small | Smallest possible syntactically valid files of different types

I need to calculate the square root of some numbers, for example √9 = 3 and √2 = 1.4142. How can I do it in Python?

The inputs will probably be all positive integers, and relatively small (say less than a billion), but just in case they're not, is there anything that might break?

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• Why does Python give the "wrong" answer for square root? (specific to Python 2)
• calculating n-th roots using Python 3's decimal module
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• Arbitrary precision of square roots

_{Note: This is an attempt at a canonical question after a discussion on Meta about an existing question with the same title.}

I've deployed hundreds of function and this is the first time I encounter this issue. Simply, it stops deploying function process, saying:

Unhandled error cleaning up build images. This could result in a small monthly bill if not corrected. You can attempt to delete these images by redeploying or you can delete them manually at https://console.cloud.google.com/gcr/images/[project-name]/us/gcf

The way I deploy is through Firebase CLI command: firebase deploy --only functions:nameOfFunction

Question is what are those images I have to delete? Why? How can I solve it?

In vuejs2 app having select input with rather big options list it breaks design of my page on extra small devices. Searching in net I found “size” property, but that not what I I need : I want to have dropdown selection, which is the default. Are there some other decision, maybe with CSS to set max-height of dropdown selection area.

Modeified PART # 1: I made testing demo page at http://photographers.my-demo-apps.tk/sel_test it has 2 select inputs with custom design and events as in this example link How to Set Height for the Drop Down of Select box and following workaround at js fiddle:

I am trying to setup a very small GraphQL API using NestJS 8. I installed all required redepndencies from the documentation, but when I start the server, I get this error:

I have a small loop of code which is throwing Uncaught RangeError: Invalid Array Length

I was able to reproduce it with just this in the Google Chrome console

I am trying to find a more efficient solution to a combinatorics problem than the solution I have already found.

Suppose I have a set of N objects (indexed 0..N-1) and wish to consider each subset of size K (0<=K<=N). There are S=C(N,K) (i.e., "N choose K") such subsets. I wish to map (or "encode") each such subset to a unique integer in the range 0..S-1.

Using N=7 (i.e., indexes are 0..6) and K=4 (S=35) as an example, the following mapping is the goal:
0 1 2 3 --> 0
0 1 2 4 --> 1
...
2 4 5 6 --> 33
3 4 5 6 --> 34

N and K were chosen small for the purposes of illustration. However, in my actual application, C(N,K) is far too large to obtain these mappings from a lookup table. They must be computed on-the-fly.

In the code that follows, combinations_table is a pre-computed two-dimensional array for fast lookup of C(N,K) values.

All code given is compliant with the C++14 standard.

If the objects in a subset are ordered by increasing order of their indexes, the following code will compute that subset's encoding:

I will clarify my question for a very specific use case.

Let's say, I've designed my code as follows:

And this is the content:

src/inner/inner.darwin.ts:

I have a vector of random positive integers. I would like to select only those elements of the vector whose sum will be exactly equal to a certain predetermined value.

Let's take an example like this. x=1:5, I am looking for elements whose sum is equal to 14. The solution is of course the vector c(2, 3, 4, 5).

Of course, there may be several solutions. Example 2. x=1:5, I'm looking for elements whose sum is equal to 7. Here, of course, should be the following three solutions:
1.c(2, 5),
2.c(3, 4),
3.c(1, 2, 4).

There may also be a situation where there will be no solutions at all. Example 3. x=c(1, 2, 7), I'm looking for elements whose sum equals 5. Of course, there are no correct solutions here.

Everything seems trivially simple if we have vectors of several elements. Here, I even came up with a few alternative solutions. However, the problem becomes when the size of the vector increases.

My vector looks like this:

In short:

I have implemented a simple (multi-key) hash table with buckets (containing several elements) that exactly fit a cacheline. Inserting into a cacheline bucket is very simple, and the critical part of the main loop.

I have implemented three versions that produce the same outcome and should behave the same.

The mystery

However, I'm seeing wild performance differences by a surprisingly large factor 3, despite all versions having the exact same cacheline access pattern and resulting in identical hash table data.

The best implementation insert_ok suffers around a factor 3 slow down compared to insert_bad & insert_alt on my CPU (i7-7700HQ). One variant insert_bad is a simple modification of insert_ok that adds an extra unnecessary linear search within the cacheline to find the position to write to (which it already knows) and does not suffer this x3 slow down.

The exact same executable shows insert_ok a factor 1.6 faster compared to insert_bad & insert_alt on other CPUs (AMD 5950X (Zen 3), Intel i7-11800H (Tiger Lake)).