Understanding how to create a heap in Python

Question

The collections.Count.most_common function in Python uses the heapq module to return the count of the most common word in a file, for instance.

Answer 1

Here's another variation based on Sedgewick

The heap is represented internally in an array where if a node is at k, it's children are at 2*k and 2*k + 1. The first element of the array is not used, to make the math more convenient.

To add a new element to the heap, you append it to the end of the array and then call swim repeatedly until the new element finds its place in the heap.

To delete the root, you swap it with the last element in the array, delete it and then call sink until the swapped element finds its place.

swim(k):
  while k > 1 and less(k/2, k):
    exch(k, k/2)
    k = k/2

sink(k):
  while 2*k <= N:
    j = 2*k
    if j < N and less(j, j+1):
      j++
    if not less(k, j):
      break
    exch(k, j)
    k = j

Here's a visualization of heap insert, inserting the first 15 letters of the alphabet: [a-o]