Aug 15, 2019 How to Fix the Most Annoying Things in Windows 10. If you hit the Shift key five times in a row in Windows. To get non-equals (≠), etc. Same goes for the letters to get variativons, such. Common C# Programming Mistake #4: Using iterative (instead of declarative) statements to manipulate collections. In C# 3.0, the addition of Language-Integrated Query (LINQ) to the language changed forever the way collections are queried and manipulated. Since then, if you’re using iterative statements to manipulate collections, you didn’t use LINQ when you probably should have. One mathematical function in C programming that’s relatively easy to grasp is the rand function. It generates random numbers. Though that may seem silly, it’s the basis for just about every computer game ever invented. Random numbers are a big deal in programming. A computer cannot generate truly random numbers. Instead, it produces what are. Mar 12, 2018 Whether it's wearing the same shirt as everyone else in class, accidentally buying ten extra things in your haul, and what ever happened to that dog? This is Every Target Ever!
One mathematical function in C programming that’s relatively easy to grasp is the rand() function. It generates random numbers. Though that may seem silly, it’s the basis for just about every computer game ever invented. Random numbers are a big deal in programming.
A computer cannot generate truly random numbers. Instead, it produces what are known as pseudo–random numbers. That’s because conditions inside the computer can be replicated. Therefore, serious mathematicians scoff that any value a computer calls random isn’t a truly random number. Can you hear them scoffing?
How to generate random numbers
The rand() function is the simplest of C’s random-number functions. It requires the stdlib.h header file, and it coughs up an int value that’s supposedly random. Now, That’s Random demonstrates sample code.
NOW, THAT’S RANDOM
Now, That’s Random uses a nested for loop to display 100 random values. The rand() function in Line 13 generates the values. The printf() function in Line 14 displays the values by using the %d conversion character, which displays int values.
Exercise 1: Create a new project by using the source code shown in Now, That’s Random. Build and run to behold 100 random values.
Exercise 2: Modify the code so that all the values displayed are in the range 0 through 20.
Here’s a hint for Now, That’s Random: Use the modulus assignment operator to limit the range of the random numbers. The format looks like this:
r is the number returned from the rand() function. %= is the modulus assignment operator. n is the range limit, plus 1. After the preceding statement, values returned are in the range 0 through n-1. So if you want to generate values between 1 and 100, you would use this formula:
How to increase the randomness of numbersin C programming
Just to give some credit to the snooty mathematicians who claim that computers generate pseudo-random numbers, run the program you generated from Exercise 2. Observe the output. Run the program again. See anything familiar?
The rand() function is good at generating a slew of random values, but they’re predictable values. To make the output less predictable, you need to seed the random-number generator. That’s done by using the srand() function.
Like the rand() function, the srand() function requires the stdlib.h header, shown at Line 2 in Even More Randomness. The function requires an unsigned int value, seed, which is declared at Line 6. The scanf() function at Line 10 reads in the unsigned value by using the %u placeholder. Then the srand() function uses the seed value in Line 11.
EVEN MORE RANDOMNESS
The rand() function is used at Line 16, although the results are now based on the seed, which is set when the program runs.
Exercise 3: Create a new project using the source code shown in Even More Randomness. Build it. Run the program a few times, trying different seed values. The output is different every time.
Alas, the random values that are generated are still predictable when you type the same seed number. In fact, when the value 1 is used as the seed, you see the same “random” values you saw in Exercise 1, when you didn’t even use srand()!
There has to be a better way.
The best way to write a random-number generator is not to ask the user to type a seed, but rather to fetch a seed from elsewhere. In More Truly Random Than Ever, the seed value is pulled from the system clock by using the time() function.
MORE TRULY RANDOM THAN EVER
The time() function returns information about the current time of day, a value that’s constantly changing. The NULL argument helps solve some problems, but time() returns an ever-changing value.
The (unsigned) part of the statement ensures that the value returned by the time() function is an unsigned integer. That’s a technique known as typecasting.
The bottom line is that the srand() function is passed a seed value, courtesy of the time() function, and the result is that the rand() function generates values that are more random than you’d get otherwise.
Exercise 4: Type the source code from More Truly Random Than Ever and build the project. Run it a few times to ensure that the numbers are as random as the computer can get them.
A hash function takes an item of a given type and generates an integer hash value within a given range. The input items can be anything: strings, compiled shader programs, files, even directories. The same input always generates the same hash value, and a good hash function tends to generate different hash values when given different inputs.
A hash function has no awareness of “other” items in the set of inputs. It just performs some arithmetic and/or bit-magic operations on the input item passed to it. Therefore, there’s always a chance that two different inputs will generate the same hash value.
Take the well-known hash function CRC32, for example. If you feed this function the two strings “plumless” and “buckeroo”, it generates the same value. This is known as a hash collision.
What is the probability of a hash collision? This question is just a general form of the birthday problem from mathematics. The answer is not always intuitive, so it’s difficult to guess correctly. Let’s derive the math and try to get a better feel for those probabilities.
Calculating the Probability of a Hash Collision
There are many choices of hash function, and the creation of a good hash function is still an active area of research. Some hash functions are fast; others are slow. Some distribute hash values evenly across the available range; others don’t. If you’re interested in the real-world performance of a few known hash functions, Charles Bloom and strchr.com offer some comparisons. For our purposes, let’s assume the hash function is pretty good — it distributes hash values evenly across the available range.
In this case, generating hash values for a collection of inputs is a lot like generating a collection of random numbers. Our question, then, translates into the following:
Given (k ) randomly generated values, where each value is a non-negative integer less than (N ), what is the probability that at least two of them are equal?
It turns out it’s actually a bit simpler to start with the reverse question: What is the probability that they are all unique? Whatever the answer to the reverse question, we can just subtract it from one, and we’ll have the answer to our original question.
Given a space of (N ) possible hash values, suppose you’ve already picked a single value. After that, there are (N-1 ) remaining values (out of a possible (N )) that are unique from the first. Therefore, the probability of randomly generating two integers that are unique from each other is (frac{N-1}{N} ).
After that, there are (N-2 ) remaining values (out of a possible (N )) that are unique from the first two, which means that the probability of randomly generating three integers that are all unique is (frac{N-1}{N}timesfrac{N-2}{N} ). (We can multiply the probabilities together because each random number generation is an independent event.)
In general, the probability of randomly generating (k ) integers that are all unique is:
On a computer, this can be quite slow to evaluate for large k. Luckily, the above expression is approximately equal to:
which is a lot faster to compute. How do we know this is a good approximation? Well, it can be shown analytically, using the Taylor expansion of (e^x ) and an epsilon-delta proof, that the approximation error tends to zero as (N ) increases. Or, you can just compute both values and compare them. Run the following Python script with different (N ), and you’ll get a feeling for just how accurate the approximation is:
Great, so this magic expression serves as our probability that all values are unique. Subtract it from one, and you have the probability of a hash collision:
$$ 1 - e^{frac{-k(k-1)}{2N}} $$
Here is a graph for (N = 2^{32} ). This illustrates the probability of collision when using 32-bit hash values. It’s worth noting that a 50% chance of collision occurs when the number of hashes is 77163. Also note that the graph takes the same S-curved shape for any value of (N ).
Chance Of Ever Generating Same Key Twice 10 Letters Printable
Simplified Approximations
It’s interesting that our approximation takes the form (1 - e^{-X} ), because it just so happens that for any (X ) that is very small, say (frac{1}{10} ) or less:
In other words, the exponent makes a pretty good approximation all by itself! In fact, the smaller the (X ), the more accurate it gets. So for small collision probabilities, we can use the simplified expression:
This is actually a handy representation, because it avoids some numerical precision problems in the original expression. Floating point numbers are not very good at representing values extremely close to 1.
Furthermore, if you’re talking about more than a handful of (k ), there isn’t a very big difference between (k(k-1) ) and (k^2 ). So the absolute simplest approximation is just:
Chance Of Ever Generating Same Key Twice 10 Letters Lyrics
Small Collision Probabilities
In certain applications — such as when using hash values as IDs — it can be very important to avoid collisions. That’s why the most interesting probabilities are the small ones.
Chance Of Ever Generating Same Key Twice 10 Letters Crossword Clue
Assuming your hash values are 32-bit, 64-bit or 160-bit, the following table contains a range of small probabilities. If you know the number of hash values, simply find the nearest matching row. To help put the numbers in perspective, I’ve included a few real-world probabilities scraped from the web, like the odds of winning the lottery.