heapq

Heap queue algorithm (a.k.a. priority queue).

Heaps are arrays for which a[k] <= a[2*k+1] and a[k] <= a[2*k+2] for
all k, counting elements from 0.  For the sake of comparison,
non-existing elements are considered to be infinite.  The interesting
property of a heap is that a[0] is always its smallest element.

Usage:

heap = []            # creates an empty heap
heappush(heap, item) # pushes a new item on the heap
item = heappop(heap) # pops the smallest item from the heap
item = heap[0]       # smallest item on the heap without popping it
heapify(x)           # transforms list into a heap, in-place, in linear time
item = heapreplace(heap, item) # pops and returns smallest item, and adds
                               # new item; the heap size is unchanged

Our API differs from textbook heap algorithms as follows:

- We use 0-based indexing.  This makes the relationship between the
  index for a node and the indexes for its children slightly less
  obvious, but is more suitable since Python uses 0-based indexing.

- Our heappop() method returns the smallest item, not the largest.

These two make it possible to view the heap as a regular Python list
without surprises: heap[0] is the smallest item, and heap.sort()
maintains the heap invariant!

Functions

heapify

heapify(heap, /)

  Transform list into a heap, in-place, in O(len(heap)) time.

heappop

heappop(heap, /)

  Pop the smallest item off the heap, maintaining the heap invariant.

heappush

heappush(heap, item, /)

  Push item onto heap, maintaining the heap invariant.

heappushpop

heappushpop(heap, item, /)

  Push item on the heap, then pop and return the smallest item from the heap.

  The combined action runs more efficiently than heappush() followed by
  a separate call to heappop().

heapreplace

heapreplace(heap, item, /)

  Pop and return the current smallest value, and add the new item.

  This is more efficient than heappop() followed by heappush(), and can be
  more appropriate when using a fixed-size heap.  Note that the value
  returned may be larger than item!  That constrains reasonable uses of
  this routine unless written as part of a conditional replacement:

      if item > heap[0]:
          item = heapreplace(heap, item)

merge

merge(*iterables, key=None, reverse=False)

  Merge multiple sorted inputs into a single sorted output.

      Similar to sorted(itertools.chain(*iterables)) but returns a generator,
      does not pull the data into memory all at once, and assumes that each of
      the input streams is already sorted (smallest to largest).

      >>> list(merge([1,3,5,7], [0,2,4,8], [5,10,15,20], [], [25]))
      [0, 1, 2, 3, 4, 5, 5, 7, 8, 10, 15, 20, 25]

      If *key* is not None, applies a key function to each element to determine
      its sort order.

      >>> list(merge(['dog', 'horse'], ['cat', 'fish', 'kangaroo'], key=len))
      ['dog', 'cat', 'fish', 'horse', 'kangaroo']

nlargest

nlargest(n, iterable, key=None)

  Find the n largest elements in a dataset.

      Equivalent to:  sorted(iterable, key=key, reverse=True)[:n]

nsmallest

nsmallest(n, iterable, key=None)

  Find the n smallest elements in a dataset.

      Equivalent to:  sorted(iterable, key=key)[:n]