Simulating the randIntNoRep( command on the TI 83 - random

The randIntNoRep( command has been released for the TI-84+/SE calculator on OS 2.53MP and above.
The command is used when you need to create a list of numbers in random order in which no integer is repeated. It is very useful for shuffling a sequence of any numbers. How can I implement this functionality on an earlier version (OS or device-wise)?

This can be achieved by creating a list of random numbers, and using it to sequence a second list of the numbers that you want randomized.
For example, randomizing a 52 card deck and saving it as a list can be done easily with randIntNoRep( :
:randIntNoRep(0,51→L₁
This can be simulated using the following code:
:rand(52→L₂
:seq(X,X,0,51→L₁
:SortA(L₂,L₁
L₂ is set to contain a set of 52 random values. L₁ is set to contain the numbers that will be randomized. By sequencing the lists in ascending order, the same method can be achieved as using randIntNoRep(.

You can randomize a list by swapping its elements, like this.
:For(F,1,dim(L1))
: iPart(dim(L1)rand+1)->R
: L1(R)->T
: L1(F)->L1(R)
: T->L1(F)
:End
This randomize L1, assuming L1 has all the elements you want it to.

Related

Using a specific seed in the `RANDOM_NUMBER` algorithm

I'm looking to use a specific set of seeds for the intrinsic function RANDOM_NUMBER (a PRNG). What I've read so far is that the seed value can be set via calling RANDOM_SEED, specifically RANDOM_SEED(GET = array). My confusion is how to (if it's possible) set a specific value for the algorithm, for instance in the RAND, RANDU, or RANDM algorithms one can specify their own seed directly. I'm not sure how to set the seed, as the get function seems to take an array. If it takes an array, does it always pull the seed value from a specific index in the array?
Basically, is there a way to set a specific single seed value? If so, would someone be able to write-it out?
As a side note - I'm attempting to set my seed because allegedly one of the other PRNGs I mentioned only works well with "large odd numbers" according to my professor, so I decided that I may as well control this when comparing the PRNG's.
First, the RANDOM_SEED is only used for controlimg the seed of RANDOM_NUMBER(). If you use any other random number generator subroutine or function, it will not affect them at all or if yes then in some compiler specific way which you must find in the manual. But most probably it does not affect them.
Second, you should not care at all whether the seed array contains 1, 4 or 42 integers, it doesn't matter because the PRNG uses the bits from the whole array in some unspecified custom way. For example you may be generating 64 bit real numbers, but the seed array is made of 32 bit integers. You cannot simply say which integer from the seed array does what. You can view the whole seed array as one big integer number that is cut into smaller pieces if you want.
Regarding your professors advice, who knows what he meant, but the seed is probably set by some procedure of that particular generator, and not by the standard RANDOM_SEED, so you must read the documentation for that generator.
And how to use a specific seed in RANDOM_SEED? It was described on this site several times,jkust search for RANDOM_SEED in the top right search field, really. But it is simple, once you know the size of the array, size it to any non-trivial numbers (you need enough non-zero bits) you want and use put=. That's really all, just don't think about individual values in the array, the whole array is one piece of data together.

I need to generate a 32 digit random number using lua, please suggest some way

I want to generate a 32 digit key containing alphanumeric characters and they should always be UNIQUE. Please suggest a way of doing that.
I've used math.random function but I get the same random number over and over again, i want it to be unique.
If you want a unique number you have to have a list of used numbers. Otherwise you will always have the chance of getting a used number again. Although it is quite unlikely with 32 digits.
You obviously did not read the documentation on math.random:
http://www.lua.org/manual/5.3/manual.html#pdf-math.random
Otherweise you would know that math.random will always give you the same pseudo random numbers unless you change the seed value using math.randomseed...
Please make sure to read the documentation on functions befor you use them.
The trivial program below generates 1000 random 32-bit keys without repetion with no wasted effort:
M=2^32-1
R={}
N=1000
n=0
for i=1,N do
local x=math.random(M)
if R[x]==nil then n=n+1 R[x]=n print(n,i,n==i,x) end
end
The point is that M is so large that repetitions are very unlikely, even if we increase N to one million.

When should I write my own random number algorithm instead of using a stock math function?

So I am taking a scripting test in Lua, and I am given this question:
Create an algorithm to generate a deck of cards, 1-52. Shuffle the deck of cards (do not use something like array.randomize() ). Then hand out 5 cards to two different players. Being that each card must be dealt to a different player at a time.
Typically I would do something like this to get a random number
local newDeck = {} --assume this array has all 52 cards in a playing deck
math.randomseed( os.time() )
local card = math.random(#newDeck)
...but it seems that the question is specifically asking that I do NOT use a stock math function.
(do not use something like array.randomize())
What would be the advantage to that? I can't imagine that the player of such a game would even notice a difference between random and pseudo random.
If only it were that simple. Most random number generators that are part of a language are linear congruential generators, meaning that the next term J, say, is related to the previous one I by
J = (aI + b) mod c
Where a, b, c are constants.
This means that it is possible to decipher the sequence from a single digit number of terms! (It's a set of simultaneous equations with bit of trickery to handle the modulus).
I'd say that an astute player is bound to notice the pseudo random nature of your sequence and may even game the system by unpicking your generator. You need to use a more sophisticated scheme. (Early attempts include Park-Miller and Bays-Durham; fairly well-known approaches).
I believe you are welcome to use the built in random number generator to get random numbers, but prohibited from using any built in array shufflers that may exist. How can you use a rng to have each card equally likely to be in each position?
you could just write something that draws a random card and puts it in the shuffled deck:
function shuf(tab)
local new = {}
for k=1,#tab do
new[#new+1]=table.remove(tab,math.random(#tab))
end
end
This approach makes sure you have no doubles.
I don't really think using a different RNG would matter that much unless you're doing cryptography, or something else that really matters.
Interpreting the question: just don't use a library function written for doing this. But there is a difference between a shuffler and a random number generator, since the latter can return double values while the former can't.

How to output array elements in random order using VHDL

I have an array of 10 elements. How do I output these in random order without repeating.
For a testbench, use the OSVVM random library to generate random indexes into your array. Or you could shuffle it (using the Fischer-Yates Algorithm in concert with the random library).
If it's something you need to synthesize, then put the array into a RAM block, and generate random addresses (for example using a linear feedback shift register).
Be aware that none of these is properly random, only pseudo-random. If you're attempting anything remotely cryptographic, they are unlikely to be what your want.
For testbenches, OSVVM's RandomPkg makes this easy.
library osvvm ;
use osvvm.RandomPkg.all ;
...
RandProc : process
variable RV : RandomPtype ;
variable IndexVals : integer_vector(0 to 9) := (others => integer'low) ;
begin
for i in IndexVals'range loop
-- min max ExcludeList
IndexVals(i) := RV.RandInt( 0, 9, IndexVals) ;
end loop ;
The problem gets more interesting if successive randomly generated permutations of 10 elements need to be different from the previous one. For that I would use the coverage model. Although, 10 is around the maximum number of permutations I would want to do this way though as there are n! permutations and the coverage model will require storage for each permutation generated.
A good way to get close to randomness is by using a linear feedback shift register.
http://en.wikipedia.org/wiki/Linear_feedback_shift_register
If this is for simulation only, you can use the uniform procedure from ieee.math_real to get a real number between 0 and 1, and scale it to the index range of your array.

Algorithms: random unique string

I need to generate string that meets the following requirements:
it should be a unique string;
string length should be 8 characters;
it should contain 2 digits;
all symbols (non-digital characters) should be upper case.
I will store them in a data base after generation (they will be assigned to other entities).
My intention is to do something like this:
Generate 2 random values from 0 to 9—they will be used for digits in the string;
generate 6 random values from 0 to 25 and add them to 64—they will be used as 6 symbols;
concatenate everything into one string;
check if the string already exists in the data base; if not—repeat.
My concern with regard to that algorithm is that it doesn't guarantee a result in finite time (if there are already A LOT of values in the data base).
Question: could you please give advice on how to improve this algorithm to be more deterministic?
Thanks.
it should be unique string;
string length should be 8 characters;
it should contains 2 digits;
all symbols (non-digital characters) - should be upper case.
Assuming:
requirements #2 and #3 are exact (exactly 8 chars, exactly 2 digits) and not a minimum
the "symbols" in requirement #4 are the 26 capital letters A through Z
you would like an evenly-distributed random string
Then your proposed method has two issues. One is that the letters A - Z are ASCII 65 - 90, not 64 - 89. The other is that it doesn't distribute the numbers evenly within the possible string space. That can be remedied by doing the following:
Generate two different integers between 0 and 7, and sort them.
Generate 2 random numbers from 0 to 9.
Generate 6 random letters from A to Z.
Use the two different integers in step #1 as positions, and put the 2 numbers in those positions.
Put the 6 random letters in the remaining positions.
There are 28 possibilities for the two different integers ((8*8 - 8 duplicates) / 2 orderings), 266 possibilities for the letters, and 100 possibilities for the numbers, the total # of valid combinations being Ncomb = 864964172800 = 8.64 x 1011.
edit: If you want to avoid the database for storage, but still guarantee both uniqueness of strings and have them be cryptographically secure, your best bet is a cryptographically random bijection from a counter between 0 and Nmax <= Ncomb to a subset of the space of possible output strings. (Bijection meaning there is a one-to-one correspondence between the output string and the input counter.)
This is possible with Feistel networks, which are commonly used in hash functions and symmetric cryptography (including AES). You'd probably want to choose Nmax = 239 which is the largest power of 2 <= Ncomb, and use a 39-bit Feistel network, using a constant key you keep secret. You then plug in your counter to the Feistel network, and out comes another 39-bit number X, which you then transform into the corresponding string as follows:
Repeat the following step 6 times:
Take X mod 26, generate a capital letter, and set X = X / 26.
Take X mod 100 to generate your two digits, and set X = X / 100.
X will now be between 0 and 17 inclusive (239 / 266 / 100 = 17.796...). Map this number to two unique digit positions (probably easiest using a lookup table, since we're only talking 28 possibilities. If you had more, use Floyd's algorithm for generating a unique permutation, and use the variable-base technique of mod + integer divide instead of generating a random number).
Follow the random approach above, but use the numbers generated by this algorithm instead.
Alternatively, use 40-bit numbers, and if the output of your Feistel network is > Ncomb, then increment the counter and try again. This covers the entire string space at the cost of rejecting invalid numbers and having to re-execute the algorithm. (But you don't need a database to do this.)
But this isn't something to get into unless you know what you're doing.
Are these user passwords? If so, there are a couple of things you need to take into account:
You must avoid 0/O and I/1, which can easily be mistaken for each other.
You must avoid too many consecutive letters, which might spell out a rude word.
As far as 2 is concerned, you can avoid the problem by using LLNLLNLL as your pattern (L = letter, N = number).
If you need 1 million passwords out of a pool of 2.5 billion, you will certainly get clashes in your database, so you have to deal with them gracefully. But a simple retry is enough, if your random number generator is robust.
I don't see anything in your requirements that states that the string needs to be random. You could just do something like the following pseudocode:
for letters in ( 'AAAAAA' .. 'ZZZZZZ' ) {
for numbers in ( 00 .. 99 ) {
string = letters + numbers
}
}
This will create unique strings eight characters long, with two digits and six upper-case letters.
If you need randomly-generated strings, then you need to keep some kind of record of which strings have been previously generated, so you're going to have to hit a DB (or keep them all in memory, or write them to a textfile) and check against that list.
I think you're safe well into your tens of thousands of such ID's, and even after that you're most likely alright.
Now if you want some determinism, you can always force a password after a certain number of failures. Say after 50 failures, you select a password at random and increment a part of it by 1 until you get a free one.
I'm willing to bet money though that you'll never see the extra functionality kick in during your life time :)
Do it the other way around: generate one big random number that you will split up to obtain the individual characters:
long bigrandom = ...;
int firstDigit = bigRandom % 10;
int secondDigit = ( bigrandom / 10 ) % 10;
and so on.
Then you only store the random number in your database and not the string. Since there's a one-to-one relationship between the string and the number, this doesn't really make a difference.
However, when you try to insert a new value, and it's already in the databse, you can easily find the smallest unallocated number graeter than the originally generated number, and use that instead of the one you generated.
What you gain from this method is that you're guaranteed to find an available code relatively quickly, even when most codes are already allocated.
For one thing, your list of requirements doesn't state that string has to be necessary random, so you might consider something like database index.
If 'random' is a requirement, you can do a few improvements.
Store string as a number in database. Not sure how much this improves perfromance.
Do not store used strings at all. You can employ 'index' approach above, but convert integer number to a string in a seemingly random fashion (e.g., employing bit shift). Without much research, nobody will notice pattern.
E.g., if we have sequence 1, 2, 3, 4, ... and use cyclic binary shift right by 1 bit, it'll be turned into 4, 1, 5, 2, ... (assuming we have 3 bits only)
It doesn't have to be a shift too, it can be a permutation or any other 'randomization'.
The problem with your approach is clearly that while you have few records, you are very unlikely to get collisions but as your number of records grows the chance will increase until it becomes more likely than not that you'll get a collision. Eventually you will be hitting multiple collisions before you get a 'valid' result. Every time will require a table scan to determine if the code is valid, and the whole thing turns into a mess.
The simplest solution is to precalculate your codes.
Start with the first code 00AAAA, and increment to generate 00AAAB, 00AAAC ... 99ZZZZ. Insert them into a table in random order. When you need a new code, retrieve to top record unused record from the table (then mark it as used). It's not a huge table, as pointed out above - only a few million records.
You don't need to calculate any random numbers and generate strings for each user (already done)
You don't need to check whether anything has already been used, just get the next available
No chance of getting multiple collisions before finding something usable.
If you ever need more 'codes', just generate some more 'random' strings and append them to the table.

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