Priority Queue Random Int Push Pop Timing Test

# Priority Queue Random Integer `push` and `pop` Timing Test

## Description

This test inserts a number of values with i.i.d. integer keys into a container using `push` , then removes them using `pop` . It measures the average time for `push` and `pop` as a function of the number of values.

(The test was executed with `priority_queue_random_int_push_pop_timing_test` thirty_years_among_the_dead_preproc.txt 200 200 2100)

## Purpose

The test checks the effect of different underlying data structures (see Design::Priority Queues::Implementations).

## Results

Figures NPG, NPM, and NPL shows the results for the native priority queues and `pb_ds` 's priority queues in g++, msvc++, and local, respectively.

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NPG: Native and `pb ds` priority queue `push` `pop` timing test - g++

In the above figure, the names in the legends have the following meaning:

1. thin_heap- `priority_queue` with `Tag` = `thin_heap_tag`
2. rc_binomial_heap- `priority_queue` with `Tag` = `rc_binomial_heap_tag`
3. binomial_heap- `priority_queue` with `Tag` = `binomial_heap_tag`
4. pairing_heap- `priority_queue` with `Tag` = `pairing_heap_tag`
5. n_pq_deque- `std::priority_queue` adapting `std::deque`
6. n_pq_vector- `std::priority_queue` adapting `std::vector`
7. binary_heap- `priority_queue` with `Tag` = `binary_heap_tag`

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NPM: Native and `pb ds` priority queue `push` `pop` timing test - msvc++

In the above figure, the names in the legends have the following meaning:

1. thin_heap- `priority_queue` with `Tag` = `thin_heap_tag`
2. rc_binomial_heap- `priority_queue` with `Tag` = `rc_binomial_heap_tag`
3. binomial_heap- `priority_queue` with `Tag` = `binomial_heap_tag`
4. pairing_heap- `priority_queue` with `Tag` = `pairing_heap_tag`
5. n_pq_deque- `std::priority_queue` adapting `std::deque`
6. n_pq_vector- `std::priority_queue` adapting `std::vector`
7. binary_heap- `priority_queue` with `Tag` = `binary_heap_tag`

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NPL: Native and `pb ds` priority queue `push` `pop` timing test - local

## Observations

Binary heaps are the most suited for sequences of `push` and `pop` operations of primitive types (e.g. `int`s). This is explained in Priority Queue Random Int `push` Timing Test . (See Priority Queue Text `push` Timing Test for the case of primitive types.)

At first glance it seems that the STL's vector-based priority queue is approximately on par with `pb_ds`'s corresponding priority queue. There are two differences however:

1. The STL's priority queue does not downsize the underlying vector (or deque) as the priority queue becomes smaller (see Priority Queue Text `pop` Memory Use Test). It is therefore gaining some speed at the expense of space.
2. From Priority Queue Random Integer `push` and `pop` Timing Test, it seems that the STL's priority queue is slower in terms of `pus` operations. Since the number of `pop` operations is at most that of `push` operations, the test here is the "best" for the STL's priority queue.

Priority-Queue Performance Tests::Observations discusses this further and summarizes.