Priority Queue Text Modify (Down) Timing Test

# Priority Queue Text `modify` Timing Test - II

## Description

This test inserts a number of values with keys from an arbitrary text ([ wickland96thirty ]) into into a container then modifies each one "down" (i.e., it makes it smaller). It uses `modify` for `pb_ds`'s priority queues; for the STL's priority queues, it pops values from a container until it reaches the value that should be modified, then pushes values back in. It measures the average time for `modify` as a function of the number of values.

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

## Purpose

The main purpose of this test is to contrast Priority Queue Text `modify` Timing Test - I.

## 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 NRTG, NRTM, and NRTL show the results for the pairing heap and thin heaps in g++, msvc++, and local, respectively,

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NPG: Native and `pb ds` priority queue `modify` 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`
4. thin_heap- `priority_queue` with `Tag` = `thin_heap_tag`
5. rc_binomial_heap- `priority_queue` with `Tag` = `rc_binomial_heap_tag`
6. binomial_heap- `priority_queue` with `Tag` = `binomial_heap_tag`
7. pairing_heap- `priority_queue` with `Tag` = `pairing_heap_tag`

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NPM: Native and `pb ds` priority queue `modify` 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`
4. thin_heap- `priority_queue` with `Tag` = `thin_heap_tag`
5. rc_binomial_heap- `priority_queue` with `Tag` = `rc_binomial_heap_tag`
6. binomial_heap- `priority_queue` with `Tag` = `binomial_heap_tag`
7. pairing_heap- `priority_queue` with `Tag` = `pairing_heap_tag`

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

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NRTG: Pairing and thin priority queue `modify` 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. pairing_heap- `priority_queue` with `Tag` = `pairing_heap_tag`

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NRTM: Pairing and thin priority queue `modify` 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. pairing_heap- `priority_queue` with `Tag` = `pairing_heap_tag`

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NRTL: Pairing and thin priority queue `modify` timing test - local

## Observations

Most points in these results are similar to Priority Queue Text `modify` Timing Test - I.

It is interesting to note, however, that as opposed to that test, a thin heap (`priority_queue` with `Tag` = `thin_heap_tag`) is outperformed by a pairing heap (`priority_queue` with `Tag` = `pairing_heap_tag`). In this case, both heaps essentially perform an `erase` operation followed by a `push` operation. As the other tests show, a pairing heap is usually far more efficient than a thin heap, so this is not surprising.

Most algorithms that involve priority queues increase values (in the sense of the priority queue's comparison functor), and so Priority Queue Text `modify` Timing Test - I is more interesting than this test.