# Priority Queue Random Integer `push` Timing Test

## Description

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

(The test was executed with `priority_queue_random_intpush_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 show the results for the native priority queues and `pb_ds` 's priority queues in g++, msvc++, and local, respectively; Figures NBPG, NBPM, and NBPL shows the results for the binary-heap based 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` timing test - g++

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

1. rc_binomial_heap- `priority_queue` with `Tag` = `rc_binomial_heap_tag`
2. binomial_heap- `priority_queue` with `Tag` = `binomial_heap_tag`
3. n_pq_deque- `std::priority_queue` adapting `std::deque`
4. pairing_heap- `priority_queue` with `Tag` = `pairing_heap_tag`
5. thin_heap- `priority_queue` with `Tag` = `thin_heap_tag`
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` timing test - msvc++

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

1. rc_binomial_heap- `priority_queue` with `Tag` = `rc_binomial_heap_tag`
2. binomial_heap- `priority_queue` with `Tag` = `binomial_heap_tag`
3. pairing_heap- `priority_queue` with `Tag` = `pairing_heap_tag`
4. thin_heap- `priority_queue` with `Tag` = `thin_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` timing test - local

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NBPG: Native and `pb ds` binary priority queue `push` timing test - g++

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

1. n_pq_deque- `std::priority_queue` adapting `std::deque`
2. n_pq_vector- `std::priority_queue` adapting `std::vector`
3. binary_heap- `priority_queue` with `Tag` = `binary_heap_tag`

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NBPM: Native and `pb ds` binary priority queue `push` timing test - msvc++

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

1. n_pq_deque- `std::priority_queue` adapting `std::deque`
2. n_pq_vector- `std::priority_queue` adapting `std::vector`
3. binary_heap- `priority_queue` with `Tag` = `binary_heap_tag`

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NBPL: Native and `pb ds` binary priority queue `push` timing test - local

## Observations

Binary heaps are the most suited for sequences of `push` and `pop` operations of primitive types (e.g. `int`s). They are less constrained than any other type, and since it is very efficient to store such types in arrays, they outperform even pairing heaps. (See Priority Queue Text `push` Timing Test for the case of non-primitive types.)

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