefore daterange2 getStartDate                         amp  amp  daterange1 getEndDate   isBefore daterange2 getStartDate                             daterange1 getStartDate   isAfter daterange2 getStartDate                                 amp  amp  daterange1 getEndDate   isAfter daterange2 getEndDate

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For reasoning about temporal relations  or any other interval relations  come to that   consider Allen s Interval Algebra   It describes the 13 possible relations that two intervals can have with respect to each other   You can find other references      Allen Interval  seems to be an operative search term   You can also find information about these operations in Snodgrass s Developing Time-Oriented Applications in SQL  PDF available online at URL   and in Date  Darwen and Lorentzos Temporal Data and the Relational Model  2002  or  Time and Relational Theory  Temporal Databases in the Relational Model and SQL  2014  effectively the second edition of TD amp RM      The short ish  answer is  given two date intervals A and B with components  start and  end and the constraint  start  lt    end  then two intervals overlap if   A end  gt   B start AND A start  lt   B end   You can tune the use of  gt   vs  gt  and  lt   vs  lt  to meet your requirements for degree of overlap     ErikE comments      You can only get 13 if you count things funny    I can get  15 possible relations that two intervals can have  when I go crazy with it  By sensible counting  I get only six  and if you throw out caring whether A or B comes first  I get only three  no intersect  partially intersect  one wholly within other   15 goes like this   before before  start  within  end  after    start start  within  end  after    within within  end  after    end end  after    after after      I think that you cannot count the two entries  before before  and  after after    I could see 7 entries if you equate some relations with their inverses  see the diagram in the referenced Wikipedia URL  it has 7 entries  6 of which have a different inverse  with equals not having a distinct inverse    And whether three is sensible depends on your requirements   ---------------------- -------A------- ----------------------      ----B1----              ----B2----                  ----B3----                  ----------B4----------                  ----------------B5----------------                         ----B6----  ---------------------- -------A------- ----------------------                        ------B7-------                         ----------B8-----------                            ----B9----                            ----B10-----                            --------B11--------                                         ----B12----                                            ----B13----  ---------------------- -------A------- ----------------------

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For ruby I also found this   class Interval  lt  ActiveRecord  Base    validates presence of  start date   end date      Check if a given interval overlaps this interval       def overlaps  other       start date - other end date     other start date - end date   gt   0   end      Return a scope for all interval overlapping the given interval  including the given interval itself   named scope  overlapping  lambda    interval         conditions   gt    id  lt  gt    AND  DATEDIFF start date       DATEDIFF    end date    gt   0   interval id  interval end date  interval start date        end   Found it here with nice explaination -  http   makandracards com makandra 984-test-if-two-date-ranges-overlap-in-ruby-or-rails

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I had a situation where we had dates instead of datetimes  and the dates could overlap only on start end  Example below      Green is the current interval  blue blocks are valid intervals  red ones are overlapping intervals    I adapted Ian Nelson s answer to the following solution       startB  lt   startA  amp  amp  endB  gt  startA      startB  gt   startA  amp  amp  startB  lt  endA    This matches all overlap cases but ignores the allowed overlap ones

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The answer is too simple for me so I have created a more generic dynamic SQL statement which checks to see if a person has any overlapping dates   SELECT DISTINCT T1 EmpID FROM Table1 T1 INNER JOIN Table2 T2 ON T1 EmpID   T2 EmpID      AND T1 JobID  lt  gt  T2 JobID     AND            T1 DateFrom  gt   T2 DateFrom AND T1 dateFrom  lt   T2 DateTo           OR  T1 DateTo  gt   T2 DateFrom AND T1 DateTo  lt   T2 DateTo          OR  T1 DateFrom  lt  T2 DateFrom AND T1 DateTo IS NULL            AND NOT  T1 DateFrom   T2 DateFrom

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For reasoning about temporal relations  or any other interval relations  come to that   consider Allen s Interval Algebra   It describes the 13 possible relations that two intervals can have with respect to each other   You can find other references      Allen Interval  seems to be an operative search term   You can also find information about these operations in Snodgrass s Developing Time-Oriented Applications in SQL  PDF available online at URL   and in Date  Darwen and Lorentzos Temporal Data and the Relational Model  2002  or  Time and Relational Theory  Temporal Databases in the Relational Model and SQL  2014  effectively the second edition of TD amp RM      The short ish  answer is  given two date intervals A and B with components  start and  end and the constraint  start  lt    end  then two intervals overlap if   A end  gt   B start AND A start  lt   B end   You can tune the use of  gt   vs  gt  and  lt   vs  lt  to meet your requirements for degree of overlap     ErikE comments      You can only get 13 if you count things funny    I can get  15 possible relations that two intervals can have  when I go crazy with it  By sensible counting  I get only six  and if you throw out caring whether A or B comes first  I get only three  no intersect  partially intersect  one wholly within other   15 goes like this   before before  start  within  end  after    start start  within  end  after    within within  end  after    end end  after    after after      I think that you cannot count the two entries  before before  and  after after    I could see 7 entries if you equate some relations with their inverses  see the diagram in the referenced Wikipedia URL  it has 7 entries  6 of which have a different inverse  with equals not having a distinct inverse    And whether three is sensible depends on your requirements   ---------------------- -------A------- ----------------------      ----B1----              ----B2----                  ----B3----                  ----------B4----------                  ----------------B5----------------                         ----B6----  ---------------------- -------A------- ----------------------                        ------B7-------                         ----------B8-----------                            ----B9----                            ----B10-----                            --------B11--------                                         ----B12----                                            ----B13----  ---------------------- -------A------- ----------------------

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If you provide a date range as input and want to find out if it overlaps with the existing date range in database  the following conditions can successfully meet your demand  Assume you provide a  StartDate and  EndDate from your form input   conditions are   If  StartDate is ahead of existingStartDate and behind existingEndDate then we can say  StartDate is in the middle of a existing date range  thus we can conclude it will overlap  StartDate  gt  existing StartDate And  StartDate  lt   existing EndDate    If  StartDate is behind existingStartDate but  EndDate is ahead of existingStartDate we can say that it will overlap    StartDate  lt   existing StartDate And  EndDate  gt   existing StartDate   If  StartDate is behind existingStartDate And  EndDate is ahead of existingEndDate we can conclude that the provided date range devours a existing date range   thus overlaps    StartDate  lt   existing StartDate And  EndDate  gt   existing EndDate    If any of the condition stands true  your provided date range overlaps with existing ones in the database

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I would do   StartDate1 IsBetween StartDate2  EndDate2     EndDate1 IsBetween StartDate2  EndDate2    Where IsBetween is something like       public static bool IsBetween this DateTime value  DateTime left  DateTime right            return  value  gt  left  amp  amp  value  lt  right      value  lt  left  amp  amp  value  gt  right

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public static class NumberExtensionMethods               public static Boolean IsBetween this Int64 value  Int64 Min  Int64 Max                        if  value  gt   Min  amp  amp  value  lt   Max  return true              else return false                     public static Boolean IsBetween this DateTime value  DateTime Min  DateTime Max                        Int64 numricValue   value Ticks              Int64 numericStartDate   Min Ticks              Int64 numericEndDate   Max Ticks               if  numricValue IsBetween numericStartDate  numericEndDate                                  return true                             return false                   public static Boolean IsOverlap DateTime startDate1  DateTime endDate1  DateTime startDate2  DateTime endDate2                        Int64 numericStartDate1   startDate1 Ticks              Int64 numericEndDate1   endDate1 Ticks              Int64 numericStartDate2   startDate2 Ticks              Int64 numericEndDate2   endDate2 Ticks               if  numericStartDate2 IsBetween numericStartDate1  numericEndDate1                     numericEndDate2 IsBetween numericStartDate1  numericEndDate1                     numericStartDate1 IsBetween numericStartDate2  numericEndDate2                     numericEndDate1 IsBetween numericStartDate2  numericEndDate2                                 return true                             return false               if  IsOverlap startdate1  enddate1  startdate2  enddate2                                 Console WriteLine  IsOverlap

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The answer is too simple for me so I have created a more generic dynamic SQL statement which checks to see if a person has any overlapping dates   SELECT DISTINCT T1 EmpID FROM Table1 T1 INNER JOIN Table2 T2 ON T1 EmpID   T2 EmpID      AND T1 JobID  lt  gt  T2 JobID     AND            T1 DateFrom  gt   T2 DateFrom AND T1 dateFrom  lt   T2 DateTo           OR  T1 DateTo  gt   T2 DateFrom AND T1 DateTo  lt   T2 DateTo          OR  T1 DateFrom  lt  T2 DateFrom AND T1 DateTo IS NULL            AND NOT  T1 DateFrom   T2 DateFrom

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All the solutions that check a multitude of conditions based on where the ranges are in relation to one another can be greatly simplified by just ensuring that a specific range starts earlier  You ensure that the first range starts earlier  or at the same time  by swapping the ranges if necessary up front   Then  you can detect overlap if the other range start is less than or equal to the first range end  if ranges are inclusive  containing both the start and end times  or less than  if ranges are inclusive of start and exclusive of end    Assuming inclusive at both ends  there s only four possibilities of which one is a non-overlap    ----------------------         range 1  --- gt                            range 2 overlap   --- gt                           range 2 overlap                         --- gt     range 2 overlap                          --- gt    range 2 no overlap   The endpoint of the range 2 doesn t enter into it  So  in pseudo-code   def doesOverlap  r1  r2       if r1 s  gt  r2 s          swap r1  r2     if r2 s  gt  r1 e          return false     return true   This could be simplified even more into   def doesOverlap  r1  r2       if r1 s  gt  r2 s          swap r1  r2     return r2 s  lt   r1 e   If the ranges are inclusive at the start and exclusive at the end  you just have to replace  gt  with  gt   in the second if statement  for the first code segment  in the second code segment  you d use  lt  rather than  lt       ----------------------         range 1  --- gt                            range 2 overlap   --- gt                           range 2 overlap                         --- gt     range 2 no overlap                          --- gt    range 2 no overlap   You greatly limit the number of checks you have to make because you remove half of the problem space early by ensuring range 1 never starts after range 2

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if  StartDate1  gt  StartDate2  swap StartDate  EndDate     StartDate1  lt   EndDate2  and  StartDate2  lt   EndDate1

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a compact formula that works for me  class ValidityRuleRange           private final Date from          private final Date to              private boolean isOverlap ValidityRuleRange vrr            int c1   from compareTo vrr getTo             int c2   to compareTo vrr getFrom             return c1    0    c2    0    c1   c2    0

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I believe that it is sufficient to say that the two ranges overlap if    StartDate1  lt   EndDate2  and  StartDate2  lt   EndDate1

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Here is a generic method that can be usefull locally          Takes a list and returns all records that have overlapping time ranges      public static IEnumerable lt T gt  GetOverlappedTimes lt T gt  IEnumerable lt T gt  list  Func lt T  bool gt  filter  Func lt T DateTime gt  start  Func lt T  DateTime gt  end                   Selects all records that match filter   on left side and returns all records on right side that overlap          var overlap   from t1 in list                       where filter t1                        from t2 in list                       where  object Equals t1  t2     Don t match the same record on right side                        let in1   start t1                        let out1   end t1                        let in2   start t2                        let out2   end t2                        where in1  lt   out2  amp  amp  out1  gt   in2                       let totover   GetMins in1  out1  in2  out2                        select t2           return overlap             public static void TestOverlap                 var tl1   new TempTimeEntry     ID   1  Name    Bill   In    1 1 08 1 00pm  ToDate    Out    1 1 08 4 00pm  ToDate              var tl2   new TempTimeEntry     ID   2  Name    John   In    1 1 08 5 00pm  ToDate    Out    1 1 08 6 00pm  ToDate              var tl3   new TempTimeEntry     ID   3  Name    Lisa   In    1 1 08 7 00pm  ToDate    Out    1 1 08 9 00pm  ToDate              var tl4   new TempTimeEntry     ID   4  Name    Joe   In    1 1 08 3 00pm  ToDate    Out    1 1 08 8 00pm  ToDate              var tl5   new TempTimeEntry     ID   1  Name    Bill   In    1 1 08 8 01pm  ToDate    Out    1 1 08 8 00pm  ToDate              var list   new List lt TempTimeEntry gt      tl1  tl2  tl3  tl4  tl5            var overlap   GetOverlappedTimes list   TempTimeEntry t1   gt t1 ID  1   TempTimeEntry tIn    gt  tIn In   TempTimeEntry tOut    gt  tOut Out            Console WriteLine   nRecords overlap             foreach  var tl in overlap              Console WriteLine  Name  0  T1In  1  T1Out  2    tl Name  tl In  tl Out           Console WriteLine  Done                 Output              Records overlap              Name Joe T1In 1 1 2008 3 00 00 PM T1Out 1 1 2008 8 00 00 PM             Name Lisa T1In 1 1 2008 7 00 00 PM T1Out 1 1 2008 9 00 00 PM             Done

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This article Time Period Library for  NET describes the relation of two time periods by the enumeration PeriodRelation      ------------------------------------------------------------------------ public enum PeriodRelation       After      StartTouching      StartInside      InsideStartTouching      EnclosingStartTouching      Enclosing      EnclosingEndTouching      ExactMatch      Inside      InsideEndTouching      EndInside      EndTouching      Before       enum PeriodRelation

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The easiest way to do it in my opinion would be to compare if either EndDate1 is before StartDate2 and EndDate2 is before StartDate1   That of course if you are considering intervals where StartDate is always before EndDate

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Short answer using momentjs   function isOverlapping startDate1  endDate1  startDate2  endDate2        return moment startDate1  isSameOrBefore endDate2   amp  amp       moment startDate2  isSameOrBefore endDate1       the answer is based on above answers  but its shortened

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All the solutions that check a multitude of conditions based on where the ranges are in relation to one another can be greatly simplified by just ensuring that a specific range starts earlier  You ensure that the first range starts earlier  or at the same time  by swapping the ranges if necessary up front   Then  you can detect overlap if the other range start is less than or equal to the first range end  if ranges are inclusive  containing both the start and end times  or less than  if ranges are inclusive of start and exclusive of end    Assuming inclusive at both ends  there s only four possibilities of which one is a non-overlap    ----------------------         range 1  --- gt                            range 2 overlap   --- gt                           range 2 overlap                         --- gt     range 2 overlap                          --- gt    range 2 no overlap   The endpoint of the range 2 doesn t enter into it  So  in pseudo-code   def doesOverlap  r1  r2       if r1 s  gt  r2 s          swap r1  r2     if r2 s  gt  r1 e          return false     return true   This could be simplified even more into   def doesOverlap  r1  r2       if r1 s  gt  r2 s          swap r1  r2     return r2 s  lt   r1 e   If the ranges are inclusive at the start and exclusive at the end  you just have to replace  gt  with  gt   in the second if statement  for the first code segment  in the second code segment  you d use  lt  rather than  lt       ----------------------         range 1  --- gt                            range 2 overlap   --- gt                           range 2 overlap                         --- gt     range 2 no overlap                          --- gt    range 2 no overlap   You greatly limit the number of checks you have to make because you remove half of the problem space early by ensuring range 1 never starts after range 2

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I would do   StartDate1 IsBetween StartDate2  EndDate2     EndDate1 IsBetween StartDate2  EndDate2    Where IsBetween is something like       public static bool IsBetween this DateTime value  DateTime left  DateTime right            return  value  gt  left  amp  amp  value  lt  right      value  lt  left  amp  amp  value  gt  right

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An easy way to remember the solution would be min ends  gt max starts

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For reasoning about temporal relations  or any other interval relations  come to that   consider Allen s Interval Algebra   It describes the 13 possible relations that two intervals can have with respect to each other   You can find other references      Allen Interval  seems to be an operative search term   You can also find information about these operations in Snodgrass s Developing Time-Oriented Applications in SQL  PDF available online at URL   and in Date  Darwen and Lorentzos Temporal Data and the Relational Model  2002  or  Time and Relational Theory  Temporal Databases in the Relational Model and SQL  2014  effectively the second edition of TD amp RM      The short ish  answer is  given two date intervals A and B with components  start and  end and the constraint  start  lt    end  then two intervals overlap if   A end  gt   B start AND A start  lt   B end   You can tune the use of  gt   vs  gt  and  lt   vs  lt  to meet your requirements for degree of overlap     ErikE comments      You can only get 13 if you count things funny    I can get  15 possible relations that two intervals can have  when I go crazy with it  By sensible counting  I get only six  and if you throw out caring whether A or B comes first  I get only three  no intersect  partially intersect  one wholly within other   15 goes like this   before before  start  within  end  after    start start  within  end  after    within within  end  after    end end  after    after after      I think that you cannot count the two entries  before before  and  after after    I could see 7 entries if you equate some relations with their inverses  see the diagram in the referenced Wikipedia URL  it has 7 entries  6 of which have a different inverse  with equals not having a distinct inverse    And whether three is sensible depends on your requirements   ---------------------- -------A------- ----------------------      ----B1----              ----B2----                  ----B3----                  ----------B4----------                  ----------------B5----------------                         ----B6----  ---------------------- -------A------- ----------------------                        ------B7-------                         ----------B8-----------                            ----B9----                            ----B10-----                            --------B11--------                                         ----B12----                                            ----B13----  ---------------------- -------A------- ----------------------

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As there have been several answers for different languages and environments  here is one for standard ANSI SQL  In standard SQL it is as as simple as  StartDate1  EndDate1  overlaps  StartDate2  EndDate2   assuming all four columns are DATE or TIMESTAMP columns  It returns true if both ranges have at least one day in common  assuming DATE values   However not all DBMS products support that   In PostgreSQL it s also easy to test for inclusion by using date ranges daterange StartDate1  EndDate1    gt  daterange StartDate2  EndDate2   the above returns true if the second range is completely included in the first  which is different to  quot overlaps quot

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The easiest way to do it in my opinion would be to compare if either EndDate1 is before StartDate2 and EndDate2 is before StartDate1   That of course if you are considering intervals where StartDate is always before EndDate

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If you provide a date range as input and want to find out if it overlaps with the existing date range in database  the following conditions can successfully meet your demand  Assume you provide a  StartDate and  EndDate from your form input   conditions are   If  StartDate is ahead of existingStartDate and behind existingEndDate then we can say  StartDate is in the middle of a existing date range  thus we can conclude it will overlap  StartDate  gt  existing StartDate And  StartDate  lt   existing EndDate    If  StartDate is behind existingStartDate but  EndDate is ahead of existingStartDate we can say that it will overlap    StartDate  lt   existing StartDate And  EndDate  gt   existing StartDate   If  StartDate is behind existingStartDate And  EndDate is ahead of existingEndDate we can conclude that the provided date range devours a existing date range   thus overlaps    StartDate  lt   existing StartDate And  EndDate  gt   existing EndDate    If any of the condition stands true  your provided date range overlaps with existing ones in the database

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You can try this     custom date for example  d1   new DateTime  2012-07-08     d2   new DateTime  2012-07-11     d3   new DateTime  2012-07-08     d4   new DateTime  2012-07-15       create a date period object  interval   new DateInterval  P1D     daterange   iterator to array new DatePeriod  d1   interval   d2     daterange1   iterator to array new DatePeriod  d3   interval   d4    array map function  v  use   daterange1    if in array  v   daterange1   print  Bingo       daterange

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Easy solution   compare the two dates       A   the one with smaller start date  B   the one with bigger start date if A end  lt  B start      return false return true

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I believe that it is sufficient to say that the two ranges overlap if    StartDate1  lt   EndDate2  and  StartDate2  lt   EndDate1

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This is an extension to the excellent answer by  charles-bretana   The answer however does not make a distinction among open  closed  and half-open  or half-closed  intervals   Case 1  A  B are closed intervals  A    StartA  EndA  B    StartB  EndB                             ---- DateRange A ------     True if StartA  gt  EndB   --- Date Range B -----                                ---- DateRange A -----                               True if EndA  lt  StartB                            --- Date Range B ----    Overlap iff   StartA  lt   EndB   and   EndA  gt   StartB   Case 2  A  B are open intervals  A    StartA  EndA  B    StartB  EndB                             ---- DateRange A ------     True if StartA  gt   EndB   --- Date Range B -----                               ---- DateRange A -----                               True if EndA  lt   StartB                            --- Date Range B ----    Overlap iff   StartA  lt  EndB   and   EndA  gt  StartB   Case 3  A  B right open   A    StartA  EndA  B    StartB  EndB                             ---- DateRange A ------     True if StartA  gt   EndB    --- Date Range B -----                               ---- DateRange A -----                               True if EndA  lt   StartB                            --- Date Range B ----    Overlap condition   StartA  lt  EndB   and   EndA  gt  StartB   Case 4  A  B left open  A    StartA  EndA  B    StartB  EndB                             ---- DateRange A ------     True if StartA  gt   EndB   --- Date Range B -----                               ---- DateRange A -----                               True if EndA  lt   StartB                            --- Date Range B ----    Overlap condition   StartA  lt  EndB   and   EndA  gt  StartB   Case 5  A right open  B closed  A    StartA  EndA  B    StartB  EndB                             ---- DateRange A ------      True if StartA  gt  EndB   --- Date Range B -----                                ---- DateRange A -----                                True if EndA  lt   StartB                              --- Date Range B ----    Overlap condition   StartA  lt   EndB   and   EndA  gt  StartB   etc     Finally  the general condition for two intervals to overlap is    StartA  lt  EndB   and   EndA   StartB   where  turns a strict inequality into a non-strict one whenever the comparison is made between two included endpoint

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The mathematical solution given by  Bretana is good but neglects two specific details    aspect of closed or half-open intervals empty intervals     About the closed or open state of interval boundaries  the solution of  Bretana valid for closed intervals       StartA  lt   EndB   and   EndA    StartB    can be rewritten for half-open intervals to       StartA  lt  EndB  and  EndA   StartB    This correction is necessary because an open interval boundary does not belong to the value range of an interval by definition     And about empty intervals  well  here the relationship shown above does NOT hold  Empty intervals which do not contain any valid value by definition must be handled as special case  I demonstrate it by my Java time library Time4J via this example   MomentInterval a   MomentInterval between Instant now    Instant now   plusSeconds 2    MomentInterval b   a collapse       make b an empty interval out of a  System out println a       2017-04-10T05 28 11 909000000Z 2017-04-10T05 28 13 909000000Z  System out println b       2017-04-10T05 28 11 909000000Z 2017-04-10T05 28 11 909000000Z    The leading square bracket     indicates a closed start while the last bracket     indicates an open end   System out println         startA  lt  endB      a getStartAsInstant   isBefore b getEndAsInstant         false System out println         endA  gt  startB      a getEndAsInstant   isAfter b getStartAsInstant         true  System out println  a overlaps b      a intersects b       a overlaps b  false   As shown above  empty intervals violate the overlap condition above  especially startA  lt  endB   so Time4J  and other libraries  too  has to handle it as special edge case in order to guarantee that the overlap of any arbitrary interval with an empty interval does not exist  Of course  date intervals  which are closed by default in Time4J but can be half-open  too  like empty date intervals  are handled in a similar way

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I had a situation where we had dates instead of datetimes  and the dates could overlap only on start end  Example below      Green is the current interval  blue blocks are valid intervals  red ones are overlapping intervals    I adapted Ian Nelson s answer to the following solution       startB  lt   startA  amp  amp  endB  gt  startA      startB  gt   startA  amp  amp  startB  lt  endA    This matches all overlap cases but ignores the allowed overlap ones

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This is an extension to the excellent answer by  charles-bretana   The answer however does not make a distinction among open  closed  and half-open  or half-closed  intervals   Case 1  A  B are closed intervals  A    StartA  EndA  B    StartB  EndB                             ---- DateRange A ------     True if StartA  gt  EndB   --- Date Range B -----                                ---- DateRange A -----                               True if EndA  lt  StartB                            --- Date Range B ----    Overlap iff   StartA  lt   EndB   and   EndA  gt   StartB   Case 2  A  B are open intervals  A    StartA  EndA  B    StartB  EndB                             ---- DateRange A ------     True if StartA  gt   EndB   --- Date Range B -----                               ---- DateRange A -----                               True if EndA  lt   StartB                            --- Date Range B ----    Overlap iff   StartA  lt  EndB   and   EndA  gt  StartB   Case 3  A  B right open   A    StartA  EndA  B    StartB  EndB                             ---- DateRange A ------     True if StartA  gt   EndB    --- Date Range B -----                               ---- DateRange A -----                               True if EndA  lt   StartB                            --- Date Range B ----    Overlap condition   StartA  lt  EndB   and   EndA  gt  StartB   Case 4  A  B left open  A    StartA  EndA  B    StartB  EndB                             ---- DateRange A ------     True if StartA  gt   EndB   --- Date Range B -----                               ---- DateRange A -----                               True if EndA  lt   StartB                            --- Date Range B ----    Overlap condition   StartA  lt  EndB   and   EndA  gt  StartB   Case 5  A right open  B closed  A    StartA  EndA  B    StartB  EndB                             ---- DateRange A ------      True if StartA  gt  EndB   --- Date Range B -----                                ---- DateRange A -----                                True if EndA  lt   StartB                              --- Date Range B ----    Overlap condition   StartA  lt   EndB   and   EndA  gt  StartB   etc     Finally  the general condition for two intervals to overlap is    StartA  lt  EndB   and   EndA   StartB   where  turns a strict inequality into a non-strict one whenever the comparison is made between two included endpoint

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An easy way to remember the solution would be min ends  gt max starts

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In case you re using a date range that has not ended yet  still on going  e g  not set  endDate    0000-00-00  you can not use BETWEEN because 0000-00-00 is not a valid date   I used this solution    Startdate BETWEEN     startdate2    AND     enddate2        overlap  starts between start2 end2 OR  Startdate  lt      startdate2       AND  enddate    0000-00-00  OR enddate  gt       startdate2         overlap  starts before start2 and enddate not set 0000-00-00  still on going  or if enddate is set but higher then startdate2   If startdate2 is higher then enddate there is no overlap

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In Microsoft SQL SERVER  - SQL Function     CREATE FUNCTION IsOverlapDates         startDate1 as datetime       endDate1 as datetime       startDate2 as datetime       endDate2 as datetime   RETURNS int AS BEGIN DECLARE  Overlap as int SET  Overlap    SELECT CASE WHEN              startDate1 BETWEEN  startDate2 AND  endDate2  -- caters for inner and end date outer         OR           endDate1 BETWEEN  startDate2 AND  endDate2  -- caters for inner and start date outer         OR           startDate2 BETWEEN  startDate1 AND  endDate1  -- only one needed for outer range where dates are inside            THEN 1 ELSE 0 END           RETURN  Overlap  END GO  --Execution of the above code DECLARE  startDate1 as datetime DECLARE  endDate1 as datetime DECLARE  startDate2 as datetime DECLARE  endDate2 as datetime DECLARE  Overlap as int SET  startDate1    2014-06-01 01 00 00   SET  endDate1      2014-06-01 02 00 00  SET  startDate2    2014-06-01 01 00 00   SET  endDate2      2014-06-01 01 30 00   SET  Overlap    dbo   IsOverlapDates     startDate1   endDate1   startDate2   endDate2   SELECT Overlap    Overlap

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StartA  lt   EndB   and   EndA  gt   StartB  Proof  Let ConditionA Mean that DateRange A Completely After DateRange B                           ---- DateRange A ------   ---Date Range B -----                               True if StartA  gt  EndB  Let ConditionB Mean that DateRange A is Completely Before DateRange B  ---- DateRange A -----                                                        ---Date Range B ----    True if EndA  lt  StartB  Then Overlap exists if Neither A Nor B is true -  If one range is neither completely after the other  nor completely before the other  then they must overlap   Now one of De Morgan s laws says that  Not  A Or B    lt   gt   Not A And Not B Which translates to   StartA  lt   EndB   and   EndA  gt   StartB   NOTE  This includes conditions where the edges overlap exactly   If you wish to exclude that  change the  gt   operators to  gt   and  lt    to  lt   NOTE2  Thanks to  Baodad  see this blog  the actual overlap is least of    endA-startA  endA - startB  endB-startA  endB - startB    StartA  lt   EndB   and   EndA  gt   StartB   StartA  lt   EndB   and   StartB  lt   EndA   NOTE3  Thanks to  tomosius  a shorter version reads  DateRangesOverlap   max start1  start2   lt  min end1  end2  This is actually a syntactical shortcut for what is a longer implementation  which includes extra checks to verify that the start dates are on or before the endDates   Deriving this from above  If start and end dates can be out of order  i e   if it is possible that startA  gt  endA or startB  gt  endB  then you also have to check that they are in order  so that means you have to add two additional validity rules   StartA  lt   EndB  and  StartB  lt   EndA  and  StartA  lt   EndA  and  StartB  lt   EndB  or   StartA  lt   EndB  and  StartA  lt   EndA  and  StartB  lt   EndA  and  StartB  lt   EndB  or   StartA  lt   Min EndA  EndB  and  StartB  lt   Min EndA  EndB   or   Max StartA  StartB   lt   Min EndA  EndB  But to implement Min   and Max    you have to code   using C ternary for terseness     StartA  gt  StartB  Start A  StartB   lt    EndA  lt  EndB  EndA  EndB

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Split the problem into cases then handle each case   The situation  two date ranges intersect  is covered by two cases - the first date range starts within the second  or the second date range starts within the first

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In case you re using a date range that has not ended yet  still on going  e g  not set  endDate    0000-00-00  you can not use BETWEEN because 0000-00-00 is not a valid date   I used this solution    Startdate BETWEEN     startdate2    AND     enddate2        overlap  starts between start2 end2 OR  Startdate  lt      startdate2       AND  enddate    0000-00-00  OR enddate  gt       startdate2         overlap  starts before start2 and enddate not set 0000-00-00  still on going  or if enddate is set but higher then startdate2   If startdate2 is higher then enddate there is no overlap

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For ruby I also found this   class Interval  lt  ActiveRecord  Base    validates presence of  start date   end date      Check if a given interval overlaps this interval       def overlaps  other       start date - other end date     other start date - end date   gt   0   end      Return a scope for all interval overlapping the given interval  including the given interval itself   named scope  overlapping  lambda    interval         conditions   gt    id  lt  gt    AND  DATEDIFF start date       DATEDIFF    end date    gt   0   interval id  interval end date  interval start date        end   Found it here with nice explaination -  http   makandracards com makandra 984-test-if-two-date-ranges-overlap-in-ruby-or-rails

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def if lives overlap s1  s2        quot  quot  quot      https   stackoverflow com a 325964 827391         5   10    15  20         ----------------     s1  -----     s2            -----      gt  gt  gt  if lives overlap s1   start   datetime 2020  1  5                                  end   datetime 2020  1  10                             s2   start   datetime 2020  1  15                                  end   datetime 2020  1  20        False       s1            -----     s2  -----      gt  gt  gt  if lives overlap s1   start   datetime 2020  1  15                                  end   datetime 2020  1  20                             s2   start   datetime 2020  1  5                                  end   datetime 2020  1  10        False      s1  ----------     s2       ----------      gt  gt  gt  if lives overlap s1   start   datetime 2020  1  5                                  end   datetime 2020  1  15                             s2   start   datetime 2020  1  10                                  end   datetime 2020  1  20        True      s1       ----------     s2  ----------      gt  gt  gt  if lives overlap s1   start   datetime 2020  1  10                                  end   datetime 2020  1  20                             s2   start   datetime 2020  1  5                                  end   datetime 2020  1  15        True       s1  ---------------     s2       -----      gt  gt  gt  if lives overlap s1   start   datetime 2020  1  5                                  end   datetime 2020  1  20                             s2   start   datetime 2020  1  10                                  end   datetime 2020  1  15        True      s1       -----     s2  ---------------      gt  gt  gt  if lives overlap s1   start   datetime 2020  1  10                                  end   datetime 2020  1  15                             s2   start   datetime 2020  1  5                                  end   datetime 2020  1  20        True      quot  quot  quot       return  s1  start    lt   s2  end    and  s1  end    gt   s2  start

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I believe that it is sufficient to say that the two ranges overlap if    StartDate1  lt   EndDate2  and  StartDate2  lt   EndDate1

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I would do   StartDate1 IsBetween StartDate2  EndDate2     EndDate1 IsBetween StartDate2  EndDate2    Where IsBetween is something like       public static bool IsBetween this DateTime value  DateTime left  DateTime right            return  value  gt  left  amp  amp  value  lt  right      value  lt  left  amp  amp  value  gt  right

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I found another quite simple approach  If start and end date of daterange1 falls before start date of daterange2 or start and end date of daterange1 falls after end date of daterange2 this means they don t intersect with each other  public boolean doesIntersect DateRangeModel daterange1  DateRangeModel  daterange2        return                 daterange1 getStartDate   isBefore daterange2 getStartDate                         amp  amp  daterange1 getEndDate   isBefore daterange2 getStartDate                             daterange1 getStartDate   isAfter daterange2 getStartDate                                 amp  amp  daterange1 getEndDate   isAfter daterange2 getEndDate

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If the overlap itself should be calculated as well  you can use the following formula   overlap   max 0  min EndDate1  EndDate2  - max StartDate1  StartDate2   if  overlap  gt  0

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Here is the code that does the magic    var isOverlapping      A    null    D    null    A  lt   D                amp  amp   C    null    B    null    C  lt   B               amp  amp   A    null    B    null    A  lt   B               amp  amp   C    null    D    null    C  lt   D      Where      A -  1Start B -  1End  C -  2Start  D -  2End   Proof  Check out this test console code gist

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In Microsoft SQL SERVER  - SQL Function     CREATE FUNCTION IsOverlapDates         startDate1 as datetime       endDate1 as datetime       startDate2 as datetime       endDate2 as datetime   RETURNS int AS BEGIN DECLARE  Overlap as int SET  Overlap    SELECT CASE WHEN              startDate1 BETWEEN  startDate2 AND  endDate2  -- caters for inner and end date outer         OR           endDate1 BETWEEN  startDate2 AND  endDate2  -- caters for inner and start date outer         OR           startDate2 BETWEEN  startDate1 AND  endDate1  -- only one needed for outer range where dates are inside            THEN 1 ELSE 0 END           RETURN  Overlap  END GO  --Execution of the above code DECLARE  startDate1 as datetime DECLARE  endDate1 as datetime DECLARE  startDate2 as datetime DECLARE  endDate2 as datetime DECLARE  Overlap as int SET  startDate1    2014-06-01 01 00 00   SET  endDate1      2014-06-01 02 00 00  SET  startDate2    2014-06-01 01 00 00   SET  endDate2      2014-06-01 01 30 00   SET  Overlap    dbo   IsOverlapDates     startDate1   endDate1   startDate2   endDate2   SELECT Overlap    Overlap

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Using Java util Date  here what I did       public static boolean checkTimeOverlaps Date startDate1  Date endDate1  Date startDate2  Date endDate2                if  startDate1    null    endDate1    null    startDate2    null    endDate2    null             return false           if   startDate1 getTime    lt   endDate2 getTime     amp  amp   startDate2 getTime    lt   endDate1 getTime                return true           return false

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This article Time Period Library for  NET describes the relation of two time periods by the enumeration PeriodRelation      ------------------------------------------------------------------------ public enum PeriodRelation       After      StartTouching      StartInside      InsideStartTouching      EnclosingStartTouching      Enclosing      EnclosingEndTouching      ExactMatch      Inside      InsideEndTouching      EndInside      EndTouching      Before       enum PeriodRelation

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Below query gives me the ids  for which the supplied date range  start and end dates overlaps with any of the dates  start and end dates  in my table name  select id from table name where  START DT TM  gt    END DATE TIME   OR     END DT TM BETWEEN  START DATE TIME  AND  END DATE TIME

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You can try this     custom date for example  d1   new DateTime  2012-07-08     d2   new DateTime  2012-07-11     d3   new DateTime  2012-07-08     d4   new DateTime  2012-07-15       create a date period object  interval   new DateInterval  P1D     daterange   iterator to array new DatePeriod  d1   interval   d2     daterange1   iterator to array new DatePeriod  d3   interval   d4    array map function  v  use   daterange1    if in array  v   daterange1   print  Bingo       daterange

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This was my javascript solution with moment js      Current row dates var dateStart   moment  2014-08-01    YYYY-MM-DD    var dateEnd   moment  2014-08-30    YYYY-MM-DD        Check with dates above var rangeUsedStart   moment  2014-08-02    YYYY-MM-DD    var rangeUsedEnd   moment  2014-08-015    YYYY-MM-DD        Range covers other   if  dateStart  lt   rangeUsedStart   amp  amp   rangeUsedEnd  lt   dateEnd         return false       Range intersects with other start   if  dateStart  lt   rangeUsedStart   amp  amp   rangeUsedStart  lt   dateEnd         return false       Range intersects with other end   if  dateStart  lt   rangeUsedEnd   amp  amp   rangeUsedEnd  lt   dateEnd         return false        All good return true

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Here is yet another solution using JavaScript  Specialities of my solution    Handles null values as infinity Assumes that the lower bound is inclusive and the upper bound exclusive  Comes with a bunch of tests   The tests are based on integers but since date objects in JavaScript are comparable you can just throw in two date objects as well  Or you could throw in the millisecond timestamp   Code          Compares to comparable objects to find out whether they overlap     It is assumed that the interval is in the format  from to   read  from is inclusive  to is exclusive      A null value is interpreted as infinity     function intervalsOverlap from1  to1  from2  to2        return  to2     null    from1  lt  to2   amp  amp   to1     null    to1  gt  from2       Tests   describe     function         function generateTest firstRange  secondRange  expected            it JSON stringify firstRange      and     JSON stringify secondRange   function                 expect intervalsOverlap firstRange 0   firstRange 1   secondRange 0   secondRange 1    toBe expected                          describe  no overlap  touching ends    function             generateTest  10 20    20 30   false           generateTest  20 30    10 20   false            generateTest  10 20    20 null   false           generateTest  20 null    10 20   false            generateTest  null 20    20 30   false           generateTest  20 30    null 20   false                describe  do overlap  one end overlaps    function             generateTest  10 20    19 30   true           generateTest  19 30    10 20   true            generateTest  10 20    null 30   true           generateTest  10 20    19 null   true           generateTest  null 30    10 20   true           generateTest  19 null    10 20   true                describe  do overlap  one range included in other range    function             generateTest  10 40    20 30   true           generateTest  20 30    10 40   true            generateTest  10 40    null null   true           generateTest  null null    10 40   true                describe  do overlap  both ranges equal    function             generateTest  10 20    10 20   true            generateTest  null 20    null 20   true           generateTest  10 null    10 null   true           generateTest  null null    null null   true                 Result when run with karma amp jasmine amp PhantomJS      PhantomJS 1 9 8  Linux   Executed 20 of 20 SUCCESS  0 003 secs   0 004 secs

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This was my solution  it returns true when the values don t overlap   X START 1 Y END 1  A START 2 B END 2  TEST1   X  lt   A    X  gt   B           amp  amp  TEST2   Y  gt   B    Y  lt   A            amp  amp   TEST3   X  gt   B    Y  lt   A    X-------------Y     A-----B  TEST1   TRUE TEST2   TRUE TEST3   FALSE RESULT  FALSE  ---------------------------------------  X---Y       A---B  TEST1   TRUE TEST2   TRUE TEST3   TRUE RESULT  TRUE  ---------------------------------------        X---Y A---B  TEST1   TRUE TEST2   TRUE TEST3   TRUE RESULT  TRUE  ---------------------------------------       X----Y A---------------B  TEST1   FALSE TEST2   FALSE TEST3   FALSE RESULT  FALSE

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if  StartDate1  gt  StartDate2  swap StartDate  EndDate     StartDate1  lt   EndDate2  and  StartDate2  lt   EndDate1

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If the overlap itself should be calculated as well  you can use the following formula   overlap   max 0  min EndDate1  EndDate2  - max StartDate1  StartDate2   if  overlap  gt  0

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the simplest   The simplest way is to use a well-engineered dedicated library for date-time work   someInterval overlaps  anotherInterval     java time  amp  ThreeTen-Extra  The best in the business is the java time framework built into Java 8 and later  Add to that the ThreeTen-Extra project that supplements java time with additional classes  specifically the Interval class we need here   As for the language-agnostic tag on this Question  the source code for both projects is available for use in other languages  mind their licenses     Interval  The org threeten extra Interval class is handy  but requires date-time moments  java time Instant objects  rather than date-only values  So we proceed by using the first moment of the day in UTC to represent the date   Instant start   Instant parse   2016-01-01T00 00 00Z     Instant stop   Instant parse   2016-02-01T00 00 00Z       Create an Interval to represent that span of time   Interval interval A   Interval of  start   stop      We can also define an Interval with a starting moment plus a Duration   Instant start B   Instant parse   2016-01-03T00 00 00Z     Interval interval B   Interval of  start B   Duration of  3   ChronoUnit DAYS        Comparing to test for overlaps is easy   Boolean overlaps   interval A overlaps  interval B      You can compare an Interval against another Interval or Instant    abuts contains encloses equals isAfter isBefore overlaps   All of these use the Half-Open approach to defining a span of time where the beginning is inclusive and the ending is exclusive

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Here is a generic method that can be usefull locally          Takes a list and returns all records that have overlapping time ranges      public static IEnumerable lt T gt  GetOverlappedTimes lt T gt  IEnumerable lt T gt  list  Func lt T  bool gt  filter  Func lt T DateTime gt  start  Func lt T  DateTime gt  end                   Selects all records that match filter   on left side and returns all records on right side that overlap          var overlap   from t1 in list                       where filter t1                        from t2 in list                       where  object Equals t1  t2     Don t match the same record on right side                        let in1   start t1                        let out1   end t1                        let in2   start t2                        let out2   end t2                        where in1  lt   out2  amp  amp  out1  gt   in2                       let totover   GetMins in1  out1  in2  out2                        select t2           return overlap             public static void TestOverlap                 var tl1   new TempTimeEntry     ID   1  Name    Bill   In    1 1 08 1 00pm  ToDate    Out    1 1 08 4 00pm  ToDate              var tl2   new TempTimeEntry     ID   2  Name    John   In    1 1 08 5 00pm  ToDate    Out    1 1 08 6 00pm  ToDate              var tl3   new TempTimeEntry     ID   3  Name    Lisa   In    1 1 08 7 00pm  ToDate    Out    1 1 08 9 00pm  ToDate              var tl4   new TempTimeEntry     ID   4  Name    Joe   In    1 1 08 3 00pm  ToDate    Out    1 1 08 8 00pm  ToDate              var tl5   new TempTimeEntry     ID   1  Name    Bill   In    1 1 08 8 01pm  ToDate    Out    1 1 08 8 00pm  ToDate              var list   new List lt TempTimeEntry gt      tl1  tl2  tl3  tl4  tl5            var overlap   GetOverlappedTimes list   TempTimeEntry t1   gt t1 ID  1   TempTimeEntry tIn    gt  tIn In   TempTimeEntry tOut    gt  tOut Out            Console WriteLine   nRecords overlap             foreach  var tl in overlap              Console WriteLine  Name  0  T1In  1  T1Out  2    tl Name  tl In  tl Out           Console WriteLine  Done                 Output              Records overlap              Name Joe T1In 1 1 2008 3 00 00 PM T1Out 1 1 2008 8 00 00 PM             Name Lisa T1In 1 1 2008 7 00 00 PM T1Out 1 1 2008 9 00 00 PM             Done

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The easiest way to do it in my opinion would be to compare if either EndDate1 is before StartDate2 and EndDate2 is before StartDate1   That of course if you are considering intervals where StartDate is always before EndDate

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the simplest   The simplest way is to use a well-engineered dedicated library for date-time work   someInterval overlaps  anotherInterval     java time  amp  ThreeTen-Extra  The best in the business is the java time framework built into Java 8 and later  Add to that the ThreeTen-Extra project that supplements java time with additional classes  specifically the Interval class we need here   As for the language-agnostic tag on this Question  the source code for both projects is available for use in other languages  mind their licenses     Interval  The org threeten extra Interval class is handy  but requires date-time moments  java time Instant objects  rather than date-only values  So we proceed by using the first moment of the day in UTC to represent the date   Instant start   Instant parse   2016-01-01T00 00 00Z     Instant stop   Instant parse   2016-02-01T00 00 00Z       Create an Interval to represent that span of time   Interval interval A   Interval of  start   stop      We can also define an Interval with a starting moment plus a Duration   Instant start B   Instant parse   2016-01-03T00 00 00Z     Interval interval B   Interval of  start B   Duration of  3   ChronoUnit DAYS        Comparing to test for overlaps is easy   Boolean overlaps   interval A overlaps  interval B      You can compare an Interval against another Interval or Instant    abuts contains encloses equals isAfter isBefore overlaps   All of these use the Half-Open approach to defining a span of time where the beginning is inclusive and the ending is exclusive

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As there have been several answers for different languages and environments  here is one for standard ANSI SQL  In standard SQL it is as as simple as  StartDate1  EndDate1  overlaps  StartDate2  EndDate2   assuming all four columns are DATE or TIMESTAMP columns  It returns true if both ranges have at least one day in common  assuming DATE values   However not all DBMS products support that   In PostgreSQL it s also easy to test for inclusion by using date ranges daterange StartDate1  EndDate1    gt  daterange StartDate2  EndDate2   the above returns true if the second range is completely included in the first  which is different to  quot overlaps quot

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Using Java util Date  here what I did       public static boolean checkTimeOverlaps Date startDate1  Date endDate1  Date startDate2  Date endDate2                if  startDate1    null    endDate1    null    startDate2    null    endDate2    null             return false           if   startDate1 getTime    lt   endDate2 getTime     amp  amp   startDate2 getTime    lt   endDate1 getTime                return true           return false

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Here is yet another solution using JavaScript  Specialities of my solution    Handles null values as infinity Assumes that the lower bound is inclusive and the upper bound exclusive  Comes with a bunch of tests   The tests are based on integers but since date objects in JavaScript are comparable you can just throw in two date objects as well  Or you could throw in the millisecond timestamp   Code          Compares to comparable objects to find out whether they overlap     It is assumed that the interval is in the format  from to   read  from is inclusive  to is exclusive      A null value is interpreted as infinity     function intervalsOverlap from1  to1  from2  to2        return  to2     null    from1  lt  to2   amp  amp   to1     null    to1  gt  from2       Tests   describe     function         function generateTest firstRange  secondRange  expected            it JSON stringify firstRange      and     JSON stringify secondRange   function                 expect intervalsOverlap firstRange 0   firstRange 1   secondRange 0   secondRange 1    toBe expected                          describe  no overlap  touching ends    function             generateTest  10 20    20 30   false           generateTest  20 30    10 20   false            generateTest  10 20    20 null   false           generateTest  20 null    10 20   false            generateTest  null 20    20 30   false           generateTest  20 30    null 20   false                describe  do overlap  one end overlaps    function             generateTest  10 20    19 30   true           generateTest  19 30    10 20   true            generateTest  10 20    null 30   true           generateTest  10 20    19 null   true           generateTest  null 30    10 20   true           generateTest  19 null    10 20   true                describe  do overlap  one range included in other range    function             generateTest  10 40    20 30   true           generateTest  20 30    10 40   true            generateTest  10 40    null null   true           generateTest  null null    10 40   true                describe  do overlap  both ranges equal    function             generateTest  10 20    10 20   true            generateTest  null 20    null 20   true           generateTest  10 null    10 null   true           generateTest  null null    null null   true                 Result when run with karma amp jasmine amp PhantomJS      PhantomJS 1 9 8  Linux   Executed 20 of 20 SUCCESS  0 003 secs   0 004 secs

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Split the problem into cases then handle each case   The situation  two date ranges intersect  is covered by two cases - the first date range starts within the second  or the second date range starts within the first

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Here is the code that does the magic    var isOverlapping      A    null    D    null    A  lt   D                amp  amp   C    null    B    null    C  lt   B               amp  amp   A    null    B    null    A  lt   B               amp  amp   C    null    D    null    C  lt   D      Where      A -  1Start B -  1End  C -  2Start  D -  2End   Proof  Check out this test console code gist

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I believe that it is sufficient to say that the two ranges overlap if    StartDate1  lt   EndDate2  and  StartDate2  lt   EndDate1

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The solution posted here did not work for all overlapping ranges      ---------------------- -------A------- ----------------------      ----B1----              ----B2----                  ----B3----                  ----------B4----------                  ----------------B5----------------                         ----B6----  ---------------------- -------A------- ----------------------                        ------B7-------                         ----------B8-----------                            ----B9----                            ----B10-----                            --------B11--------                                         ----B12----                                            ----B13----  ---------------------- -------A------- ----------------------  my working solution was    AND       start date  BETWEEN STARTDATE AND ENDDATE  -- caters for inner and end date outer   OR     end date  BETWEEN STARTDATE AND ENDDATE  -- caters for inner and start date outer   OR    STARTDATE BETWEEN  start date  AND  end date   -- only one needed for outer range where dates are inside

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The solution posted here did not work for all overlapping ranges      ---------------------- -------A------- ----------------------      ----B1----              ----B2----                  ----B3----                  ----------B4----------                  ----------------B5----------------                         ----B6----  ---------------------- -------A------- ----------------------                        ------B7-------                         ----------B8-----------                            ----B9----                            ----B10-----                            --------B11--------                                         ----B12----                                            ----B13----  ---------------------- -------A------- ----------------------  my working solution was    AND       start date  BETWEEN STARTDATE AND ENDDATE  -- caters for inner and end date outer   OR     end date  BETWEEN STARTDATE AND ENDDATE  -- caters for inner and start date outer   OR    STARTDATE BETWEEN  start date  AND  end date   -- only one needed for outer range where dates are inside

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StartA  lt   EndB   and   EndA  gt   StartB  Proof  Let ConditionA Mean that DateRange A Completely After DateRange B                           ---- DateRange A ------   ---Date Range B -----                               True if StartA  gt  EndB  Let ConditionB Mean that DateRange A is Completely Before DateRange B  ---- DateRange A -----                                                        ---Date Range B ----    True if EndA  lt  StartB  Then Overlap exists if Neither A Nor B is true -  If one range is neither completely after the other  nor completely before the other  then they must overlap   Now one of De Morgan s laws says that  Not  A Or B    lt   gt   Not A And Not B Which translates to   StartA  lt   EndB   and   EndA  gt   StartB   NOTE  This includes conditions where the edges overlap exactly   If you wish to exclude that  change the  gt   operators to  gt   and  lt    to  lt   NOTE2  Thanks to  Baodad  see this blog  the actual overlap is least of    endA-startA  endA - startB  endB-startA  endB - startB    StartA  lt   EndB   and   EndA  gt   StartB   StartA  lt   EndB   and   StartB  lt   EndA   NOTE3  Thanks to  tomosius  a shorter version reads  DateRangesOverlap   max start1  start2   lt  min end1  end2  This is actually a syntactical shortcut for what is a longer implementation  which includes extra checks to verify that the start dates are on or before the endDates   Deriving this from above  If start and end dates can be out of order  i e   if it is possible that startA  gt  endA or startB  gt  endB  then you also have to check that they are in order  so that means you have to add two additional validity rules   StartA  lt   EndB  and  StartB  lt   EndA  and  StartA  lt   EndA  and  StartB  lt   EndB  or   StartA  lt   EndB  and  StartA  lt   EndA  and  StartB  lt   EndA  and  StartB  lt   EndB  or   StartA  lt   Min EndA  EndB  and  StartB  lt   Min EndA  EndB   or   Max StartA  StartB   lt   Min EndA  EndB  But to implement Min   and Max    you have to code   using C ternary for terseness     StartA  gt  StartB  Start A  StartB   lt    EndA  lt  EndB  EndA  EndB

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The easiest way to do it in my opinion would be to compare if either EndDate1 is before StartDate2 and EndDate2 is before StartDate1   That of course if you are considering intervals where StartDate is always before EndDate

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I would do   StartDate1 IsBetween StartDate2  EndDate2     EndDate1 IsBetween StartDate2  EndDate2    Where IsBetween is something like       public static bool IsBetween this DateTime value  DateTime left  DateTime right            return  value  gt  left  amp  amp  value  lt  right      value  lt  left  amp  amp  value  gt  right

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This was my javascript solution with moment js      Current row dates var dateStart   moment  2014-08-01    YYYY-MM-DD    var dateEnd   moment  2014-08-30    YYYY-MM-DD        Check with dates above var rangeUsedStart   moment  2014-08-02    YYYY-MM-DD    var rangeUsedEnd   moment  2014-08-015    YYYY-MM-DD        Range covers other   if  dateStart  lt   rangeUsedStart   amp  amp   rangeUsedEnd  lt   dateEnd         return false       Range intersects with other start   if  dateStart  lt   rangeUsedStart   amp  amp   rangeUsedStart  lt   dateEnd         return false       Range intersects with other end   if  dateStart  lt   rangeUsedEnd   amp  amp   rangeUsedEnd  lt   dateEnd         return false        All good return true

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public static class NumberExtensionMethods               public static Boolean IsBetween this Int64 value  Int64 Min  Int64 Max                        if  value  gt   Min  amp  amp  value  lt   Max  return true              else return false                     public static Boolean IsBetween this DateTime value  DateTime Min  DateTime Max                        Int64 numricValue   value Ticks              Int64 numericStartDate   Min Ticks              Int64 numericEndDate   Max Ticks               if  numricValue IsBetween numericStartDate  numericEndDate                                  return true                             return false                   public static Boolean IsOverlap DateTime startDate1  DateTime endDate1  DateTime startDate2  DateTime endDate2                        Int64 numericStartDate1   startDate1 Ticks              Int64 numericEndDate1   endDate1 Ticks              Int64 numericStartDate2   startDate2 Ticks              Int64 numericEndDate2   endDate2 Ticks               if  numericStartDate2 IsBetween numericStartDate1  numericEndDate1                     numericEndDate2 IsBetween numericStartDate1  numericEndDate1                     numericStartDate1 IsBetween numericStartDate2  numericEndDate2                     numericEndDate1 IsBetween numericStartDate2  numericEndDate2                                 return true                             return false               if  IsOverlap startdate1  enddate1  startdate2  enddate2                                 Console WriteLine  IsOverlap

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Easy solution   compare the two dates       A   the one with smaller start date  B   the one with bigger start date if A end  lt  B start      return false return true

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Below query gives me the ids  for which the supplied date range  start and end dates overlaps with any of the dates  start and end dates  in my table name  select id from table name where  START DT TM  gt    END DATE TIME   OR     END DT TM BETWEEN  START DATE TIME  AND  END DATE TIME

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def if lives overlap s1  s2        quot  quot  quot      https   stackoverflow com a 325964 827391         5   10    15  20         ----------------     s1  -----     s2            -----      gt  gt  gt  if lives overlap s1   start   datetime 2020  1  5                                  end   datetime 2020  1  10                             s2   start   datetime 2020  1  15                                  end   datetime 2020  1  20        False       s1            -----     s2  -----      gt  gt  gt  if lives overlap s1   start   datetime 2020  1  15                                  end   datetime 2020  1  20                             s2   start   datetime 2020  1  5                                  end   datetime 2020  1  10        False      s1  ----------     s2       ----------      gt  gt  gt  if lives overlap s1   start   datetime 2020  1  5                                  end   datetime 2020  1  15                             s2   start   datetime 2020  1  10                                  end   datetime 2020  1  20        True      s1       ----------     s2  ----------      gt  gt  gt  if lives overlap s1   start   datetime 2020  1  10                                  end   datetime 2020  1  20                             s2   start   datetime 2020  1  5                                  end   datetime 2020  1  15        True       s1  ---------------     s2       -----      gt  gt  gt  if lives overlap s1   start   datetime 2020  1  5                                  end   datetime 2020  1  20                             s2   start   datetime 2020  1  10                                  end   datetime 2020  1  15        True      s1       -----     s2  ---------------      gt  gt  gt  if lives overlap s1   start   datetime 2020  1  10                                  end   datetime 2020  1  15                             s2   start   datetime 2020  1  5                                  end   datetime 2020  1  20        True      quot  quot  quot       return  s1  start    lt   s2  end    and  s1  end    gt   s2  start

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StartA  lt   EndB   and   EndA  gt   StartB  Proof  Let ConditionA Mean that DateRange A Completely After DateRange B                           ---- DateRange A ------   ---Date Range B -----                               True if StartA  gt  EndB  Let ConditionB Mean that DateRange A is Completely Before DateRange B  ---- DateRange A -----                                                        ---Date Range B ----    True if EndA  lt  StartB  Then Overlap exists if Neither A Nor B is true -  If one range is neither completely after the other  nor completely before the other  then they must overlap   Now one of De Morgan s laws says that  Not  A Or B    lt   gt   Not A And Not B Which translates to   StartA  lt   EndB   and   EndA  gt   StartB   NOTE  This includes conditions where the edges overlap exactly   If you wish to exclude that  change the  gt   operators to  gt   and  lt    to  lt   NOTE2  Thanks to  Baodad  see this blog  the actual overlap is least of    endA-startA  endA - startB  endB-startA  endB - startB    StartA  lt   EndB   and   EndA  gt   StartB   StartA  lt   EndB   and   StartB  lt   EndA   NOTE3  Thanks to  tomosius  a shorter version reads  DateRangesOverlap   max start1  start2   lt  min end1  end2  This is actually a syntactical shortcut for what is a longer implementation  which includes extra checks to verify that the start dates are on or before the endDates   Deriving this from above  If start and end dates can be out of order  i e   if it is possible that startA  gt  endA or startB  gt  endB  then you also have to check that they are in order  so that means you have to add two additional validity rules   StartA  lt   EndB  and  StartB  lt   EndA  and  StartA  lt   EndA  and  StartB  lt   EndB  or   StartA  lt   EndB  and  StartA  lt   EndA  and  StartB  lt   EndA  and  StartB  lt   EndB  or   StartA  lt   Min EndA  EndB  and  StartB  lt   Min EndA  EndB   or   Max StartA  StartB   lt   Min EndA  EndB  But to implement Min   and Max    you have to code   using C ternary for terseness     StartA  gt  StartB  Start A  StartB   lt    EndA  lt  EndB  EndA  EndB

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Here s my solution in Java  which works on unbounded intervals too    private Boolean overlap  Timestamp startA  Timestamp endA                           Timestamp startB  Timestamp endB        return  endB    null    startA    null     startA after endB            amp  amp   endA    null    startB    null     endA before startB

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StartA  lt   EndB   and   EndA  gt   StartB  Proof  Let ConditionA Mean that DateRange A Completely After DateRange B                           ---- DateRange A ------   ---Date Range B -----                               True if StartA  gt  EndB  Let ConditionB Mean that DateRange A is Completely Before DateRange B  ---- DateRange A -----                                                        ---Date Range B ----    True if EndA  lt  StartB  Then Overlap exists if Neither A Nor B is true -  If one range is neither completely after the other  nor completely before the other  then they must overlap   Now one of De Morgan s laws says that  Not  A Or B    lt   gt   Not A And Not B Which translates to   StartA  lt   EndB   and   EndA  gt   StartB   NOTE  This includes conditions where the edges overlap exactly   If you wish to exclude that  change the  gt   operators to  gt   and  lt    to  lt   NOTE2  Thanks to  Baodad  see this blog  the actual overlap is least of    endA-startA  endA - startB  endB-startA  endB - startB    StartA  lt   EndB   and   EndA  gt   StartB   StartA  lt   EndB   and   StartB  lt   EndA   NOTE3  Thanks to  tomosius  a shorter version reads  DateRangesOverlap   max start1  start2   lt  min end1  end2  This is actually a syntactical shortcut for what is a longer implementation  which includes extra checks to verify that the start dates are on or before the endDates   Deriving this from above  If start and end dates can be out of order  i e   if it is possible that startA  gt  endA or startB  gt  endB  then you also have to check that they are in order  so that means you have to add two additional validity rules   StartA  lt   EndB  and  StartB  lt   EndA  and  StartA  lt   EndA  and  StartB  lt   EndB  or   StartA  lt   EndB  and  StartA  lt   EndA  and  StartB  lt   EndA  and  StartB  lt   EndB  or   StartA  lt   Min EndA  EndB  and  StartB  lt   Min EndA  EndB   or   Max StartA  StartB   lt   Min EndA  EndB  But to implement Min   and Max    you have to code   using C ternary for terseness     StartA  gt  StartB  Start A  StartB   lt    EndA  lt  EndB  EndA  EndB

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This was my solution  it returns true when the values don t overlap   X START 1 Y END 1  A START 2 B END 2  TEST1   X  lt   A    X  gt   B           amp  amp  TEST2   Y  gt   B    Y  lt   A            amp  amp   TEST3   X  gt   B    Y  lt   A    X-------------Y     A-----B  TEST1   TRUE TEST2   TRUE TEST3   FALSE RESULT  FALSE  ---------------------------------------  X---Y       A---B  TEST1   TRUE TEST2   TRUE TEST3   TRUE RESULT  TRUE  ---------------------------------------        X---Y A---B  TEST1   TRUE TEST2   TRUE TEST3   TRUE RESULT  TRUE  ---------------------------------------       X----Y A---------------B  TEST1   FALSE TEST2   FALSE TEST3   FALSE RESULT  FALSE

[datetime] Determine Whether Two Date Ranges Overlap

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