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I am trying out the following codility.com exercise to improve my skills online, I was presented with the following problem.
This is a demo task.
Write a function:
class Solution { public int solution(int[] A); }
that, given an array A of N integers, returns the smallest positive
integer (greater than 0) that does not occur in A.
For example,
given A = [1, 3, 6, 4, 1, 2], the function should return 5.
Given A = [1, 2, 3], the function should return 4.
Given A = [-1, -3], the function should return 1.
Write an efficient algorithm for the following assumptions:
• N is an
integer within the range [1..100,000);
• each element of array A is an
integer within the range (-1,000,000..1,000,000).
Copyright 2009– by Codility Limited
rendered description
I solved it using the following solution:
<?php
class Solution {
public function($A) {
$posInts = [1, 2, 3, 4, 5, 6, 7, 8, 9];
$diffs = array_diff($postInts, $A);
$smallestPosInt = min($diffs);
return $smallestPosInt;
}
}
However upon submitting I got the following score:
Now I am very unsure of what I did wrong here or how I can rewrite the code with a better algorithm.
Check out this answer using Javascript in a way that works with the best possible performance -If I am not mistaken- O(N).
function solution(A) {
const set = new Set(A)
let i = 1
while (set.has(i)) {
i++
}
return i
}
I would just loop over (increment) any possible integers:
function solution($A) {
$result = 1;
$maxNumber = max($A);
for (; $result <= $maxNumber; $result++) {
if (!in_array($result, $A)) {
break;
}
}
return $result;
}
var_dump(solution([1, 3, 6, 4, 1, 2])); // int(5)
var_dump(solution([1, 2, 3])); // int(4)
var_dump(solution([-1, -3])); // int(1)
// As a bonus, this also works for larger numbers:
var_dump(solution([1, 3, 6, 4, 1, 2, 7, 8, 9, 10, 11, 12, 13, 5, 15])); // int(14)
Edit regarding performance:
As pointed out in the comments (and you already said yourself), this is not a very efficient solution.
While I do not have enough time on my hands currently to do real performance testing, I think this should be close to an O(n) solution: (keeping in mind that I am not sure how arrays are implemented on the C-side of PHP)
function solution($A) {
$result = 1;
$maxNumber = max($A);
$values = array_flip($A);
for (; $result <= $maxNumber; $result++) {
if (!isset($values[$result])) {
break;
}
}
return $result;
}
// Not posting the output again because it is naturally the same ;)
The "trick" here is to flip the array first so that the values become the indexes. Since a) we do not care about the original indexes and b) we do not care if duplicated values overwrite each other, we can safely do that.
Using isset() instead of in_array() should be a lot quicker since it basically just checks if a variable (in this case stored at a specific index of the array) exists and PHP does therefore not have to iterate through the array in order to check whether or not each number we loop over exists within it.
P.S.: After thinking twice I think this may still be closer to O(n*2) because max() probably loops to find the highest value. You could also remove that line and just check against the highest number there is in PHP as an emergency exit, like so: for (; $result <= PHP_INT_MAX; $result++) { ... } as a further optimization. Or maybe just hard-code the highest allowed number as specified in the task.
If we're allowed to modify the input, perform this in place, otherwise create a new array of size n + 1:
For each element encountered in the original array, if it is greater than n + 1 or smaller than 1, assign 0 at the element's index (index - 1 if performing in place); otherwise assign 1 at the index of the array the value is and assign 0 at its own index if it is different. After that run a second traversal and report the first index (index + 1 if performing in place) greater than zero with value 0, or n + 1.
[1, 3, 6, 4, 1, 2]
=>
[1, 1, 1, 1, 0, 1]
report 5
I know how to generate a random number in PHP but lets say I want a random number between 1-10 but I want more 3,4,5's then 8,9,10's. How is this possible? I would post what I have tried but honestly, I don't even know where to start.
Based on #Allain's answer/link, I worked up this quick function in PHP. You will have to modify it if you want to use non-integer weighting.
/**
* getRandomWeightedElement()
* Utility function for getting random values with weighting.
* Pass in an associative array, such as array('A'=>5, 'B'=>45, 'C'=>50)
* An array like this means that "A" has a 5% chance of being selected, "B" 45%, and "C" 50%.
* The return value is the array key, A, B, or C in this case. Note that the values assigned
* do not have to be percentages. The values are simply relative to each other. If one value
* weight was 2, and the other weight of 1, the value with the weight of 2 has about a 66%
* chance of being selected. Also note that weights should be integers.
*
* #param array $weightedValues
*/
function getRandomWeightedElement(array $weightedValues) {
$rand = mt_rand(1, (int) array_sum($weightedValues));
foreach ($weightedValues as $key => $value) {
$rand -= $value;
if ($rand <= 0) {
return $key;
}
}
}
For an efficient random number skewed consistently towards one end of the scale:
Choose a continuous random number between 0..1
Raise to a power γ, to bias it. 1 is unweighted, lower gives more of the higher numbers and vice versa
Scale to desired range and round to integer
eg. in PHP (untested):
function weightedrand($min, $max, $gamma) {
$offset= $max-$min+1;
return floor($min+pow(lcg_value(), $gamma)*$offset);
}
echo(weightedrand(1, 10, 1.5));
There's a pretty good tutorial for you.
Basically:
Sum the weights of all the numbers.
Pick a random number less than that
subtract the weights in order until the result is negative and return that number if it is.
This tutorial walks you through it, in PHP, with multiple cut and paste solutions. Note that this routine is slightly modified from what you'll find on that page, as a result of the comment below.
A function taken from the post:
/**
* weighted_random_simple()
* Pick a random item based on weights.
*
* #param array $values Array of elements to choose from
* #param array $weights An array of weights. Weight must be a positive number.
* #return mixed Selected element.
*/
function weighted_random_simple($values, $weights){
$count = count($values);
$i = 0;
$n = 0;
$num = mt_rand(1, array_sum($weights));
while($i < $count){
$n += $weights[$i];
if($n >= $num){
break;
}
$i++;
}
return $values[$i];
}
/**
* #param array $weightedValues
* #return string
*/
function getRandomWeightedElement(array $weightedValues)
{
$array = array();
foreach ($weightedValues as $key => $weight) {
$array = array_merge(array_fill(0, $weight, $key), $array);
}
return $array[array_rand($array)];
}
getRandomWeightedElement(array('A'=>10, 'B'=>90));
This is very easy method. How get random weighted element. I fill array variable $key. I get $key to array $weight x. After that, use array_rand to array. And I have random value ;).
Plain and fair.
Just copy/paste and test it.
/**
* Return weighted probability
* #param (array) prob=>item
* #return key
*/
function weightedRand($stream) {
$pos = mt_rand(1,array_sum(array_keys($stream)));
$em = 0;
foreach ($stream as $k => $v) {
$em += $k;
if ($em >= $pos)
return $v;
}
}
$item['30'] = 'I have more chances than everybody :]';
$item['10'] = 'I have good chances';
$item['1'] = 'I\'m difficult to appear...';
for ($i = 1; $i <= 10; $i++) {
echo weightedRand($item).'<br />';
}
Edit: Added missing bracket at the end.
You can use weightedChoice from Non-standard PHP library. It accepts a list of pairs (item, weight) to have the possibility to work with items that can't be array keys. You can use pairs function to convert array(item => weight) to the needed format.
use function \nspl\a\pairs;
use function \nspl\rnd\weightedChoice;
$weights = pairs(array(
1 => 10,
2 => 15,
3 => 15,
4 => 15,
5 => 15,
6 => 10,
7 => 5,
8 => 5,
9 => 5,
10 => 5
));
$number = weightedChoice($weights);
In this example, 2-5 will appear 3 times more often than 7-10.
i used Brad's answar and changed it a little to fit my situation and add more flexibility
i have an array with array value
$products = [
['id'=>1,'name'=> 'product1' , 'chance'=>2] ,
['id'=>2,'name'=> 'product2' , 'chance'=>7]
]
first i shuffle the products array
shuffle($products );
then you can pass it to the function
function getRandomWeightedElement(array $products) {
$chancesSum = 0;
foreach ($products as $product){
$chancesSum += (int) $product['chance'];
}
$rand = mt_rand(1, $chancesSum);
$range = 0;
foreach ($products as $product) {
$range += (int) $product['chance'];
$compare = $rand - $range;
if ($compare <= 0){
return (int) $product['id'];
}
}}
Since I used IainMH's solution, I may as well share my PHP code:
<pre><?php
// Set total number of iterations
$total = 1716;
// Set array of random number
$arr = array(1, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5);
$arr2 = array(0, 0, 1, 1, 2, 2, 2, 3, 3, 4, 5);
// Print out random numbers
for ($i=0; $i<$total; $i++){
// Pick random array index
$rand = array_rand($arr);
$rand2 = array_rand($arr2);
// Print array values
print $arr[$rand] . "\t" . $arr2[$rand2] . "\r\n";
}
?></pre>
I just released a class to perform weighted sorting easily.
It's based on the same algorithm mentioned in Brad's and Allain's answers, and is optimized for speed, unit-tested for uniform distribution, and supports elements of any PHP type.
Using it is simple. Instantiate it:
$picker = new Brick\Random\RandomPicker();
Then add elements as an array of weighted values (only if your elements are strings or integers):
$picker->addElements([
'foo' => 25,
'bar' => 50,
'baz' => 100
]);
Or use individual calls to addElement(). This method supports any kind of PHP values as elements (strings, numbers, objects, ...), as opposed to the array approach:
$picker->addElement($object1, $weight1);
$picker->addElement($object2, $weight2);
Then get a random element:
$element = $picker->getRandomElement();
The probability of getting one of the elements depends on its associated weight. The only restriction is that weights must be integers.
Many of the answers on this page seem to use array bloating, excessive iteration, a library, or a hard-to-read process. Of course, everyone thinks their own baby is the cutest, but I honestly think my approach is lean, simple and easy to read/modify...
Per the OP, I will create an array of values (declared as keys) from 1 to 10, with 3, 4, and 5 having double the weight of the other values (declared as values).
$values_and_weights=array(
1=>1,
2=>1,
3=>2,
4=>2,
5=>2,
6=>1,
7=>1,
8=>1,
9=>1,
10=>1
);
If you are only going to make one random selection and/or your array is relatively small* (do your own benchmarking to be sure), this is probably your best bet:
$pick=mt_rand(1,array_sum($values_and_weights));
$x=0;
foreach($values_and_weights as $val=>$wgt){
if(($x+=$wgt)>=$pick){
echo "$val";
break;
}
}
This approach involves no array modification and probably won't need to iterate the entire array (but may).
On the other hand, if you are going to make more than one random selection on the array and/or your array is sufficiently large* (do your own benchmarking to be sure), restructuring the array may be better.
The cost in memory for generating a new array will be increasingly justified as:
array size increases and
number of random selections increases.
The new array requires the replacement of "weight" with a "limit" for each value by adding the previous element's weight to the current element's weight.
Then flip the array so that the limits are the array keys and the values are the array values.
The logic is: the selected value will have the lowest limit that is >= $pick.
// Declare new array using array_walk one-liner:
array_walk($values_and_weights,function($v,$k)use(&$limits_and_values,&$x){$limits_and_values[$x+=$v]=$k;});
//Alternative declaration method - 4-liner, foreach() loop:
/*$x=0;
foreach($values_and_weights as $val=>$wgt){
$limits_and_values[$x+=$wgt]=$val;
}*/
var_export($limits_and_values);
Creates this array:
array (
1 => 1,
2 => 2,
4 => 3,
6 => 4,
8 => 5,
9 => 6,
10 => 7,
11 => 8,
12 => 9,
13 => 10,
)
Now to generate the random $pick and select the value:
// $x (from walk/loop) is the same as writing: end($limits_and_values); $x=key($limits_and_values);
$pick=mt_rand(1,$x); // pull random integer between 1 and highest limit/key
while(!isset($limits_and_values[$pick])){++$pick;} // smallest possible loop to find key
echo $limits_and_values[$pick]; // this is your random (weighted) value
This approach is brilliant because isset() is very fast and the maximum number of isset() calls in the while loop can only be as many as the largest weight (not to be confused with limit) in the array. For this case, maximum iterations = 2!
THIS APPROACH NEVER NEEDS TO ITERATE THE ENTIRE ARRAY
I used this:
mt_rand($min, mt_rand($min, $max));
it give more lower values and less higher values, since the more the value is high the more is cutted out by one of the mt_rand
The probability is linearly increasing in the lower values, forming a square diagonal (see maths lower)
PRO: easy and strightforward
CON: maybe too simple so not enough weightable or balanceable for some use case
Maths:
let i index of i-nth value from min to max,
let P(i) the probability of obtaining the i-nth value,
let N=max-min:
P(i)=(1+N-i)/sum(1,N)
Since N is equals for all terms:
P(i) is proportional to N-i
so, in facts, the probability is linearly increasing in the lower values, forming a square diagonal
Variants:
you can write variants:
mt_rand($min, mt_rand(1, mt_rand(1, $max))); //value more given in low part
mt_rand(mt_rand($min, $max), $max); //mirrored, more upper values than lower
...
function getBucketFromWeights($values) {
$total = $currentTotal = $bucket = 0;
foreach ($values as $amount) {
$total += $amount;
}
$rand = mt_rand(0, $total-1);
foreach ($values as $amount) {
$currentTotal += $amount;
if ($rand => $currentTotal) {
$bucket++;
}
else {
break;
}
}
return $bucket;
}
I ugh modified this from an answer here Picking random element by user defined weights
After I wrote this I saw someone else had an even more elegant answer. He he he he.
I've got an array per default:
array( 1=>1,2 =>2, 3=>3, 4=>4, 5=>5, 6=>6, 7=>7, 8=>8, 9=>9 )
Now an operation is possible to change the numbers for example into:
array( 1=>1, 2=>1, 3=>3, 4=>1, 5=>1, 6=>6, 7=>7, 8=>8, 9=>9 )
--> changed the value of key 1, 2, 4 and 5
After this I need the following result
array( 1=>1, 2=1, 3=>2, 4=>1, 5=>1, 6=>3, 7=>4, 8=>5, 9=>6 )
--> changed the value of key 3, 6, 7, 8, 9 in the right order that no number is missing like the operation has done above.
Its a grid 3x3. Position 1 is 1, Position 2 is 2 and so on. Now a database could set that Position 1, 2, 4, 5 are the same and threated as 1. So the database sends: 1, 1, 3, 1, 1, 6, 7, 8, 9. Now the field from place 3 is 3, but should be the field from 2. Also the field from 6 must now be field 3 and so on.
Note: The operation is able to change every value in the array. for example the value of the
keys 4, 5, 7, 8
How can I do this?
Create a variable, in which you will store the max number. If you then iterate, check if the number from the array is lower then max, and if it is, then you do nothing, and if it is larger than max, so you put it in the third array and increase max.
$max = 0; // maximum value
$array3 = array(); // output array
foreach($array2 as $key=>$element){ // iterate for all elements
if($array2[$key] > $max){
$max++;
$array3[$key] = $max;
}
else
$array3[$key]=1; // *
} // end foreach
In the line marked with // * it puts 1 everytime. You may need to search if the value was once before, because it does not need to be always 1. You may use for example something like array_search.
Supposing I'm having the constants 3,5,6,9,10. How can I detect how to write $n, which is the input, as a sum of these constants with the least number of terms?
Examples
$n=10, S=10
$n=18, S=9+9
$n=24, S=9+9+6
$n=27, S=9+9+9
$n=28, S=10+9+9
Thanks
This is another Python solution, but hopefully it's easy for you to convert to PHP (I would do it myself, but I'm no PHP expert - I'm sure you could do a better job of it). I've tried not to use any advanced Python funcitons, so that it is easier for non-Python readers to understand, but if some Python syntax is not clear, please just ask.
allowed = [3, 5, 6, 9, 10]
n = 28
solutions = [ None ] * (n + 1)
solutions[0] = []
for i in range(n + 1):
if solutions[i] is None: continue
for a in allowed:
if i + a > n: continue
if solutions[i + a] is None or len(solutions[i]) + 1 < len(solutions[i + a]):
solutions[i + a] = solutions[i] + [a]
print solutions[28]
It works by starting from 0 and building up to the desired number, keeping a cache of the shortest solution seen so far for each possible total. It has a running time of O(n * a), where a is the number of different allowed values.
By the way, your answer to n=28 is wrong. It should be [9, 9, 10].
Update: here's my attempt at a PHP solution:
<?php
$allowed = array(3, 5, 6, 9, 10);
$n = 28;
$solutions = array();
$solutions[0] = array();
foreach (range(0, $n) as $i) {
if (is_null($solutions[$i])) continue;
foreach ($allowed as $a) {
if ($i + $a > $n) continue;
if (is_null($solutions[$i + $a]) ||
sizeof($solutions[$i]) + 1 < sizeof($solutions[$i + $a])) {
$solutions[$i + $a] = array_merge($solutions[$i], array($a));
}
}
}
var_dump($solutions[$n]);
?>
It gives the right answer, but please be aware that I'm not a professional PHP coder - I just looked up the equivalent functions in the PHP documentation.
This is Mark Byers' algorithm, rewritten using loop structures that are more familiar to PHP developers, and constructs that won't generate PHP notices. $C is your set of integers, $S the solutions.
$n = 28;
$C = array(3, 5, 6, 9, 10);
$S = array(array());
// if your set isn't sorted already, you have to call sort()
//sort($C);
for ($i = 0; $i <= $n; ++$i)
{
if (!isset($S[$i]))
{
continue;
}
foreach ($C as $v)
{
if ($i + $v > $n)
{
break;
}
if (!isset($S[$i + $v])
|| count($S[$i + $v]) > 1 + count($S[$i]))
{
$S[$i + $v] = $S[$i];
$S[$i + $v][] = $v;
}
}
}
print_r($S[$n]);
Two obvious approaches suggest themselves:
Write a series of linear equations,
and solve to find various solutions.
Choose one with the least number of
terms.
Trial and error, starting
with the largest terms first.
Find all possible solutions for "S=3A+5B+6C+9D+10E" then choose the one with the most 0 values for A,B,C,D,E
a rough sketch of an unscalable but correct solution (sorry, so far its only python ..):
#!/usr/bin/env python
import itertools, sys
pool = [3, 5, 6, 9, 10]
repeat, found, solutions = 1, False, set()
try: x = int(sys.argv[1])
except: x = 42
while not found:
for n in itertools.product(pool, repeat=repeat):
s = sum(n)
if s == x:
solutions.add(n)
found = True
break
repeat = repeat + 1
print solutions
would yield:
$ python 1850629.py 11
set([(5, 6)])
$ python 1850629.py 19
set([(9, 10)])
$ python 1850629.py 21
set([(3, 9, 9)])
$ python 1850629.py 42
set([(3, 9, 10, 10, 10)])
In addition to the excellent general answers already provided, bear in mind that if your set of values has certain properties, much more optimal solutions exist.
Specifically, if your solution is 'minimal' - that is, a single best solution exists for any value - then you can find the smallest number of elements using a 'greedy' algorithm: Simply add the largest value until the remainder is smaller than it, repeat with the next largest value, and so forth.
As an example, the denominations used for money in many countries are .01, .02, .05, .10, .20, .50, 1, 2, 5, .... This set is minimal, so you can just repeatedly add the largest valid denomination.
NP-complete problem
Subset sum problem
I know how to generate a random number in PHP but lets say I want a random number between 1-10 but I want more 3,4,5's then 8,9,10's. How is this possible? I would post what I have tried but honestly, I don't even know where to start.
Based on #Allain's answer/link, I worked up this quick function in PHP. You will have to modify it if you want to use non-integer weighting.
/**
* getRandomWeightedElement()
* Utility function for getting random values with weighting.
* Pass in an associative array, such as array('A'=>5, 'B'=>45, 'C'=>50)
* An array like this means that "A" has a 5% chance of being selected, "B" 45%, and "C" 50%.
* The return value is the array key, A, B, or C in this case. Note that the values assigned
* do not have to be percentages. The values are simply relative to each other. If one value
* weight was 2, and the other weight of 1, the value with the weight of 2 has about a 66%
* chance of being selected. Also note that weights should be integers.
*
* #param array $weightedValues
*/
function getRandomWeightedElement(array $weightedValues) {
$rand = mt_rand(1, (int) array_sum($weightedValues));
foreach ($weightedValues as $key => $value) {
$rand -= $value;
if ($rand <= 0) {
return $key;
}
}
}
For an efficient random number skewed consistently towards one end of the scale:
Choose a continuous random number between 0..1
Raise to a power γ, to bias it. 1 is unweighted, lower gives more of the higher numbers and vice versa
Scale to desired range and round to integer
eg. in PHP (untested):
function weightedrand($min, $max, $gamma) {
$offset= $max-$min+1;
return floor($min+pow(lcg_value(), $gamma)*$offset);
}
echo(weightedrand(1, 10, 1.5));
There's a pretty good tutorial for you.
Basically:
Sum the weights of all the numbers.
Pick a random number less than that
subtract the weights in order until the result is negative and return that number if it is.
This tutorial walks you through it, in PHP, with multiple cut and paste solutions. Note that this routine is slightly modified from what you'll find on that page, as a result of the comment below.
A function taken from the post:
/**
* weighted_random_simple()
* Pick a random item based on weights.
*
* #param array $values Array of elements to choose from
* #param array $weights An array of weights. Weight must be a positive number.
* #return mixed Selected element.
*/
function weighted_random_simple($values, $weights){
$count = count($values);
$i = 0;
$n = 0;
$num = mt_rand(1, array_sum($weights));
while($i < $count){
$n += $weights[$i];
if($n >= $num){
break;
}
$i++;
}
return $values[$i];
}
/**
* #param array $weightedValues
* #return string
*/
function getRandomWeightedElement(array $weightedValues)
{
$array = array();
foreach ($weightedValues as $key => $weight) {
$array = array_merge(array_fill(0, $weight, $key), $array);
}
return $array[array_rand($array)];
}
getRandomWeightedElement(array('A'=>10, 'B'=>90));
This is very easy method. How get random weighted element. I fill array variable $key. I get $key to array $weight x. After that, use array_rand to array. And I have random value ;).
Plain and fair.
Just copy/paste and test it.
/**
* Return weighted probability
* #param (array) prob=>item
* #return key
*/
function weightedRand($stream) {
$pos = mt_rand(1,array_sum(array_keys($stream)));
$em = 0;
foreach ($stream as $k => $v) {
$em += $k;
if ($em >= $pos)
return $v;
}
}
$item['30'] = 'I have more chances than everybody :]';
$item['10'] = 'I have good chances';
$item['1'] = 'I\'m difficult to appear...';
for ($i = 1; $i <= 10; $i++) {
echo weightedRand($item).'<br />';
}
Edit: Added missing bracket at the end.
You can use weightedChoice from Non-standard PHP library. It accepts a list of pairs (item, weight) to have the possibility to work with items that can't be array keys. You can use pairs function to convert array(item => weight) to the needed format.
use function \nspl\a\pairs;
use function \nspl\rnd\weightedChoice;
$weights = pairs(array(
1 => 10,
2 => 15,
3 => 15,
4 => 15,
5 => 15,
6 => 10,
7 => 5,
8 => 5,
9 => 5,
10 => 5
));
$number = weightedChoice($weights);
In this example, 2-5 will appear 3 times more often than 7-10.
i used Brad's answar and changed it a little to fit my situation and add more flexibility
i have an array with array value
$products = [
['id'=>1,'name'=> 'product1' , 'chance'=>2] ,
['id'=>2,'name'=> 'product2' , 'chance'=>7]
]
first i shuffle the products array
shuffle($products );
then you can pass it to the function
function getRandomWeightedElement(array $products) {
$chancesSum = 0;
foreach ($products as $product){
$chancesSum += (int) $product['chance'];
}
$rand = mt_rand(1, $chancesSum);
$range = 0;
foreach ($products as $product) {
$range += (int) $product['chance'];
$compare = $rand - $range;
if ($compare <= 0){
return (int) $product['id'];
}
}}
Since I used IainMH's solution, I may as well share my PHP code:
<pre><?php
// Set total number of iterations
$total = 1716;
// Set array of random number
$arr = array(1, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5);
$arr2 = array(0, 0, 1, 1, 2, 2, 2, 3, 3, 4, 5);
// Print out random numbers
for ($i=0; $i<$total; $i++){
// Pick random array index
$rand = array_rand($arr);
$rand2 = array_rand($arr2);
// Print array values
print $arr[$rand] . "\t" . $arr2[$rand2] . "\r\n";
}
?></pre>
I just released a class to perform weighted sorting easily.
It's based on the same algorithm mentioned in Brad's and Allain's answers, and is optimized for speed, unit-tested for uniform distribution, and supports elements of any PHP type.
Using it is simple. Instantiate it:
$picker = new Brick\Random\RandomPicker();
Then add elements as an array of weighted values (only if your elements are strings or integers):
$picker->addElements([
'foo' => 25,
'bar' => 50,
'baz' => 100
]);
Or use individual calls to addElement(). This method supports any kind of PHP values as elements (strings, numbers, objects, ...), as opposed to the array approach:
$picker->addElement($object1, $weight1);
$picker->addElement($object2, $weight2);
Then get a random element:
$element = $picker->getRandomElement();
The probability of getting one of the elements depends on its associated weight. The only restriction is that weights must be integers.
Many of the answers on this page seem to use array bloating, excessive iteration, a library, or a hard-to-read process. Of course, everyone thinks their own baby is the cutest, but I honestly think my approach is lean, simple and easy to read/modify...
Per the OP, I will create an array of values (declared as keys) from 1 to 10, with 3, 4, and 5 having double the weight of the other values (declared as values).
$values_and_weights=array(
1=>1,
2=>1,
3=>2,
4=>2,
5=>2,
6=>1,
7=>1,
8=>1,
9=>1,
10=>1
);
If you are only going to make one random selection and/or your array is relatively small* (do your own benchmarking to be sure), this is probably your best bet:
$pick=mt_rand(1,array_sum($values_and_weights));
$x=0;
foreach($values_and_weights as $val=>$wgt){
if(($x+=$wgt)>=$pick){
echo "$val";
break;
}
}
This approach involves no array modification and probably won't need to iterate the entire array (but may).
On the other hand, if you are going to make more than one random selection on the array and/or your array is sufficiently large* (do your own benchmarking to be sure), restructuring the array may be better.
The cost in memory for generating a new array will be increasingly justified as:
array size increases and
number of random selections increases.
The new array requires the replacement of "weight" with a "limit" for each value by adding the previous element's weight to the current element's weight.
Then flip the array so that the limits are the array keys and the values are the array values.
The logic is: the selected value will have the lowest limit that is >= $pick.
// Declare new array using array_walk one-liner:
array_walk($values_and_weights,function($v,$k)use(&$limits_and_values,&$x){$limits_and_values[$x+=$v]=$k;});
//Alternative declaration method - 4-liner, foreach() loop:
/*$x=0;
foreach($values_and_weights as $val=>$wgt){
$limits_and_values[$x+=$wgt]=$val;
}*/
var_export($limits_and_values);
Creates this array:
array (
1 => 1,
2 => 2,
4 => 3,
6 => 4,
8 => 5,
9 => 6,
10 => 7,
11 => 8,
12 => 9,
13 => 10,
)
Now to generate the random $pick and select the value:
// $x (from walk/loop) is the same as writing: end($limits_and_values); $x=key($limits_and_values);
$pick=mt_rand(1,$x); // pull random integer between 1 and highest limit/key
while(!isset($limits_and_values[$pick])){++$pick;} // smallest possible loop to find key
echo $limits_and_values[$pick]; // this is your random (weighted) value
This approach is brilliant because isset() is very fast and the maximum number of isset() calls in the while loop can only be as many as the largest weight (not to be confused with limit) in the array. For this case, maximum iterations = 2!
THIS APPROACH NEVER NEEDS TO ITERATE THE ENTIRE ARRAY
I used this:
mt_rand($min, mt_rand($min, $max));
it give more lower values and less higher values, since the more the value is high the more is cutted out by one of the mt_rand
The probability is linearly increasing in the lower values, forming a square diagonal (see maths lower)
PRO: easy and strightforward
CON: maybe too simple so not enough weightable or balanceable for some use case
Maths:
let i index of i-nth value from min to max,
let P(i) the probability of obtaining the i-nth value,
let N=max-min:
P(i)=(1+N-i)/sum(1,N)
Since N is equals for all terms:
P(i) is proportional to N-i
so, in facts, the probability is linearly increasing in the lower values, forming a square diagonal
Variants:
you can write variants:
mt_rand($min, mt_rand(1, mt_rand(1, $max))); //value more given in low part
mt_rand(mt_rand($min, $max), $max); //mirrored, more upper values than lower
...
function getBucketFromWeights($values) {
$total = $currentTotal = $bucket = 0;
foreach ($values as $amount) {
$total += $amount;
}
$rand = mt_rand(0, $total-1);
foreach ($values as $amount) {
$currentTotal += $amount;
if ($rand => $currentTotal) {
$bucket++;
}
else {
break;
}
}
return $bucket;
}
I ugh modified this from an answer here Picking random element by user defined weights
After I wrote this I saw someone else had an even more elegant answer. He he he he.