# priority_queue big o notation with vector and deque

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What's the big o notation for push() and pop() in priority_queue with vector or deque as its underlying container.
I can't find this anywhere.
I'm guessing linear complexity at worst for push() because it has to search for right place to insert. Edited by lride

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The complexity should be logarithmic in the size of the queue, regardless of which of those underlying containers you are using (but expect a larger constant in front of it for deque). I can try to justify my answer but I don't have the time right now.

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[quote name='Álvaro' timestamp='1353364794' post='5002480']
The complexity should be logarithmic in the size of the queue, regardless of which of those underlying containers you are using
[/quote]
What?!!
Can someone please tell me the pro/cons and big o notation of having which particular underlying containers in a priority_queue[list]
[*]set
[*]vector
[*]list
[*]deque
[/list]

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Talked in IM, it probably isn't homework.

Consider the underlying container.

A set is a tree. What is the complexity of adding and removing from the beginning and end of a tree? At worst you need to shuffle your way back up the tree to balance it.

A vector is an array. What is the complexity of adding and removing from the beginning and end of an array? At worst you need to move every single element in the array over by one space.

A list is a linked list. What is the complexity of adding and removing from the beginning and ending of a list? At worst you need to move some pointers.

A deque is specially designed for this purpose, it is a linked list of arrays. What is the complexity of adding or removing from the endpoints of a list-of-arrays? Endpoint manipulation at worst requires adding a page.

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[quote name='lride' timestamp='1353365896' post='5002486']
[quote name='Álvaro' timestamp='1353364794' post='5002480']
The complexity should be logarithmic in the size of the queue, regardless of which of those underlying containers you are using
[/quote]
What?!!
Can someone please tell me the pro/cons and big o notation of having which particular underlying containers in a priority_queue[list]
[*]set
[*]vector
[*]list
[*]deque
[/list]
[/quote]
I'm pretty sure [font=courier new,courier,monospace]set[/font] and [font=courier new,courier,monospace]list[/font] can't be used in a [font=courier new,courier,monospace]priority_queue[/font], as one of the basic requirements for the underlying storage container of a [font=courier new,courier,monospace]priority_queue[/font] is that it must have random access iterators. On that list, only [font=courier new,courier,monospace]deque[/font] and [font=courier new,courier,monospace]vector[/font] meet that requirement. [font=courier new,courier,monospace]list[/font] and [font=courier new,courier,monospace]set[/font] have bidirectional iterators.

[font=courier new,courier,monospace]vector[/font] and [font=courier new,courier,monospace]deque[/font] allow for constant-time insertion/deletion to/from the end of the container, as well as constant-time random element access. You might be surprised about this for deque, but behind the scenes, it's not using a naive double linked list (as some might believe); rather, it's using a paging technique.

frob obviously wants you to think about it all, so I won't give answers away, but here's some simple answers (but seriously try to think about it and answer frob's questions before peaking):
[spoiler]
[code]
list-based priority_queue: O(impossible) for everything
set-based priority_queue: O(impossible) for everything
vector-based priority_queue: O(log(n)) for push/pop
deque-based priority_queue: O(log(n)) for push/pop
[/code]
[/spoiler]

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Why would pop() be log n? It's just removing an element from the end. And how does priority_queue have all of its element sorted?

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[quote name='lride' timestamp='1353384159' post='5002568']
Why would pop() be log n? It's just removing an element from the end. And how does priority_queue have all of its element sorted?
[/quote]

priority_queue implements basically a [url="http://en.wikipedia.org/wiki/Heap_(data_structure)"]heap[/url]. After popping the element, you need to move O(log(n)) elements to fill the tree while keeping the feature that each node is less than its successors.

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[quote name='Álvaro' timestamp='1353388057' post='5002587']
priority_queue implements basically a heap
[/quote]

How is priority_queue implemented as a heap when I'm using a vector or a deque as its internal container?

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[quote name='lride' timestamp='1353421016' post='5002666']
[quote name='Álvaro' timestamp='1353388057' post='5002587']
priority_queue implements basically a heap
[/quote]

How is priority_queue implemented as a heap when I'm using a vector or a deque as its internal container?
[/quote]
A heap is just a way of organizing/ordering the data. [font=courier new,courier,monospace]vector[/font] and [font=courier new,courier,monospace]deque[/font] are just ways of storing (not organizing) the data.

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In more detail, nodes in a heap can be assigned indices that are small consecutive integers, which makes it possible to use a vector or a deque for storage. Node 0 is the root, nodes 2*i+1 and 2*i+2 are the children of node i, and node (i-1)/2 is its parent. The resulting implementation of a heap is quite efficient, and that's probably how priority_queue is implemented by your library (although there are other possibilities).

You can read more about it [url="http://en.wikipedia.org/wiki/Priority_queue#Usual_implementation"]here[/url].

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[quote name='Álvaro' timestamp='1353439358' post='5002733']
In more detail, nodes in a heap can be assigned indices that are small consecutive integers, which makes it possible to use a vector or a deque for storage. Node 0 is the root, nodes 2*i+1 and 2*i+2 are the children of node i, and node (i-1)/2 is its parent. The resulting implementation of a heap is quite efficient, and that's probably how priority_queue is implemented by your library (although there are other possibilities).

You can read more about it [url="http://en.wikipedia.org/wiki/Priority_queue#Usual_implementation"]here[/url].
[/quote]
Thank you. That cleared up my question.

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