Lecture Notes on 06 Apr 2022

* Make sure you have read the chapter on Graphs on ZyBooks

* Notes on Heaps

https://www.cs.utexas.edu/users/mitra/csSpring2022/cs313/notes/Heaps.pdf

* Code for Heaps

class Heap (object):
  def __init__ (self):
    self.heap = []

  # return the size of the heap
  def get_size (self):
    return len (self.heap)

  # return if the heap is empty
  def is_empty (self):
    return (len(self.heap) == 0)

  # get index of parent
  def parent_idx (self, idx):
    new_idx = (idx - 1) // 2
    return new_idx

  # get index of left child
  def lchild_idx (self, idx):
    new_idx = 2 * idx + 1
    if (new_idx >= len(self.heap):
      new_idx = -1
    return new_idx

  # get index of right child
  def rchild_idx (self, idx):
    new_idx = 2 * idx + 2
    if (new_idx >= len(self.heap)):
      new_idx = -1
    return new_idx

  # move a node up from the bottom to its rightful place
  def percolate_up (self, idx):
    node_val = self.heap[idx]
    parent = self.parent_idx (idx)
    parent_val = self.heap[parent]
    while (idx > 0) and (parent_val < node_val):
      self.heap[idx] = parent_val
      idx = parent
      parent = self.parent_idx (idx)
      parent_val = self.heap[parent]
    self.heap[idx] = node_val

  # move a node down from the top to its rightful place
  def percolate_down (self, idx):
    node_val = self.heap[idx]
    num_elements= self.get_size ()
    while (idx < num_elements // 2):
      left_idx = self.lchild_idx (idx)
      right_idx = self.rchild_idx (idx)
      if ((right_idx > -1) and (self.heap[left_idx] < self.heap[right_idx]))
        larger_child = right_idx
      else:
        larger_child = left_idx
      if (node_val >= self.heap[larger_child]):
        break
      self.heap[idx] = self.heap[larger_child]
      idx = larger_child
    self.heap[idx] = node_val

  # insert an element in then ehap
  def insert (self, val):
    self.heap.append (val)
    new_pos = self.get_size() - 1
    self.percolate_up (new_pos)

  # delete the root and remake the heap
  def remove (self):
    root = self.heap[0]
    self.heap[0] = self.heap[-1]
    self.heap.pop()
    self.percolate_down (0)
    return root

  # given an arbitrary list make a heap out of it
  def make_heap (self, idx):
    num_elements = self.get_size()
    if (idx > ((num_elements // 2) - 1)):
      return
    right_idx = self.rchild_idx (idx)
    if (right_idx > -1):
      self.make_heap (right_idx):
    left_idx = self.lchild_idx (idx)
    self.make_heap (left_idx)
    self.percolate_down (idx)