fix docs: change some description in w2d3 documentation for tiered compaction trigger condition

[jackyYang6]

1. compaction trigger precondition The original text stated that compaction triggers when the number of tiers is 'larger than' num_tiers, which could be interpreted as strictly greater than (>). This has been corrected to 'greater than or equal to (or can say reaches)' to accurately reflect the intended behavior and align with the actual implementation.
2. min_merge_width condition same as above, it should be 'at least' not 'more than'
3. reduce sorted run conditions accurately states the aim to reduce tiers to num_tiers - 1

[skyzh]

Is the changes from your output? I'm currently investigating issues related to tier/level id, there might be some mismatches between the write-up and the actual code.

[jackyYang6]

Is the changes from your output? I'm currently investigating issues related to tier/level id, there might be some mismatches between the write-up and the actual code.

In your tutorial, we always set the tier/level id as the first sst id in this tier/level. But when you use the compaction simulator, choose the --dump-real-id option or the default --dump-origin-id option, it will be different. In compaction simulator, u code after apply compaction result, write like this

for file in files {
    let new_sst_id = storage.generate_sst_id();
    sst_ids.push(new_sst_id);
    storage.file_list.insert(new_sst_id, *file);
    storage.total_writes += 1;
}

It's not change the actual file in file_list. so when we use the compaction simulator on default option (dump origin id, it will be use file, it's not change when we apply result),

println!(
    "L{level} ({}): {:?}",
    files.len(),
    files.iter().map(|x| self.file_list[x]).collect::<Vec<_>>()
);

the output will be just like current example in docs

--- After Flush ---
L3 (1): [3]
L2 (1): [2]
L1 (1): [1]
--- Compaction Task ---
--- Compaction Task ---
compaction trigger by space amplification ratio: 200
L3 [3] L2 [2] L1 [1] -> [4, 5, 6]
--- After Compaction ---
L4 (3): [3, 2, 1]

and then, when we use the '--dump-real-id` option, it will use those new generated sst ids; at this time, tier id will observe the rule.

println!("L{level} ({}): {:?}", files.len(), files);

this output maybe more readable and meet our expectations.

--- After Flush ---
L3 (1): [3]
L2 (1): [2]
L1 (1): [1]
--- Compaction Task ---
--- Compaction Task ---
compaction triggered by space amplification ratio: 200
L3 [3] L2 [2] L1 [1] -> [4, 5, 6]
--- After Compaction ---
L4 (3): [4, 5, 6]

[jackyYang6]

So my changes in the example aren't absolutely right. It simply changes the tier id to make it observe tier id equal to the first sst id in the tier.

[skyzh]

Hey -- we have updated docs wrt tiered compaction last year, and I guess all the issues should be fixed :) Thank you for the patch anyways!