Predict malignancy in cancer tumors with your own neural network built from scratch in Python. Understand the keys of deep learning in 100 lines of code.

Is a million lines of code a lot? How many lines of code are there in Windows? Facebook? iPhone apps? Let our data-visualization program your brain.

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How many millions of lines of code does it take to make the modern program, web service, car, or airplane possible? The range is extraordinary: the average iPhone app has less than 50,000 lines of code, while Googleâ€™s entire code base is two billion lines for all services.Of course, every engineer knows that "lines of code" is a silly measure, and besides, the lines of code we are counting here are much less complex than the code written by professional software engineers. No software engineer measures the value or their work in lines of code.

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## Is it true that professional software engineers produce only 50 to 100 lines of code per day? - Quora 100 lines of code

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## How to Create Generative Art In Less Than 100 Lines Of Code 100 lines of code

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## 100 lines of code

In math and economics, there is a long, proud history of placing imaginary prisoners into nasty, complicated scenarios.We have, of course, the classicas well as.

Add to that list the focus of this post, 100 prisoners and 100 boxes.

In this game, the warden places 100 numbers in 100 boxes, at random with equal probability that any number will be in any box.

Each convict is assigned a number.

One by one they enter the room with the boxes, and try to find their corresponding number.

They can open up to 50 different boxes.

Once they either find their number or fail, they move on to a different room and all of the boxes are returned to exactly how they were before the prisoner entered the room.

The prisoners can communicate with each other before the game begins, but as soon as it starts they have no way to signal to each other.

The warden is requiring that all 100 prisoners find their numbers, otherwise she will force them to listen to hundreds of hours of non-stop, loud rock musician interviews.

Can they avoid this fate?

Can they do better?

Of course they can.

Before I explain how, and go into a Monte Carlo simulation in R, you might want to think about how they can do it.

Did you find a better way?

The trick should be clear from the code below, but if not skip on to the explanation.

How many times should we run this experiment?

The theoretical success rate is about 31%.

One way to look at the distribution of numbers in boxes is to see it as a permutation of the numbers from 1 to 100.

Each permutation can be partitioned into 100 lines of code are called cycles.

A cycle works like here pick any number in your permutation.

Then you look at the number the 23 rd place ie the number in the 23rd box, counting from the left.

If that number is 16, you look at the number in the 16 th place.

If that number is 87, go open box number 87 and follow that number.

Eventually, the box you open up will have the number that brings you 100 lines of code to where you started, completing the cycle.

Different permutations have different cycles.

The key for the prisoner is that by starting with the box that is the same place from the left as his number, and by following the numbers in the boxes, the prisoner guarantees that if he is in a cycle of length less than 50, he will eventually open the box with his number in it, which would complete the cycle he began.

One way to envision cycles of different lengths is to think about the extreme cases.

If a particular permutation shifted every single number over one to the left and wrapped number 1 onto the endyou would have a single cycle of length 100.

Box 1 would contain number 2, box 2 number 3 and so on.

On the other hand, if a permutation flipped every pair of consecutive numbers, you would have 50 cycles, each of length 2: box 1 would have number 2, box 2 would have number 1.

As you can see from the 100 lines of code, when using this strategy you can never have between 50 and 100 winning prisoners.

Anytime you have a single cycle of length greater than 50, for example 55, then 100 lines of code 55 prisoners who start on that cycle will fail to find their number.

If no cycles are longer than 50, everyone wins.

Just how rare are different cycles of different lengths?

Before moving on I wanted to visualize these cycles.

You can follow any comments to this entry through the feed.

Both comments and pings are currently closed.

It works, but on the unstated condition that the prisoners know of a surjective function from the 100 numbers the warden places in the 100 boxes to those 100 boxes, https://games-free-deposit.website/100/100-lions-slot-machine-free.html example if the prisoners know that the warden will choose the first 100 counting numbers.

There are other tricks one can play too.

Random strategy: 25% odds of success Optimal strategy: Prisoner 1 looks in one box.

Prisoner 2 looks in the other box.

Worst strategy: Both prisoners look in the same box.

So my follow-up question: Is what you described optimal, or is there something better?

For those who want to try it, add: library sna to the beginning of the code, then replace segments â€¦ with gplot.

Douglas McClean: I suppose I should state that the warden has put each of the prisoners numbers in one of the boxes.

I thought the same as Jonathan mentioned ealier, you need a linear ordering, maybe wooden boxes with numbers at them, too.

Looking in the first box and discovering the number 37 + sqrt 11 which does not match his number 6, the first prisoner does not know what to do next.

To echo Jonathan, I assumed that the prisoners would not be able to assume that the boxes in the room were laid out in a line.

Maybe you could restate 100 line slots contrived problem using doors down a corridor instead of boxes?

This seems to be a good way to get the maximum chance of everyone being freed.

I would imagine the prisoners being a bit more selfish, what if they wanted to maximize the chance that each individual commit 100 slot photo album does freed?

The first strategy I thought of guarantees that exactly 50% of the prisoners would be freed, every time, and it might be possible to improve upon it, with a small change to the box selection: The prisoners all agree to each open the 50 leftmost boxes.

This way, 50 prisoners will find their number, since they all open the same box.

Not only that, there is also a history of mathematics being developed in prison.

Scratch that link it actually works against this scheme, because the prisoners stop following a path through the boxes.

It works out at about 17% efficient.

Thinking about it some more, https://games-free-deposit.website/100/bank-of-america-100-sign-up-bonus.html define a cycle at all?

Any cycle through the boxes followed by all prisoners who each take a unique starting point, even if that cycle is just to iterate sequentially over the boxes, results in the same chance of finding the correct boxes.

If the first prisoners opens a box and then goes to the next one that got the number he found in the first box, everybody know what the number of the second box was.

So in reality this would be probably some kind of memoryâ€¦.

Hi ran2, The way the problem is stated usually implies that every time a new prisoner enters the room, all of the boxes are put back to exactly how they were at the beginning.

No other cycle can exist because that would require opening a box with a number that has already been foundâ€¦ per the parameters of the game this is impossible each number exists only once in the 100 boxes.

Here is a counterexample where no loop-cycle combina-tricks gets the expected survivability to 31%.

Simple fractal in Haskell in under 100 lines of code

## 100 lines of Python code to understand the key concepts of in-depth learning: building a malignant tumor detection network from scratch | Develop Paper 100 lines of code

## 100 lines of Python code to understand the key concepts of in-depth learning: building a malignant tumor detection network from scratch | Develop Paper 100 lines of code

As a rule, no, thatâ€™s far too little. On my bog-standard 22â€ł display, I can see about 50 lines of Java in my IDE before I have to scroll, so 50 lines really is an *incredibly* small amount of code.How I got control of my spending with a couple no-code services and only 100 lines of Python code. Josh Peters Blocked Unblock Follow Following. May 5.

When you write 100+ lines of code and it works on the first try . 6:52 PM - 29 Dec 2017.. Twitter may be over capacity or experiencing a momentary hiccup.