Uniform distribution in a small range to generate precise big probability - php

Currently I'm using a uniform distribution to generate a winning probability.
For a probability of let's say 1% I define a winning number 47 then I do a mt_rand(1,100) and if the number is 47 the user win. Which is fine.
This work well for small probability like 1/100'000 but when I want a probability of let's say 40% which is 1/0.4 = 2.5
I cannot make mt_rand(1,2.5) I have to do mt_rand(1,2) or mt_rand(1,3) which mean respectively 50% and 33%.
How should I do to get a 40% probability?

let's say you want winning probability as x (assuming an integer), then generate
$num = mt_rand (1,100)
if ($num<=$prob) {//user wins}
If you don't have $prob as an integer and is a number with 2 decimal places eg: 47.23%, then you could generate
$num = mt_rand(1,10000)
if ($num/100 <= $prob), {//user wins}
Similarly you can extend it to whatever accuracy you want

if (mt_rand(1, 100) / $probability <= 1) {
// success
}
E.g. if you have now $probability = 10; you have ten (of hundred) cases where the number between 1 and 100 is smaller or equal to one.

Related

How to get web server average load level in percentages using PHP function sys_getloadavg()?

PHP function sys_getloadavg() returns an array with three values showing average number of processes in the system run-queue over the last 1, 5 and 15 minutes, respectively.
How to convert this production to percentages?
Percentages are relative measurement units. This means that we must know a range or minimum and maximum values of the measured quantity. Function sys_getloadavg() evaluates performance of whole system, not separate CPU load level, or usage of memory, file system or database. It returns float numbers showing how many processes were in run-queue for the last interval of time.
I did some experiment with my MacBook Pro (8 CPU cores) and PHP 7.0 to figure out range of values produced by sys_getloadavg(). I've got average figures between 1.3 and 3.2. When I run video conversion program in parallel, the maximum result jumped up to 18.9. By the way, in all cases I didn't fix substantial losses in web page loading speed. It means that whole system was not overloaded.
Let's take for 100% of system load situation when web page don't load for reasonable time, let say 10 sec. I don't know what values will return sys_getloadavg() in this case, but I think it will be something big.
My solution is very simple. Let's measure system average load level and persistently store results as minimum and maximum values. When system works faster or slower we will update min and max by new values. So, our program will 'learn' the system and becomes more and more precise. The value of the last minute will be compared with stored range and converted to percents like (loadavg - min)/((max - min) / 100):
$performance = sys_getloadavg();
try {
$rangeFile = 'sys_load_level.txt';
$range = file($rangeFile, FILE_IGNORE_NEW_LINES | FILE_SKIP_EMPTY_LINES);
$performance = array_merge($performance, $range);
$min = min($performance);
$max = max($performance);
if ($range[0] > $min || $range[1] < $max)
file_put_contents($rangeFile, [$min.PHP_EOL, $max.PHP_EOL]);
}
catch (Exception $e) {
$min = min($performance);
$max = max($performance);
file_put_contents($rangeFile, [$min.PHP_EOL, $max.PHP_EOL]);
}
$level = intval(($performance[0] - $min) / (($max - $min) / 100.0));

Using round() to get exact value - PHP

Hey guy's I am working on a project of mine which involves the use of money. I am trying to not use round anymore because, it's rounding things to nearest tenth and I need exact numbers. One reason I was using it, was because it was giving a whole number.
The way I am working my number system is that 100 = $1, 2000 = $20, etc.. I was currently using the round function because it would get rid of the decimal point for me and give me a whole number, lets say: 223 which in turn would = $2.23.
Here is what I am using:
$amount += round(($amount / 29) + 30);
Here are the numbers:
Lets say we have a charge of 100 and we add 125 which equal 225 (USD $2.25). Now we add taxes and processing: + 2.9% + $.30. After multiplying 2.25 by 2.9% and adding .30 the amount would be: 0.36525 - this is the amount that should be added than to the $2.25 which than would be 261 = $2.61
The issue is because of the rounding, when I look in my Stripe panel (I am using Stripe API for payments) I see a charge of $2.63. So my question is, how would I go about making it exact without having any rounding and decimal places.
UPDATE:
Here is the above example more explained:
Lets say we have a charge of 100 and we add 125 which equal 225 (USD $2.25). Now we add taxes and processing: + 2.9% + $.30. After multiplying 2.25 by 2.9% and adding .30 the amount would be: 0.36525 - this is the amount that should be added than to the $2.25 which than would be 261 = $2.61
So now with that the actual value of amount that should be charged is $2.61 but instead when using the round it gives me 263 which also means $2.63. The above example is the simple math that is correct.
In order to avoid calculation hiccups like that, only round the final result. Keep all other calculations as accurate as possible:
$original = 100;
$original += 125;
$tax = $original * 2.9 / 100; //+2.9%
$tax += 30; //+$.30
$original += $tax; //Add tax.
echo $original; //Result is 261.525. Round as you please.
You can specify precision and rounding method to keep it consistent (PHP round()), then you can deal with the actual values. Doing math tricks like multiplication by a multiple of 10 will only make it more confusing in the long run.
$amount += round(($amount / 29) + 30, 2, PHP_ROUND_HALF_UP);
Will this solve your problem?

PHP - get closest number given a certain number?

I'm modifying one of OpenCart's product filters to filter products in/out by price. What I do is get all products belonging to a certain category and extract their prices to put them in a slider, but this is not elegant or 'professional' at all, and I would like to code a proper solution.
Let's say I have the following prices: 125, 270, 517, 1680 and 14790. What I would like to do (ideally) is get the highest number (14790 in this short example) and, from it, get something like '15000', so I can divide that between a given factor (like 100) and put that into a slider.
Is there a PHP function to do this kind of calculation?
If I understand your question, and you're asking to round to essentially the nearest 100, there isn't a specific function, but with a bit of maths you can round to the nearest hundred like so:
$price = ceil($price / 100) * 100;
Using:
$price = ceil($price / 1000) * 1000;
Would round to the nearest 1000.
Get the max number, then round it up to the nearest thousand?
<?php
$largest = max(125, 270, 517, 1680, 14790);
$nearest = ceil($largest / 1000) * 1000;
You could just loop through the numbers, remembering the highest value as you go. It's common coding practice. (Ok there really is a max() function as well, echo max(1, 3, 5, 6, 7); // 7)
Then you could divide the highest number by your factor, take the integer you get and add one to it, then multiply by the factor again and there you go.
just do : x=floor(14790/100) ; the floor function returns the next lowest integer value

How can I create a specified amount of random values that all equal up to a specified number in PHP?

For example, say I enter '10' for the amount of values, and '10000' as a total amount.
The script would need to randomize 10 different numbers that all equal up to 10000. No more, no less.
But it needs to be dynamic, as well. As in, sometimes I might enter '5' or '6' or even '99' for the amount of values, and any number (up to a billion or even higher) as the total amount.
How would I go about doing this?
EDIT: I should also mention that all numbers need to be a positive integer
The correct answer here is unbelievably simple.
Just imagine a white line, let's say 1000 units long.
You want to divide the line in to ten parts, using red marks.
VERY SIMPLY, CHOOSE NINE RANDOM NUMBERS and put a red paint mark at each of those points.
It's just that simple. You're done!
Thus, the algorithm is:
(1) pick nine random numbers between 0 and 1000
(2) put the nine numbers, a zero, and a 1000, in an array
(3) sort the array
(4) using subtraction get the ten "distances" between array values
You're done.
(Obviously if you want to have no zeros in your final set, in part (1) simply rechoose another random number if you get a collision.)
Ideally as programmers, we can "see" visual algorithms like this in our heads -- try to think visually whatever we do!
Footnote - for any non-programmers reading this, just to be clear pls note that this is like "the first thing you ever learn when studying computer science!" i.e. I do not get any credit for this, I just typed in the answer since I stumbled on the page. No kudos to me!
Just for the record another common approach (depending on the desired outcome, whether you're dealing with real or whole numbers, and other constraints) is also very "ah hah!" elegant. All you do is this: get 10 random numbers. Add them up. Remarkably simply, just: multiply or divide them all by some number, so that, the total is the desired total! It's that easy!
maybe something like this:
set max amount remaining to the target number
loop for 1 to the number of values you want - 1
get a random number from 0 to the max amount remaining
set new max amount remaining to old max amount remaining minus the current random number
repeat loop
you will end up with a 'remainder' so the last number is determined by whatever is left over to make up the original total.
Generate 10 random numbers till 10000 .
Sort them from big to small : g0 to g9
g0 = 10000 - r0
g1 = r0 - r1
...
g8 = r8 - r9
g9 = r9
This will yield 10 random numbers over the full range which add up to 10000.
I believe the answer provided by #JoeBlow is largely correct, but only if the 'randomness' desired requires uniform distribution. In a comment on that answer, #Artefacto said this:
It may be simple but it does not generate uniformly distributed numbers...
Itis biased in favor of numbers of size 1000/10 (for a sum of 1000 and 10 numbers).
This begs the question which was mentioned previously regarding the desired distribution of these numbers. JoeBlow's method does ensure a that element 1 has the same chance at being number x as element 2, which means that it must be biased towards numbers of size Max/n. Whether the OP wanted a more likely shot at a single element approaching Max or wanted a uniform distribution was not made clear in the question. [Apologies - I am not sure from a terminology perspective whether that makes a 'uniform distribution', so I refer to it in layman's terms only]
In all, it is incorrect to say that a 'random' list of elements is necessarily uniformly distributed. The missing element, as stated in other comments above, is the desired distribution.
To demonstrate this, I propose the following solution, which contains sequential random numbers of a random distribution pattern. Such a solution would be useful if the first element should have an equal chance at any number between 0-N, with each subsequent number having an equal chance at any number between 0-[Remaining Total]:
[Pseudo code]:
Create Array of size N
Create Integer of size Max
Loop through each element of N Except the last one
N(i) = RandomBetween (0, Max)
Max = Max - N(i)
End Loop
N(N) = Max
It may be necessary to take these elements and randomize their order after they have been created, depending on how they will be used [otherwise, the average size of each element decreases with each iteration].
Update: #Joe Blow has the perfect answer. My answer has the special feature of generating chunks of approximately the same size (or at least a difference no bigger than (10000 / 10)), leaving it in place for that reason.
The easiest and fastest approach that comes to my mind is:
Divide 10000 by 10 and store the values in an array. (10 times the value 10000)
Walk through every one of the 10 elements in a for loop.
From each element, subtract a random number between (10000 / 10).
Add that number to the following element.
This will give you a number of random values that, when added, will result in the end value (ignoring floating point issues).
Should be half-way easy to implement.
You'll reach PHP's maximum integer limit at some point, though. Not sure how far this can be used for values towards a billion and beyond.
Related: http://www.mathworks.cn/matlabcentral/newsreader/view_thread/141395
See this MATLAB package. It is accompanied with a file with the theory behind the implementation.
This function generates random, uniformly distributed vectors, x = [x1,x2,x3,...,xn]', which have a specified sum s, and for which we have a <= xi <= b, for specified values a and b. It is helpful to regard such vectors as points belonging to n-dimensional Euclidean space and lying in an n-1 dimensional hyperplane constrained to the sum s. Since, for all a and b, the problem can easily be rescaled to the case where a = 0 and b = 1, we will henceforth assume in this description that this is the case, and that we are operating within the unit n-dimensional "cube".
This is the implementation (© Roger Stafford):
function [x,v] = randfixedsum(n,m,s,a,b)
% Rescale to a unit cube: 0 <= x(i) <= 1
s = (s-n*a)/(b-a);
% Construct the transition probability table, t.
% t(i,j) will be utilized only in the region where j <= i + 1.
k = max(min(floor(s),n-1),0); % Must have 0 <= k <= n-1
s = max(min(s,k+1),k); % Must have k <= s <= k+1
s1 = s - [k:-1:k-n+1]; % s1 & s2 will never be negative
s2 = [k+n:-1:k+1] - s;
w = zeros(n,n+1); w(1,2) = realmax; % Scale for full 'double' range
t = zeros(n-1,n);
tiny = 2^(-1074); % The smallest positive matlab 'double' no.
for i = 2:n
tmp1 = w(i-1,2:i+1).*s1(1:i)/i;
tmp2 = w(i-1,1:i).*s2(n-i+1:n)/i;
w(i,2:i+1) = tmp1 + tmp2;
tmp3 = w(i,2:i+1) + tiny; % In case tmp1 & tmp2 are both 0,
tmp4 = (s2(n-i+1:n) > s1(1:i)); % then t is 0 on left & 1 on right
t(i-1,1:i) = (tmp2./tmp3).*tmp4 + (1-tmp1./tmp3).*(~tmp4);
end
% Derive the polytope volume v from the appropriate
% element in the bottom row of w.
v = n^(3/2)*(w(n,k+2)/realmax)*(b-a)^(n-1);
% Now compute the matrix x.
x = zeros(n,m);
if m == 0, return, end % If m is zero, quit with x = []
rt = rand(n-1,m); % For random selection of simplex type
rs = rand(n-1,m); % For random location within a simplex
s = repmat(s,1,m);
j = repmat(k+1,1,m); % For indexing in the t table
sm = zeros(1,m); pr = ones(1,m); % Start with sum zero & product 1
for i = n-1:-1:1 % Work backwards in the t table
e = (rt(n-i,:)<=t(i,j)); % Use rt to choose a transition
sx = rs(n-i,:).^(1/i); % Use rs to compute next simplex coord.
sm = sm + (1-sx).*pr.*s/(i+1); % Update sum
pr = sx.*pr; % Update product
x(n-i,:) = sm + pr.*e; % Calculate x using simplex coords.
s = s - e; j = j - e; % Transition adjustment
end
x(n,:) = sm + pr.*s; % Compute the last x
% Randomly permute the order in the columns of x and rescale.
rp = rand(n,m); % Use rp to carry out a matrix 'randperm'
[ig,p] = sort(rp); % The values placed in ig are ignored
x = (b-a)*x(p+repmat([0:n:n*(m-1)],n,1))+a; % Permute & rescale x
return

Finding similar number patterns in table

Ok, let's suppose we have members table. There is a field called, let's say, about_member. There will be a string like this 1-1-2-1-2 for everybody. Let's suppose member_1 has this string 1-1-2-2-1 and he searches who has the similar string or as much similar as possible. For example if member_2 has string 1-1-2-2-1 it will be 100% match, but if member_3 has string like this 2-1-1-2-1 it will be 60% match. And it has to be ordered by match percent. What is the most optimal way to do it with MYSQL and PHP? It's really hard to explain what I mean, but maybe you got it, if not, ask me. Thanks.
Edit: Please give me ideas without Levenshtein method. That answer will get bounty. Thanks. (bounty will be announced when I will be able to do that)
convert your number sequences to bit masks and use BIT_COUNT(column ^ search) as similarity function, ranged from 0 (= 100% match, strings are equal) to [bit length] (=0%, strings are completely different). To convert this similarity function to the percent value use
100 * (bit_length - similarity) / bit_length
For example, "1-1-2-2-1" becomes "00110" (assuming you have only two states), 2-1-1-2-1 is "10010", bit_count(00110 ^ 10010) = 2, bit-length = 5, and 100 * (5 - 2) / 5 = 60%.
Jawa posted this idea originally; here is my attempt.
^ is the XOR function. It compares 2 binary numbers bit-by-bit and returns 0 if both bits are the same, and 1 otherwise.
0 1 0 0 0 1 0 1 0 1 1 1 (number 1)
^ 0 1 1 1 0 1 0 1 1 0 1 1 (number 2)
= 0 0 1 1 0 0 0 0 1 1 0 0 (result)
How this applies to your problem:
// In binary...
1111 ^ 0111 = 1000 // (1 bit out of 4 didn't match: 75% match)
1111 ^ 0000 = 1111 // (4 bits out of 4 didn't match: 0% match)
// The same examples, except now in decimal...
15 ^ 7 = 8 (1000 in binary) // (1 bit out of 4 didn't match: 75% match)
15 ^ 0 = 15 (1111 in binary) // (4 bits out of 4 didn't match: 0% match)
How we can count these bits in MySQL:
BIT_COUNT(b'0111') = 3 // Bit count of binary '0111'
BIT_COUNT(7) = 3 // Bit count of decimal 7 (= 0111 in binary)
BIT_COUNT(b'1111' ^ b'0111') = 1 // (1 bit out of 4 didn't match: 75% match)
So to get the similarity...
// First we focus on calculating mismatch.
(BIT_COUNT(b'1111' ^ b'0111') / YOUR_TOTAL_BITS) = 0.25 (25% mismatch)
(BIT_COUNT(b'1111' ^ b'1111') / YOUR_TOTAL_BITS) = 0 (0% mismatch; 100% match)
// Now, getting the proportion of matched bits is easy
1 - (BIT_COUNT(b'1111' ^ b'0111') / YOUR_TOTAL_BITS) = 0.75 (75% match)
1 - (BIT_COUNT(b'1111' ^ b'1111') / YOUR_TOTAL_BITS) = 1.00 (100% match)
If we could just make your about_member field store data as bits (and be represented by an integer), we could do all of this easily! Instead of 1-2-1-1-1, use 0-1-0-0-0, but without the dashes.
Here's how PHP can help us:
bindec('01000') == 8;
bindec('00001') == 1;
decbin(8) == '01000';
decbin(1) == '00001';
And finally, here's the implementation:
// Setting a member's about_member property...
$about_member = '01100101';
$about_member_int = bindec($about_member);
$query = "INSERT INTO members (name,about_member) VALUES ($name,$about_member_int)";
// Getting matches...
$total_bits = 8; // The maximum length the member_about field can be (8 in this example)
$my_member_about = '00101100';
$my_member_about_int = bindec($my_member_about_int);
$query = "
SELECT
*,
(1 - (BIT_COUNT(member_about ^ $my_member_about_int) / $total_bits)) match
FROM members
ORDER BY match DESC
LIMIT 10";
This last query will have selected the 10 members most similar to me!
Now, to recap, in layman's terms,
We use binary because it makes things easier; the binary number is like a long line of light switches. We want to save our "light switch configuration" as well as find members that have the most similar configurations.
The ^ operator, given 2 light switch configurations, does a comparison for us. The result is again a series of switches; a switch will be ON if the 2 original switches were in different positions, and OFF if they were in the same position.
BIT_COUNT tells us how many switches are ON--giving us a count of how many switches were different. YOUR_TOTAL_BITS is the total number of switches.
But binary numbers are still just numbers... and so a string of 1's and 0's really just represents a number like 133 or 94. But it's a lot harder to visualize our "light switch configuration" if we use decimal numbers. That's where PHP's decbin and bindec come in.
Learn more about the binary numeral system.
Hope this helps!
The obvious solution is to look at the levenstein distance (there isn't an implementation built into mysql but there are other implementations accesible e.g. this one in pl/sql and some extensions), however as usual, the right way to solve the problem would be to have normalised the data properly in the first place.
One way to do this is to calculate the Levenshtein distance between your search string and the about_member fields for each member. Here's an implementation of the function as a MySQL stored function.
With that you can do:
SELECT name, LEVENSHTEIN(about_member, '1-1-2-1-2') AS diff
FROM members
ORDER BY diff ASC
The % of similarity is related to diff; if diff=0 then it's 100%, if diff is the size of the string (minus the amount of dashes), it's 0%.
Having read the clarification comments on the original question, the Levenshtein distance is not the answer you are looking for.
You are not trying to compute the smallest number of edits to change one string into another.
You are trying to compare one set of numbers with another set of numbers. What you are looking for is the minimum (weighted) sum of the differences between the two sets of numbers.
Place each answer in a separate column (Ans1, Ans2, Ans3, Ans4, .... )
Assume you are searching for similarities to 1-2-1-2.
SELECT UserName, Abs( Ans1 - 1 ) + Abs( Ans2 - 2 ) + Abs( Ans3 - 1 ) + Abs( Ans4 - 2) as Difference ORDER BY Difference ASC
Will list users by similarity to answers 1-2-1-2, assuming all questions are weighted evenly.
If you want to make certain answers more important, just multiply each of the terms by a weighting factor.
If the questions will always be yes/no and the number of answers is small enough that all the answers can be fitted into a single integer and all answers are equally weighted, then you could encode all the answers in a single column and use BIT_COUNT as suggested. This would be a faster and more space-efficient implementation.
I would go with the similar_text() PHP built-in. It seems to be exactly what you want:
$percent = 0;
similar_text($string1, $string2, $percent);
echo $percent;
It works as the question expects.
I would go with the Levenshtein distance approach, you can use it within MySQL or PHP.
If you don't have too many fields, you could create an index on the integer representation of about_member. Then you can find the 100% by an exact match on the about_member field, followed by the 80% matches by changing 1 bit, the 60% matches by changing 2 bits, and so on.
If you represent your answer patterns as bit sequences you can use the formula (100 * (bit_length - similarity) / bit_length).
Following the mentioned example, when we convert "1"s to bit off and "2"s to bit on "1-1-2-2-1" becomes 6 (as base-10, 00110 in binary) and "2-1-1-2-1" becomes 18 (10010b) etc.
Also, I think you should store the answers' bits to the least significant bits, but it doesn't matter as long as you are consistent that the answers of different members align.
Here's a sample script to be run against MySQL.
DROP TABLE IF EXISTS `test`;
CREATE TABLE `members` (
`id` VARCHAR(16) NOT NULL ,
`about_member` INT NOT NULL
) ENGINE = InnoDB;
INSERT INTO `members`
(`id`, `about_member`)
VALUES
('member_1', '6'),
('member_2', '18');
SELECT 100 * ( 5 - BIT_COUNT( about_member ^ (
SELECT about_member
FROM members
WHERE id = 'member_1' ) ) ) / 5
FROM members;
The magical 5 in the script is the number of answers (bit_length in the formula above). You should change it according to your situation, regardless of how many bits there are in the actual data type used, as BIT_COUNT doesn't know how many bytes you are using.
BIT_COUNT returns the number of bits set and is explained in MySQL manual. ^ is the binary XOR operator in MySQL.
Here the comparison of member_1's answers is compared with everybody's, including their own - which results as 100% match, naturally.

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