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13
Priority Queues Written by Irina Galata

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Queues are lists that maintain the order of elements using first in, first out (FIFO) ordering. A priority queue is another version of a queue. However, instead of using FIFO ordering, elements are dequeued in priority order.

A priority queue can have either a:

  • Max-priority: The element at the front is always the largest.
  • Min-priority: The element at the front is always the smallest.

A priority queue is especially useful when you need to identify the maximum or minimum value within a list of elements.

In this chapter, you’ll learn the benefits of a priority queue and build one by leveraging the existing queue and heap data structures that you studied in previous chapters.

Applications

Some useful applications of a priority queue include:

  • Dijkstra’s algorithm: Uses a priority queue to calculate the minimum cost.
  • A* pathfinding algorithm: Uses a priority queue to track the unexplored routes that will produce the path with the shortest length.
  • Heap sort: Many heap sorts use a priority queue.
  • Huffman coding: Useful for building a compression tree. A min-priority queue is used to repeatedly find two nodes with the smallest frequency that don’t yet have a parent node.

Priority queues have many more applications and practical uses; the list above represents only a handful.

Common operations

In Chapter 5, “Queues”, you established the following interface for queues:

interface Queue<T: Any> {

  fun enqueue(element: T): Boolean

  fun dequeue(): T?

  val count: Int
    get

  val isEmpty: Boolean
    get() = count == 0

  fun peek(): T?
}

Implementation

You can create a priority queue in the following ways:

// 1
abstract class AbstractPriorityQueue<T: Any> : Queue<T> {

  // 2
  abstract val heap: Heap<T>
    get

  // more to come ...  
}
  // 1
  override fun enqueue(element: T): Boolean {
    heap.insert(element)
    return true
  }

  // 2
  override fun dequeue() = heap.remove()

  // 3
  override val count: Int
    get() = heap.count  

  // 4
  override fun peek() = heap.peek()

Using Comparable objects

AbstractPriorityQueue<T> implements the Queue<T> interface delegating to a Heap<T>. You can implement this using either Comparable<T> objects or a Comparator<T>. In this example, you’ll use the former.

class ComparablePriorityQueueImpl<T : Comparable<T>> :
  AbstractPriorityQueue<T>() {

  override val heap = ComparableHeapImpl<T>()
}
"max priority queue" example {
  // 1
  val priorityQueue = ComparablePriorityQueueImpl<Int>()
  // 2
  arrayListOf(1, 12, 3, 4, 1, 6, 8, 7).forEach {
    priorityQueue.enqueue(it)
  }
  // 3
  while (!priorityQueue.isEmpty) {
    println(priorityQueue.dequeue())
  }
}
---Example of max priority queue---
12
8
7
6
4
3
1
1

Using Comparator objects

Providing different Comparator<T> interface implementations allows you to choose the priority criteria.

class ComparatorPriorityQueueImpl<T: Any>(
  private val comparator: Comparator<T>
) : AbstractPriorityQueue<T>() {

  override val heap = ComparatorHeapImpl(comparator)
}
"min priority queue" example {
  // 1
  val stringLengthComparator = Comparator<String> { o1, o2 ->
    val length1 = o1?.length ?: -1
    val length2 = o2?.length ?: -1
    length1 - length2
  }
  // 2
  val priorityQueue = ComparatorPriorityQueueImpl(stringLengthComparator)
  // 3
  arrayListOf("one", "two", "three", "four", "five", "six", "seven", "eight", "nine").forEach {
    priorityQueue.enqueue(it)
  }
  // 4
  while (!priorityQueue.isEmpty) {
    println(priorityQueue.dequeue())
  }
}
---Example of min priority queue---
three
eight
seven
nine
four
five
one
two
six

Challenges

Challenge 1: Constructing ArrayList priority queues

You learned to use a heap to construct a priority queue by implementing the Queue interface. Now, construct a priority queue using an ArrayList:

interface Queue<T: Any> {

  fun enqueue(element: T): Boolean

  fun dequeue(): T?

  val count: Int
    get

  val isEmpty: Boolean
    get() = count == 0

  fun peek(): T?
}

Solution 1

Recall that a priority queue dequeues elements in priority order. It could either be a min or max priority queue. To make an array-based priority queue, you need to implement the Queue interface. Instead of using a heap, you can use an array list.

// 1
abstract class AbstractPriorityQueueArrayList<T: Any> : Queue<T> {

  // 2
  protected val elements = ArrayList<T>()

  // 3
  abstract fun sort()

  // more to come ...
}
override val count: Int
  get() = elements.size

override fun peek() = elements.firstOrNull()
override fun dequeue() =
  if (isEmpty) null else elements.removeAt(0)
override fun enqueue(element: T): Boolean {
  // 1
  elements.add(element)
  // 2
  sort()
  // 3
  return true
}
override fun toString() = elements.toString()
class ComparablePriorityQueueArrayList<T : Comparable<T>> : AbstractPriorityQueueArrayList<T>() {
  override fun sort() {
    Collections.sort(elements)
  }
}
class ComparatorPriorityQueueArrayList<T: Any>(
  private val comparator: Comparator<T>
) : AbstractPriorityQueueArrayList<T>() {
  override fun sort() {
    Collections.sort(elements, comparator)
  }
}
class CustomPriorityQueueArrayList<T : Comparable<T>> : AbstractPriorityQueueArrayList<T>() {
  override fun sort() {
    var index = count - 2
    while (index >= 0 &&
      elements[index + 1].compareTo(elements[index]) > 0) {
      swap(index, index + 1)
      index--;
    }
  }

  private fun swap(i: Int, j: Int) {
    val tmp = elements[i]
    elements[i] = elements[j]
    elements[j] = tmp
  }
}
"max priority array list based queue" example {
  val priorityQueue = CustomPriorityQueueArrayList<Int>()
  arrayListOf(1, 12, 3, 4, 1, 6, 8, 7).forEach {
    priorityQueue.enqueue(it)
  }
  priorityQueue.enqueue(5)
  priorityQueue.enqueue(0)
  priorityQueue.enqueue(10)
  while (!priorityQueue.isEmpty) {
    println(priorityQueue.dequeue())
  }
}

Challenge 2: Sorting

Your favorite concert was sold out. Fortunately, there’s a waitlist for people who still want to go. However, the ticket sales will first prioritize someone with a military background, followed by seniority.

data class Person(
  val name: String,
  val age: Int,
  val isMilitary: Boolean)

Solution 2

Given a list of people on the waitlist, you would like to prioritize the people in the following order:

object MilitaryPersonComparator : Comparator<Person> {
  override fun compare(o1: Person, o2: Person): Int {
    if (o1.isMilitary && !o2.isMilitary) {
      return 1
    } else if (!o1.isMilitary && o2.isMilitary) {
      return -1
    } else if (o1.isMilitary && o2.isMilitary) {
      return o1.age.compareTo(o2.age)
    }
    return 0
  }
}
  "concert line" example {
    val p1 = Person("Josh", 21, true)
    val p2 = Person("Jake", 22, true)
    val p3 = Person("Clay", 28, false)
    val p4 = Person("Cindy", 28, false)
    val p5 = Person("Sabrina", 30, false)
    val priorityQueue = ComparatorPriorityQueueImpl(MilitaryPersonComparator)
    arrayListOf(p1, p2, p3, p4, p5).forEach {
      priorityQueue.enqueue(it)
    }
    while (!priorityQueue.isEmpty) {
      println(priorityQueue.dequeue())
    }
  }
---Example of concert line---
Jake
Josh
Cindy
Clay
Sabrina

Key points

  • A priority queue is often used to find the element in priority order.
  • The AbstractPriorityQueue<T> implementation creates a layer of abstraction by focusing on key operations of a queue and leaving out additional functionality provided by the heap data structure.
  • This makes the priority queue’s intent clear and concise. Its only job is to enqueue and dequeue elements, nothing else.
  • The AbstractPriorityQueue<T> implementation is another good example of Composition over (implementation) inheritance.

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