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performance – Writing a stable sorting algorithm that can sort a binary array in O(n) time complexity and O(1) auxiliary space complexity

So I was able to write a stable sorting algorithm that can sort a binary array in O(n) time complexity and O(1) space complexity, but it works only if we assume that our array can store integers that are not only 0, 1.

Here is the algorithm:

#include <stdio.h>
void binarySort(int arr(), int arr_length)
{
  int i, count=1;
  for(i=0 ; i<arr_length ; i++) // counting number of 1's in array and ordering them.
  {
    if(arr(i)==1)
    {
      arr(i)=count;
      count++;
    }
  }
  int num0s=arr_length-count+1; // number of 0's in array
  int j=0;
  int k=0;
  while(j<num0s) // bringing the 0's to the front of the array by swapping them with the 1's
  {
    if(arr(k)==0)
    {
      int temp=arr(k);
      arr(k)=arr(j);
      arr(j)=temp;
      j++;
    }
    k++;
  }
  int a;
  for(a=0 ; a<arr_length-num0s ; ) // sorting the 1's to make the overall sort stable.
  {
    if(arr(num0s+a)!=a+1)
    {
      int temp=arr(num0s+a);
      arr(num0s+a)=arr(num0s+temp-1);
      arr(num0s+temp-1)=temp;
    }
    else
    {
      arr(num0s+a)=1;
      a++;
    }
  }
}

void main() // example of algorithm working
{
   int arr()={1, 0, 0, 1, 0, 1, 1, 0, 0, 1};
   int i;
   for(i=0 ; i<10 ; i++)
   {
       printf("%d ", arr(i));
   }
   printf("n");
   binarySort(arr, 10);
   for(i=0 ; i<10 ; i++)
   {
       printf("%d ", arr(i));
   }
}

Now if we consider that our array cannot store any other values other than 0, 1, can we make a sorting algorithm that is stable while preserving its O(n) time complexity and O(1) auxiliary space complexity? No matter what I try in this case, it always seems like at least one of these properties cannot be satisfied.

A little context as to why I want to find an algorithm with these properties is that I want to make a binary radix sort algorithm using the stable binary sort algorithm as a subroutine.

output formatting – Writing mathematical expression in a file

I am trying to write a mathematical expression as variable = expression in the output file.

The current method that I am doing is through WriteString as

expr = -((a*b*y^2*(-1 + z)*z*(1 + a*b + z))/(1 + a*b)^2) +
        (z*(1 + a*b - a*b*z + (z + a*b*z)^2))/(1 + a*b)^2 -
        (y*z*((-1 + z)^2 + a*b*(2 - 3*z + z^2) + a^2*b^2*(1 - z + z^2)))/(1 + a*b)^2
expression = CForm(expr) /. {Power->pow};
(*expression = CForm(HornerForm(expr)) /. {Power->pow};*)
str=OpenWrite("output.hh");
WriteString(str," double variable = ", expression,";");
(*WriteString(str," double variable = ", ExportString(expression,"Text"));*)
Close(str);

The output is

 cat output.hh
 double variable = -(a*b*(-1 + z)*z*(1 + a*b + z)*pow(1 + a*b,-2)*pow(y,2)) - y*z*pow(1 + a*b,-2)*(pow(-1 + z,2) + a*b*(2 - 3*z + pow(z,2)) + pow(a,2)*pow(b,2)*(1 - z + pow(z,2))) + z*pow(1 + a*b,-2)*(1 + a*b - a*b*z + pow(z + a*b*z,2));

I want to break the line as the original expr (or after some user-specified column say 80) i.e.

 double variable = -(a*b*(-1 + z)*z*(1 + a*b + z)*pow(1 + a*b,-2)*pow(y,2)) -
                   y*z*pow(1 + a*b,-2)*(pow(-1 + z,2) + a*b*(2 - 3*z + pow(z,2)) + pow(a,2)*pow(b,2)*(1 - z + pow(z,2))) + 
                   z*pow(1 + a*b,-2)*(1 + a*b - a*b*z + pow(z + a*b*z,2));

Although this might not lead to optimized expression for numerical evaluation, however it is wanted as beautification.
Also how should one optimize expression for further processing to other languages. Any suggestion? Experimental`OptimizeExpression and HornerForm are some options. Any other recommendation? MathCode is much costly 😀

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Best practice for writing data in Python / Pandas

Hi ladies and gents,

I need some general advise regarding best practice for writing data into my MongoDB –

My project is the following:

  • Read some 3 very large CSV files 300K records each

  • Clean up the data

  • Perform data wrangling and join the data and load into a data frame

  • Perform analysis

  • Application must maintain state of data on Exit

  • The application must be run in Jupyter notebook but have a Tkinter GUI for loading the files and data clean up buttons.

  • GUI must be able to request data stats and correlation graphs etc.

Is the following design okay?

Data:

  • Convert the data to JSON as soon as read from CSV, check for duplicates in database and insert if unique

  • Load data into data frame from Database,

  • Perform clean up ,

  • Amend database record at the end

Sorry if these are basic questions I am quite new to doing real python work and don’t want to go down the wrong path

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HDD Raid 0 frozen for writing for ~30 seconds on big files

I have a several raids: RAID 0 SAS HDDs (each connected via 6Gb — SAS-2).
And 5+0 raid of SATA HDDs.

Both raids provide good read performance, but when I write to them, they start at insanely high speed (~1GB per second!). After some time, they become stuck for ~30 seconds. And then continue.

Write buffer is enabled.

Raids are from different vendors (Adaptec and IBM).

I believe they write data to the buffer and then need some time to flush it.
It is reproducible only on huge (~ 20GB) files

Question 1: is it true? How can I profile/proof that fact?

I tried both: local access (copying from one raid to another and vice versa) and network access (via 10Gb network).

Effect is the same:

  • 1GB/s
  • After some time 0B/s
  • After some time ~600MB/s
  • And again.

I limited my network speed to 1Gb and got stable performance, although not very fast.

Users are angry when copying process is frozen, so my question is does it work as it should?
If so, what can we do except migrating to SDDs (30TB of SSDs are expensive) or limiting my network speed?

We spent some time improving our network performance (by enabling RSS, jumbo frames, migrating to latest SMB version that supports multiple threads etc) and we now have ~9.7Gb/s with iperf3 between client and server.

Question 2: Is it possible to have at least 300/400 megabytes per second for writing with 10 or 50 on HDDs? Shouldn’t we have ~150MB/s for each disk, 300MB for 2 HDDs in RAID0? Big files utilize sequental access, aren’t they?

Question 3: RAIDs have huge stripe size (about 1MB). I heard that some vendors optimize their controllers for the default stripe size only. Is it true?

How are writing shaders different in Unity’s scriptable render pipeline vs the standard pipeline?

So I want to start learning how to write shaders because the shadergraph seems very limited at the moment. I’ve done some research and it seems that I should learn the HLSL language which is used by Unity. I’m becoming confused though how this will carry over between pipelines. I read that standard pipeline shaders aren’t supported in URP so I’m confused how the shader language is different in URP if they both use the HLSL language. I was wondering if someone with a better grasp on this could explain the difference between them and if the skills carry over, as most tutorials online seem to be for writing shaders in the standard pipeline. Thanks.