Implementing a Priority Queue with a Sequence

• Can we use a list or an array to maintain a priority queue?
• Using an unsorted sequence
  • Insertion is O(1), just put it anywhere
  • Extraction is O(n), search for the largest/smallest element
  • Extraction is either pop/top in STL or minElement/removeMin
  • Note this is really big Theta(n), since best case = worst case
  • Does it matter if we use a list or vector?
• Using a sorted sequence
  • We need to maintain a sorted list with easy acces to the maximium element
  • Extraction becomes O(1)
  • Insertion becomes O(n)
  • But insertion can be O(1) best case
• Using a binary search tree
  • Can we find the minimum/maximum element in a BST?
  • Maximum - go right as far as we can.
  • Consider
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  • ExtractMax

    ExtractMax(T, current)
    (0) If T.hasRightChild(current) 
    (1)    current = T.rightChild(current)
    (3)    ExtractMax(T, current)
    (4) if T.hasLeftChild(current)
    (5)    T.setRightChild(T.parent(current), T.LeftChild(current))
    (6) T.delete(current);
           

  • Here I will assume quite a bit about setRightChild
    • If the first node is the root the new child is promoted to be the root.
  • Is this better?
  • What is the timing analysis?
  • Where does it break down?