In theory, a computer program can compute 16 lines per bar by means of matrix multiplication. But there are several problems with this process:

It’s non-deterministic. You don’t always get what you want

The program has to figure out the best possible way to compute the line of output bars. It’s random (you don’t know which lines will be the first ones to appear).

As an example, assume that the first 11 steps are correct, because that’s the only way the program can get the lines to appear. Then the program has to determine where to input the next 16 lines, and, of those 16, where to output the first 1 and where to output the first 5 lines. And the line of output bars may or may not take you from step 11 to step 12. The randomness in this process has to be accounted for. This problem is even more difficult to predict, because it’s highly random in the sense that you can never know what is going to take the most time and what is going to be the fastest.

In practice, as far as I can tell, there is no way to know what the computer will do based on this process. For example, the code may run faster than 1000 lines per second. The speed depends on what the computer is doing, but there is no way of knowing. This is like a computer program that’s not programmable.

Is there a better way?

There are some approaches to the non-deterministic problems. They all have one important property in common:

They are computationally bounded.

Conversely, if your problem is impossible to solve, it has a computationally bounded solution. If it’s possible to solve and there are any good techniques in the world to get rid of the problem, you may be able to make progress.

Another way is to use a program that automatically solves a difficult problem in a relatively short time. A very common example of this is our own Jupyter Notebook, but Jupyter Notebook runs on Java, not Python. So if anyone is interested in learning Python, this is probably the tool the best option for learning.

My solution

The most natural approach in this case is to use a distributed file storage system to store the solution and the output of the program, or the current state of the program, at an intermediate point.

So the idea is that you write a file named ”

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