Priority Queues

Balanced binary tree implementation of priority queues in Kotlin

Time Complexities

1. Insertion: O(log n)
2. Removal: O(log n)
3. Returning max or min: O(1)

Implementation

1. Min Priority Queues:
   Removing and inserting to the priority queue uses helper functions heapifyDown() and heapifyUp() to maintain heap properties.

   class MinPriorityQueue<T: Comparable<T>> : PriorityQueue<T>() {
       fun removeMin(): T? {
           if (isEmpty()) return null
           if (size == 1) return heapArray.removeAt(0)
   
           val minElement = heapArray[0]
   
           heapArray[0] = heapArray.removeAt(size - 1)
           heapifyDown()
   
           return minElement
       }
   
       fun insertItem(item: T) {
           heapArray.add(item)
           heapifyUp(size - 1)
       }
   
       fun min(): T? {
           return heapArray.firstOrNull()
       }
   }

2. Max Priority Queues:
   They also maintain heap properties using the helper functions.

   class MaxPriorityQueue<T: Comparable<T>> : PriorityQueue<T>() {
       fun removeMax(): T? {
           if (isEmpty()) return null
           if (size == 1) return heapArray.removeAt(0)
   
           val maxElement = heapArray[0]
           heapArray[0] = heapArray.removeAt(size - 1)
           heapifyDown()
   
           return maxElement
       }
   
       fun insertItem(item: T) {
           heapArray.add(item)
           heapifyUp(size - 1)
       }
   
       fun max(): T? {
           return heapArray.firstOrNull()
       }
   }