# 5.4 heapq -- Heap queue algorithm

New in version 2.3.

This module provides an implementation of the heap queue algorithm, also known as the priority queue algorithm.

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

The API below differs from textbook heap algorithms in two aspects: (a) We use zero-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 zero-based indexing. (b) Our pop method returns the smallest item, not the largest (called a "min heap" in textbooks; a "max heap" is more common in texts because of its suitability for in-place sorting).

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!

To create a heap, use a list initialized to `[]`, or you can transform a populated list into a heap via function heapify().

The following functions are provided:

 heappush( heap, item)
Push the value item onto the heap, maintaining the heap invariant.

 heappop( heap)
Pop and return the smallest item from the heap, maintaining the heap invariant. If the heap is empty, IndexError is raised.

 heapify( x)
Transform list x into a heap, in-place, in linear time.

 heapreplace( heap, item)
Pop and return the smallest item from the heap, and also push the new item. The heap size doesn't change. If the heap is empty, IndexError is raised. 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)
```

Example of use:

```>>> from heapq import heappush, heappop
>>> heap = []
>>> data = [1, 3, 5, 7, 9, 2, 4, 6, 8, 0]
>>> for item in data:
...     heappush(heap, item)
...
>>> ordered = []
>>> while heap:
...     ordered.append(heappop(heap))
...
>>> print ordered
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
>>> data.sort()
>>> print data == ordered
True
>>>
```

The module also offers two general purpose functions based on heaps.

 nlargest( n, iterable[, key])
Return a list with the n largest elements from the dataset defined by iterable. key, if provided, specifies a function of one argument that is used to extract a comparison key from each element in the iterable: "key=str.lower"Equivalent to: "sorted(iterable, key=key, reverse=True)[:n]" New in version 2.4. Changed in version 2.5: Added the optional key argument.

 nsmallest( n, iterable[, key])
Return a list with the n smallest elements from the dataset defined by iterable. key, if provided, specifies a function of one argument that is used to extract a comparison key from each element in the iterable: "key=str.lower"Equivalent to: "sorted(iterable, key=key)[:n]" New in version 2.4. Changed in version 2.5: Added the optional key argument.

Both functions perform best for smaller values of n. For larger values, it is more efficient to use the sorted() function. Also, when `n==1`, it is more efficient to use the builtin min() and max() functions.

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