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Time complexity of Javascript Array.find() in modern browsers

Since array.find() iterates over an array, if I handle (potentially) large arrays, I always make sure to have an indexed object like so:
{ [id:string]: Item }
if I need to look up items by id in these arrays.
However, living in a time of V8 (and comparable engine optimisations for Safari and Firefox), I'm wondering if maybe under the hood, a simple array.find() is already optimized for it? Or will optimize for it (create such an indexed object) at runtime as soon as it has to perform this operation once?
Is it true that modern browsers already have some kind of optimization for O(N) type algorithms that could become O(1) with the proper implementation? Or am I thinking too much of what these browsers actually can / will do under the hood?

V8 developer here. The time complexity of Array.prototype.find is O(n) (with n being the array's length), and it's fair to assume that it will remain that way.
Generally speaking, it's often impossible for engines to improve the complexity class of an operation. In case of Array.prototype.find, the predicate function you pass might well care how often it gets called:
[1, 2, 3].find((value, index, object) => {
console.log(`Checking ${value}...`); // Or any other side effect.
return value === 42;
});
In such a case, the engine has no choice but to iterate over the entire array in exactly the right order, because anything else would observably break your program's behavior.
In theory, since JS engines can do dynamic optimizations, they could inspect the predicate function, and if it has no side effects, they could use it to build up some sort of index/cache. Aside from the difficulty of building such a system that works for arbitrary predicates, this technique even when it does work would only speed up repeated searches of the same array with the same function, at the cost of wasting time and memory if this exact same scenario will not occur again. It seems unlikely that an engine can ever make this prediction with sufficient confidence to justify investing this time and memory.
As a rule of thumb: when operating on large data sets, choosing efficient algorithms and data structures is worth it. Typically far more worth it than the micro-optimizations we're seeing so much in SO questions :-)
A highly optimized/optimizing engine may be able to make your O(n) code somewhere between 10% and 10x as fast as it would otherwise be. By switching to an O(log n) or O(1) solution on your end, you can speed it up by orders of magnitude. That's often accomplished by doing something that engines can't possibly do. For example, you can keep your array sorted and then use binary search over it -- that's something an engine can't do for you automatically because obviously it's not allowed to reorder your array's contents without your approval. And as #myf already points out in a comment: if you want to access things by a unique key, then using a Map will probably work better than using an Array.
That said, simple solutions tend to scale better than we intuitively assume; the standard warning against premature optimizations applies here just as everywhere else. Linearly searching through arrays is often just fine, you don't need a (hash) map just because you have more than three items in it. When in doubt, profile your app to find out where the performance bottlenecks are.

How does hidden classes really avoid dynamic lookups?

So we have all heard that v8 uses the thing called hidden classes where when many objects have the same shape, they just store a pointer to the shape struct which stores fixed offsets. I have heard this a million time, and I very much get how this reduces memory usage by A LOT (not having to store a map for each one is amazing) and potentially because of that a bit faster performance.
However I still don't understand how it avoids dynamic lookup. The only thing I have heard is storing a cache between a string (field name) and a fixed offset, and checking it every time, but if there's a cache miss (which is likely to happen) there will still be a dyanmic lookup.
Everyone says that this is almost as fast as C++ field access (which are just a mov instruction usually), however this 1 field access cache isn't even close.
Look at the following function:
function getx(o)
{
return o.x;
}
How will v8 make the access of the x field so fast and avoid dynamic lookup?

(V8 developer here.)
The key is that hidden classes allow caching. So, certainly, a few dynamic lookups will still be required. But thanks to caching, they don't have to be repeated every single time a property access like o.x is executed.
Essentially, the first time your example function getx is called, it'll have to do a full property lookup, and it'll cache both the hidden class that was queried and the result of the lookup. On subsequent calls, it'll simply check the incoming o's hidden class against the cached data, and if it matches, it uses the cached information about how to access the property. Of course, on mismatch, it has to fall back to a dynamic lookup again. (In reality it's a bit more complicated because of additional tradeoffs that are involved, but that's the basic idea.)
So if things go well, a single dynamic lookup is sufficient for an arbitrary number of calls to such a function. In practice, things go well often enough that if you started with a very simple JS engine that didn't do any such tricks, and you added caching of dynamic lookup results, you could expect approximately a 10x performance improvement across the board. Adding an optimizing compiler can then take that idea one step further and embed cached results right into the optimized code; that can easily give another 10x improvement and approach C-like performance: code still needs to contain hidden class checks, but on successful check can read properties with a single instruction. (This is also why JS engines can't just "optimize everything immediately" even if they wanted to: optimization crucially depends on well-populated caches.)

Why "Map" manipulation is much slower than "Object" in JavaScript (v8) for integer keys?

I was happily using Map for indexed accessed everywhere in my JavaScript codebase, but I've just stumbled upon this benchmark: https://stackoverflow.com/a/54385459/365104
I've re-created it here as well: https://jsben.ch/HOU3g
What benchmark is doing is basically filling a map with 1M elements, then iterating over them.
I'd expect the results for Map and Object to be on par, but they differ drastically - in favor of Object.
Is this expected behavior? Can it be explained? Is it because of the ordering requirement? Or because map is doing some key hashing? Or just because Map allows any object as key (I'd expect it using pointer address for key then, which does not need any hashing)? What is the difference between the Map and Object indexing algorithms?
This is quite unexpected and discouraging - basically I'll have to revert back to the old-school "object as map" coding style.
Update #1
As suggested in comments, the Object might be optimized to Array (since it is indexed by integer, starting from the zero).
Changing the iteration order from size to 0 - Object is still 2x faster. When using strings as index, Map performs 2x better.

(V8 developer here.)
I'll have to revert back to the old-school "object as map" coding style.
If you do that, you will have fallen victim to a misleading microbenchmark.
In the very special case of using consecutive integers as keys, a plain Object will be faster, yes. Nothing beats a contiguous array in that scenario. So if the "indexed accesses everywhere in your codebase" that you mentioned are indeed using index sets like the integers from 0 to 1M, then using an Object or Array is a good idea. But that's a special case. If the index space is sparse, things will already look different.
In the general case of using arbitrary strings in random order, a Map will perform significantly better than an Object. Even more importantly, the way such object property accesses are handled (in V8, and quite possibly in other engines too) has non-local effects: if one function puts excessive stress on the slow path of the object property lookup handling system, then that will likely slow down some other functions relying on that same slow path for their property accesses.
The fundamental reason is that engines optimize different things for different usage patterns. An engine could implement Objects and Maps pretty much the same under the hood; but that wouldn't be the ideal behavior, because different usage patterns benefit from different internal representations and implementation choices. So engines allow you to provide them with a hint: if you use a Map, the engine will know that you're planning to use the thing as a map (duh!), where random keys will come and go. If you use an Object, then the engine will (at least at first) assume that you want the set of optimizations that work best for your average object, where the set of properties is fairly small and static. If you use an Array (or Object with only integer properties, which is nearly the same thing in JS), then you're making it easy for the engine to give you fast integer-indexed accesses.
Using "x" + i as key is a good suggestion to demonstrate how quickly a microbenchmark can be changed so it appears to produce opposite results. But here's a spoiler: if you do (only) this modification, then a large part of what you're measuring will be number-to-string conversion and string internalization, not Map/Object access performance itself.
Beware of microbenchmarks; they are misleading. You really have to analyze them quite deeply (by profiling, and/or by inspecting generated code, and/or by tracing other engine internals) to be sure that they're measuring what you think they're measuring, and hence are producing results that are telling you what you think they're telling you.
In general, it is strongly recommended to use representative test cases for performance measurements. Ideally, your app itself; or by extracting a realistic part of it into a testcase operating on realistic data. And if you can't measure a difference between two implementation choices with a stress test for your entire production app, then it's not a difference worth worrying about it. With a microbenchmark (i.e. a couple of artificially crafted lines), I can "prove" almost anything that doesn't apply to the general case.

Why is 'delete' slow in javascript?

I just stumbled upon this jsperf result: http://jsperf.com/delet-is-slow
It shows that using delete is slow in javascript but I am not sure I get why. What is the javascript engine doing behind the scene to make things slow?

I think the question is not why delete is slow... The speed of a simple delete operation is not worth measuring...
The JS perf link that you show does the following:
Create two arrays of 6 elements each.
Delete at one of the indexes of one array.
Iterate through all the indexes of each array.
The script shows that iterating through an array o which delete was applied is slower than iterating though a normal array.
You should ask yourself, why delete makes an array slow?
The engine internally stores array elements in contiguous memory space, and access them using an numeric indexer.
That's what they call a fast access array.
If you delete one of the elements in this ordered and contiguous index, you force the array to mutate into dictionary mode... thus, what before was the exact location of the item in the array (the indexer) becomes the key in the dictionary under which the array has to search for the element.
So iterating becomes slow, because don't move into the next space in memory anymore, but you perform over and over again a hash search.

You'll get a lot of answers here about micro-optimisation but delete really does sometimes have supreme problems where it becomes incredibly slow in certain scenarios that people must be aware of in JS. These are to my knowledge edge cases and may or may not apply to you.
I recommend to profile and benchmark in different browsers to detect these anomalies.
I honestly don't know the reasons as I tend to workaround it this but I would guess combinations of quirks in the GC (it is might be getting invoked too often), brutal rehashing, optimisations for other cases and weird object structure/bad time complexity.
The cases usually involve moderate to large numbers of keys, for example:
Delete from objects with many keys:
(function() {
var o={},s,i,c=console;
s=new Date();for(i=0;i<1000000;i+=10)o[i]=i;c.log('Set: '+(new Date()-s));
s=new Date();for(i=0;i<50000;i+=10)delete(o[i]);c.log('Delete: '+(new Date()-s));})();
Chrome:
Set: 21
Delete: 2084
Firefox:
Set: 74
Delete: 2
I have encountered a few variations of this and they are not always easy to reproduce. A signature is that it usually seems to degrade exponentially. In one case in Firefox delete inside a for in loop would degrade to around 3-6 operations a second where as deleting when iterating Object.keys would be fine.
I personally tend to think that these cases can be considered bugs. You get massive asymptotic and disproportionate performance degradation that you can work around in ways that shouldn't change the time or space complexity or that might even normally make performance moderately worse. This means that when considered as a declarative language JS gets the implementation/optimisations wrong. Map does not have the same problem with delete so far that I have seen.
Reasons:
To be sure, you would have to look into the source code or run some profiling.
delete in various scenarios can change speed arbitrarily based on how engines are written and this can change from version to version.
JavaScript objects tend to not be used with large amounts of properties and delete is called relatively infrequently in every day usage. They're also used as part of the language heavily (they're actually just associative arrays). Virtually everything relies on an implementation of an object. IF you create a function, that makes an object, if you put in a numeric literal it's actually an object.
It's quite possible for it to be slow purely because it hasn't been well optimised (either neglect or other priorities) or due to mistakes in implementation.
There are some common possible causes aside from optimisation deficit and mistakes.
Garbage Collection:
A poorly implemented delete function may inadvertently trigger garbage collection excessively.
Garbage collection has to iterate everything in memory to find out of there are any orphans, traversing variables and references as a graph.
The need to detect circular references can make GC especially expensive. GC without circular reference detection can be done using reference counters and a simple check. Circular reference checking requires traversing the reference graph or another structure for managing references and in either case that's a lot slower than using reference counters.
In normal implementations, rather than freeing and rearranging memory every time something is deleted, things are usually marked as possible to delete with GC deferred to perform in bulk or batches intermittently.
Mistakes can potentially lead to the entire GC being triggered too frequently. That may involve someone having put an instruction to run the GC every delete or a mistake in its statistical heuristics.
Resizing:
It's quite possible for large objects as well the memory remapping to shrink them might not be well optimised. When you have dynamically sized structures internally in the engine it can be expensive to resize them. Engines will also have varying levels of their own memory management on top of that of that provides by the operating system which will significantly complicate things.
Where an engine manages its own memory efficiently, even a delete that deletes an object efficiently without the need for a full GC run (has no circular references) this can trigger the need to rearrange memory internally to fill the gap.
That may involve reallocating data of the new size, then copying everything from the old memory to the new memory before freeing the old memory. It can also require updating all of the pointers to the old memory in some cases (IE, where a pointer pointer [all roads lead to Rome] wasn't used).
Rehashing:
It may also rehash (needs as the object is an associative array) on deletes. Often people only rehash on demand, when there are hash collisions but some engines may also rehash on deletes.
Rehashing on deletes prevents a problem where you can add 10 items to an object, then add a million objects, then remove those million objects and the object left with the 10 items will both take up more memory and be slower.
A hash with ten items needs ten slots with an optimum hash, though it'll actually require 16 slots. That times the size of a pointer will be 16 * 8 bytes or 128bytes. When you add the million items then it needs a million slots, 20 bit keys or 8 megabytes. If you delete the million keys without rehashing it then the object you have with ten items is taking up 8 megabyte when it only needs 128 bytes. That makes it important to rehash on item removal.
The problem with this is that when you add you know if you need to rehash or not because there will be a collision. When deleting, you don't know if you need to rehash or not. It's easy to make a performance mistake with that and rehash every time.
There are a number of strategies for reasonable downhashing intervals although without making things complicated it can be easy to make a mistake. Simple approaches tend to work moderately well (IE, time since last rehash, size of key versus minimum size, history of collision pairs, tombstone keys and delete in bulk as part of GC, etc) on average but can also easily get stuck in corner cases. Some engines might switch to a different hash implementation for large objects such as nested where as others might try to implement one for all.
Rehashing tends to work the same as resizing for simply implementations, make an entirely new one then insert the old one into it. However for rehashing a lot more needs to be done beforehand.
No Bulk:
It doesn't let you delete a bunch of things at once from a hash. It's usually much more efficient to delete items from a hash in bulk (most operations on the same thing work better in bulk) but the delete keyword only allows you to delete one by one. That makes it slow by design for cases with multiple deletes on the same object.
Due to this, only a handful of implementation of delete would be comparable to creating a new object and inserting the items you want to keep for speed (though this doesn't explain why with some engines delete is slow in its own right for a single call).
V8:
Slow delete of object properties in JS in V8
Apparently this was caused due to switching out implementations and a problem similar to but different to the downsizing problem seen with hashes (downsizing to flat array / runthrough implementation rather than hash size). At least I was close.
Downsizing is a fairly common problem in programming which results in what is somewhat akin to a game of Jenga.

JavaScript in Chrome: Read performance differs between two objects created with different strategies

[UPDATE The discussion of "slow mode" below also pointed me to Why the convertToFastObject function make it fast?, which has a nice discussion of the V8 internal discussion that #benjamin-gruenbaum referenced.]
I was wondering about the performance of JavaScript one for optimizing reads, so I wrote a JSPerf test suite, and the results are non-intuitive.
Firstly, the question "Performance of key lookup in JavaScript object" discusses the internals of V8s object creation, but I don't see why the method of creation would change the read performance after it has been created.
Overview
I want to test read access on various data structures. I chose 3 structures:
An object literal, created and assigned in one statement
An object literal, created in one statement, then values assigned in subsequent statements
An array literal, created in one statement, but populated as an associative array, which presumably gets translated to an object in the background.
Test
http://jsperf.com/object-read-varies-by-creation-method
Methodology
In the setup method. I create 3 data structures and populate them with about random words from /usr/share/dict/words, in randomized order (but the same order on each test run). Each test case retrieves the same 10 random words from /usr/share/dict/words, but not necessarily words that are in the list, to simulate misses as well as hits.
Results
What I see on most browsers is pretty intuitive: the two objects perform better than the pseudo-associative array. My assumption is that the array literal is being proxied by an object in those cases, increasing the overall time it takes to access.
What I don't get is the Chrome 33 case, where creating and assigning an object as a single statement performs dramatically better than populating the structure after creation.
If the test included setup time, I could understand that difference, but as it stands, I don't fully get why the two object literals don't perform about the same.
The best guess I've come up with so far is that Chrome's object creation algorithm is able to optimize its hash tree better during an act of creation that includes all keys at once then it is when it's inserting the keys one at a time after the fact.
Can anyone more familiar with these structures account for the difference?