Priority Queues

• A Priority Queue is an ADT for prioritized data
  • Supports arbitrary element insertion
  • And Maximum priority element extraction
• Priority is the important element here
  • Time of insertion is irrelevent
  • Position is unknown
• Examples
  • Run time queue with priorities.
  • Waiting list (flights)
• The ADT
  • size()
  • isEmpty()
  • insertItem(k,e) (key and element)
  • minElement()
  • minKey()
  • removeMin()
  • Note: often we have a removeMax in place of remove min.
  • Note: again, removeMin (and such) may or may not return a value, if not, minElement followed by removeMin must be executed.
• Algorithm: QueueSort

       A is a list or vector that supports isEmpty, removeFirst and insertLast
       P is a priority queue
  
  QSort(A,s) 
  (1)   while !A.isEmpty()
  (2)      P.insertItem(A.removeFirst())
  (3)   while !P.isEmpty()
  (4)      A.insertLast(P.removeMin())
  
     

  • Note, this is just insertion sort
  • Timing of this sort?
  • Can we give an upper bound on insertItem and/or removeMin?
• Comparators
  • Goodrich discusses a comparator pattern
  • This is useful when comparing multiple values to form a single key
  • For example a runtime queue with priorities
    • A priority level determines the priority group a process is in
    • A nice level determines the priority within the group
    • Last reciently run determines the priority when all else is equal

    bool operator <(p1, p2) {
        if (p1.level != p2.level) 
            return (p1.level < p2.level)
        else if (p1.nice != p2.nice) 
            return(p1.nice < p2.nice
        else
            return(p1.lastrun < p2.lastrun)
    }
           

  • You can also define a three way compare
    • Return negative if the first is smaller
    • Return 0 if the elements are equal
    • Return positive if the second is smaller
    • see strcmp from the C string library (NOT C++)
• STL priority_queue
  • #include <
  • priority_queue<type> ID
  • size()
  • empty()
  • push(e)
  • top() - returns the element with largest value
  • pop() - removes the element with largest value
  • Example