Min heaps are one of my favorite data structures.

min_heap.py

class MinHeap(object):
   def __init__(self):
      self.a = []

   def insert(self, value):
      self.a.append(value)
      i = len(self.a) - 1
      parent = (i - 1) // 2
      while i != 0 and self.a[parent] > self.a[i]:
         self.a[parent], self.a[i] = self.a[i], self.a[parent]
         i = parent
         parent = (i - 1) // 2

   def remove(self):
      if len(self.a) == 0:
         return None
      elif len(self.a) == 1:
         return self.a.pop()

      value = self.a[0]
      self.a[0] = self.a.pop()

      i = 0
      while True:
         left = 2 * i + 1
         right = 2 * i + 2
         smallest = i
         if left < len(self.a) and self.a[smallest] > self.a[left]:
            smallest = left
         if right < len(self.a) and self.a[smallest] > self.a[right]:
            smallest = right
         if smallest != i:
            self.a[i], self.a[smallest] = self.a[smallest], self.a[i]
            i = smallest
         else:
            break

      return value

def heapsort(a):
   h = MinHeap()
   for x in a:
      h.insert(x)
   for i in range(len(a)):
      a[i] = h.remove()

if __name__ == '__main__':
   import random

   h = MinHeap()

   a = [random.randint(0, 100) for _ in range(10)]
   heapsort(a)
   print(a)