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I have a set of items. I need to randomly pick one. The problem is that they each have a weight of 1-10. A weight of 2 means that the item is twice as likely to be picked than a weight of 1. A weight of 3 is three times as likely.
I currently fill an array with each item. If the weight is 3, I put three copies of the item in the array. Then, I pick a random item.
My method is fast, but uses a lot of memory. I am trying to think of a faster method, but nothing comes to mind. Anyone have a trick for this problem?
EDIT: My Code...
Apparently, I wasn't clear. I do not want to use (or improve) my code. This is what I did.
//Given an array $a where $a[0] is an item name and $a[1] is the weight from 1 to 100.
$b = array();
foreach($a as $t)
$b = array_merge($b, array_fill(0,$t[1],$t));
$item = $b[array_rand($b)];
This required me to check every item in $a and uses max_weight/2*size of $a memory for the array. I wanted a COMPLETELY DIFFERENT algorithm.
Further, I asked this question in the middle of the night using a phone. Typing code on a phone is nearly impossible because those silly virtual keyboards simply suck. It auto-corrects everything, ruining any code I type.
An yet further, I woke up this morning with an entirely new algorithm that uses virtual no extra memory at all and does not require checking every item in the array. I posted it as an answer below.
This ones your huckleberry.
$arr = array(
array("val" => "one", "weight" => 1),
array("val" => "two", "weight" => 2),
array("val" => "three", "weight" => 3),
array("val" => "four", "weight" => 4)
);
$weight_sum = 0;
foreach($arr as $val)
{
$weight_sum += $val['weight'];
}
$r = rand(1, $weight_sum);
print "random value is $r\n";
for($i = 0; $i < count($arr); $i++)
{
if($r <= $arr[$i]['weight'])
{
print "$r <= {$arr[$i]['weight']}, this is our match\n";
print $arr[$i]['val'] . "\n";
break;
}
else
{
print "$r > {$arr[$i]['weight']}, subtracting weight\n";
$r -= $arr[$i]['weight'];
print "new \$r is $r\n";
}
}
No need to generate arrays containing an item for every weight, no need to fill an array with n elements for a weight of n. Just generate a random number between 1 and total weight, then loop through the array until you find a weight less than your random number. If it isn't less than the number, subtract that weight from the random and continue.
Sample output:
# php wr.php
random value is 8
8 > 1, subtracting weight
new $r is 7
7 > 2, subtracting weight
new $r is 5
5 > 3, subtracting weight
new $r is 2
2 <= 4, this is our match
four
This should also support fractional weights.
modified version to use array keyed by weight, rather than by item
$arr2 = array(
);
for($i = 0; $i <= 500000; $i++)
{
$weight = rand(1, 10);
$num = rand(1, 1000);
$arr2[$weight][] = $num;
}
$start = microtime(true);
$weight_sum = 0;
foreach($arr2 as $weight => $vals) {
$weight_sum += $weight * count($vals);
}
print "weighted sum is $weight_sum\n";
$r = rand(1, $weight_sum);
print "random value is $r\n";
$found = false;
$elem = null;
foreach($arr2 as $weight => $vals)
{
if($found) break;
for($j = 0; $j < count($vals); $j ++)
{
if($r < $weight)
{
$elem = $vals[$j];
$found = true;
break;
}
else
{
$r -= $weight;
}
}
}
$end = microtime(true);
print "random element is: $elem\n";
print "total time is " . ($end - $start) . "\n";
With sample output:
# php wr2.php
weighted sum is 2751550
random value is 345713
random element is: 681
total time is 0.017189025878906
measurement is hardly scientific - and fluctuates depending on where in the array the element falls (obviously) but it seems fast enough for huge datasets.
This way requires two random calculations but they should be faster and require about 1/4 of the memory but with some reduced accuracy if weights have disproportionate counts. (See Update for increased accuracy at the cost of some memory and processing)
Store a multidimensional array where each item is stored in the an array based on its weight:
$array[$weight][] = $item;
// example: Item with a weight of 5 would be $array[5][] = 'Item'
Generate a new array with the weights (1-10) appearing n times for n weight:
foreach($array as $n=>$null) {
for ($i=1;$i<=$n;$i++) {
$weights[] = $n;
}
}
The above array would be something like: [ 1, 2, 2, 3, 3, 3, 4, 4, 4, 4 ... ]
First calculation: Get a random weight from the weighted array we just created
$weight = $weights[mt_rand(0, count($weights)-1)];
Second calculation: Get a random key from that weight array
$value = $array[$weight][mt_rand(0, count($array[$weight])-1)];
Why this works: You solve the weighted issue by using the weighted array of integers we created. Then you select randomly from that weighted group.
Update: Because of the possibility of disproportionate counts of items per weight, you could add another loop and array for the counts to increase accuracy.
foreach($array as $n=>$null) {
$counts[$n] = count($array[$n]);
}
foreach($array as $n=>$null) {
// Calculate proportionate weight (number of items in this weight opposed to minimum counted weight)
$proportion = $n * ($counts[$n] / min($counts));
for ($i=1; $i<=$proportion; $i++) {
$weights[] = $n;
}
}
What this does is if you have 2000 10's and 100 1's, it'll add 200 10's (20 * 10, 20 because it has 20x the count, and 10 because it is weighted 10) instead of 10 10's to make it proportionate to how many are in there opposed the minimum weight count. So to be accurate, instead of adding one for EVERY possible key, you are just being proportionate based on the MINIMUM count of weights.
I greatly appreciate the answers above. Please consider this answer, which does not require checking every item in the original array.
// Given $a as an array of items
// where $a[0] is the item name and $a[1] is the item weight.
// It is known that weights are integers from 1 to 100.
for($i=0; $i<sizeof($a); $i++) // Safeguard described below
{
$item = $a[array_rand($a)];
if(rand(1,100)<=$item[1]) break;
}
This algorithm only requires storage for two variables ($i and $item) as $a was already created before the algorithm kicked in. It does not require a massive array of duplicate items or an array of intervals.
In a best-case scenario, this algorithm will touch one item in the original array and be done. In a worst-case scenario, it will touch n items in an array of n items (not necessarily every item in the array as some may be touched more than once).
If there was no safeguard, this could run forever. The safeguard is there to stop the algorithm if it simply never picks an item. When the safeguard is triggered, the last item touched is the one selected. However, in millions of tests using random data sets of 100,000 items with random weights of 1 to 10 (changing rand(1,100) to rand(1,10) in my code), the safeguard was never hit.
I made histograms comparing the frequency of items selected among my original algorithm, the ones from answers above, and the one in this answer. The differences in frequencies are trivial - easy to attribute to variances in the random numbers.
EDIT... It is apparent to me that my algorithm may be combined with the algorithm pala_ posted, removing the need for a safeguard.
In pala_'s algorithm, a list is required, which I call an interval list. To simplify, you begin with a random_weight that is rather high. You step down the list of items and subtract the weight of each one until your random_weight falls to zero (or less). Then, the item you ended on is your item to return. There are variations on this interval algorithm that I've tested and pala_'s is a very good one. But, I wanted to avoid making a list. I wanted to use only the given weighted list and never touch all the items. The following algorithm merges my use of random jumping with pala_'s interval list. Instead of a list, I randomly jump around the list. I am guaranteed to get to zero eventually, so no safeguard is needed.
// Given $a as the weighted array (described above)
$weight = rand(1,100); // The bigger this is, the slower the algorithm runs.
while($weight>0)
{
$item = $a[array_rand($a)];
$weight-= $item[1];
}
// $item is the random item you want.
I wish I could select both pala_ and this answer as the correct answers.
I'm not sure if this is "faster", but I think it may be more "balance"d between memory usage and speed.
The thought is to transform your current implementation (500000 items array) into an equal-length array (100000 items), with the lowest "origin" position as key, and origin index as value:
<?php
$set=[["a",3],["b",5]];
$current_implementation=["a","a","a","b","b","b","b","b"];
// 0=>0 means the lowest "position" 0
// points to 0 in the set;
// 3=>1 means the lowest "position" 3
// points to 1 in the set;
$my_implementation=[0=>0,3=>1];
And then randomly picks a number between 0 and highest "origin" position:
// 3 is the lowest position of the last element ("b")
// and 5 the weight of that last element
$my_implemention_pick=mt_rand(0,3+5-1);
Full code:
<?php
function randomPickByWeight(array $set)
{
$low=0;
$high=0;
$candidates=[];
foreach($set as $key=>$item)
{
$candidates[$high]=$key;
$high+=$item["weight"];
}
$pick=mt_rand($low,$high-1);
while(!array_key_exists($pick,$candidates))
{
$pick--;
}
return $set[$candidates[$pick]];
}
$cache=[];
for($i=0;$i<100000;$i++)
{
$cache[]=["item"=>"item {$i}","weight"=>mt_rand(1,10)];
}
$time=time();
for($i=0;$i<100;$i++)
{
print_r(randomPickByWeight($cache));
}
$time=time()-$time;
var_dump($time);
3v4l.org demo
3v4l.org have some time limitation on codes, so the demo didn't finished. On my laptop the above demo finished in 10 seconds (i7-4700 HQ)
ere is my offer in case I've understand you right. I offer you take a look and if there are some question I'll explain.
Some words in advance:
My sample is with only 3 stages of weight - to be clear
- With outer while I'm simulating your main loop - I count only to 100.
- The array must to be init with one set of initial numbers as shown in my sample.
- In every pass of main loop I get only one random value and I'm keeping the weight at all.
<?php
$array=array(
0=>array('item' => 'A', 'weight' => 1),
1=>array('item' => 'B', 'weight' => 2),
2=>array('item' => 'C', 'weight' => 3),
);
$etalon_weights=array(1,2,3);
$current_weights=array(0,0,0);
$ii=0;
while($ii<100){ // Simulates your main loop
// Randomisation cycle
if($current_weights==$etalon_weights){
$current_weights=array(0,0,0);
}
$ft=true;
while($ft){
$curindex=rand(0,(count($array)-1));
$cur=$array[$curindex];
if($current_weights[$cur['weight']-1]<$etalon_weights[$cur['weight']-1]){
echo $cur['item'];
$array[]=$cur;
$current_weights[$cur['weight']-1]++;
$ft=false;
}
}
$ii++;
}
?>
I'll use this input array for my explanation:
$values_and_weights=array(
"one"=>1,
"two"=>8,
"three"=>10,
"four"=>4,
"five"=>3,
"six"=>10
);
The simple version isn't going to work for you because your array is so large. It requires no array modification but may need to iterate the entire array, and that's a deal breaker.
/*$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;
}
}*/
For your case, re-structuring the array will offer great benefits.
The cost in memory for generating a new array will be increasingly justified as:
array size increases and
number of 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 selection 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);
$limits_and_values looks like this:
array (
1 => 'one',
9 => 'two',
19 => 'three',
23 => 'four',
26 => 'five',
36 => 'six',
)
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 YOUR CASE, THIS APPROACH WILL FIND THE VALUE IN 10 ITERATIONS OR LESS!
Here is my Demo that will accept a weighted array (like $values_and_weights), then in just four lines:
Restructure the array,
Generate a random number,
Find the correct value, and
Display it.
EDIT 1 -since posting I have learnt that the underlying question is about how to find the CARTESIAN PRODUCT (now go google), but not only because I don't want every perm, I want to find the cartesian products that use the same subarray Key never more than once per permuation AND my 'extra' question then is more about how to minimise the workload that a cartesian product would require (accepting a small error rate, I have to say)-
Imagine... I have four cooks and four recipes, each cook has a score for each recipe and today I'd like each cook to make one dish (but no dish should be made twice) and the decision should be based on the best (highest total scores) permutation for all four (so maybe a cook won't make his personal best).
I have put the data into a multi-dimensional array as such
array(
array (1,2,3,4),
array (35,0,0,0),
array (36,33,1,1),
array (20,20,5,3)
)
it has the same number of valuepairs in each sub array as the number of sub-arrays (if that helps any)
in reality the number of sub-arrays would reach a maximum of 8 (max perms therefore =8!, approx 40,000 not 8^8 because many combinations are not allowed)
the choice of having the data in this format is flexible if that helps
I am trying to create a second array that would output the best (ie HIGHEST value) possible combination of the sub-arrays as per KEYs where only ONE of each subarray can be used
--so here each subarray[0][1][2][3] would be used once per permutation
and each subarrayKey [0][1][2][3] would be used once per permutaion, in my actual problem I'm using associated arrays, but that is extra to this issue.--
So the example would create an array as such
newArray (35,33,5,4) // note that [2][0] was not used
IDEALLY I would prefer to not produce the ALL perms but rather, SOMEHOW, discard many combinations that would clearly not be best fit.
Any ideas for how to start? I would accept pseudo code.
For an example on SO about Cartesian Product, see PHP 2D Array output all combinations
EDIT 2
for more on making cartesian products more efficient, and maybe why it has to be case specific if you want to see if you can cut corners (with risk) Efficient Cartesian Product algorithm
Apologies, but this is going to be more of a logic layout than code...
It's not quite clear to me whether the array(1,2,3,4) are the scores for the first dish or for the first cook, but I would probably use an array such that
$array[$cook_id][$dish_number] = $score;
asort() each array so that $array[$cook_id] = array($lowest_scored_dish,...,$highest);
Consider a weighted preference for a particular cook to make a dish to be the difference between the score of the best dish and another.
As a very simple example, cooks a,b,c and dishes 0,1,2
$array['a'] = array(0=>100, 1=>50, 2=>0); // cook a prefers 0 over 1 with weight 50, over 2 with weight 100
$array['b'] = array(0=>100, 1=>100, 2=>50); // cook b prefers 0,1 over 2 with weight 50
$array['c'] = array(0=>50, 1=>50, 2=>100); // cook c prefers 2 with weight 50
After asort():
$array['a'] = array(0=>100, 1=>50, 2=>0);
$array['b'] = array(0=>100, 1=>100, 2=>50);
$array['c'] = array(2=>100, 0=>50, 1=>50);
Start with cook 'a' who prefers dish 0 over his next best dish by 50 points (weight). Cook 'b' also prefers dih 0, but with a weight of 0 over the next dish. Therefore it's likely (though not yet certain that cook 'a' should make dish 0.
Consider dish 0 to be reserved and move on to cook 'b'. Excluding dish 0, cook 'b' prefers dish 1. No other cook prefers dish 1, so cook 'b' is assigned dish 1.
Cook 'c' gets dish 2 by default.
This is a VERY convenient example where each cook gets to cook something that's a personal max, but I hope it's illustrative of some logic that would work out.
Let's make it less convenient:
$array['a'] = array(0=>75, 1=>50, 2=>0);
$array['b'] = array(0=>100, 1=>50, 2=>50);
$array['c'] = array(0=>100, 1=>25, 2=>25);
Start again with cook 'a' and see that 0 is preferred, but this time with weight 25. Cook 'b' prefers with a weight of 50 and cook 'c' prefers with a weight of 75. Cook 'c' wins dish 0.
Going back to the list of available cooks, 'a' prefers 1 with a weight of 50, but 'b' prefers it with weight 0. 'a' gets dish 1 and 'b' gets dish 2.
This still doesn't take care of all complexities, but it's a step in the right direction. Sometimes the assumption made for the first cook/dish combination will be wrong.
WAY less convenient:
$array['a'] = array(0=>200, 1=>148, 2=>148, 3=>0);
$array['b'] = array(0=>200, 1=>149, 2=>0, 3=>0);
$array['c'] = array(0=>200, 1=>150, 2=>147, 3=>147);
$array['d'] = array(0=>69, 1=>18, 2=>16, 3=>15);
'a' gets 0 since that's the max and no one else who prefers 0 has a higher weight
'b' wins 1 with a weight of 149
'd' wins 2 since 'c' doesn't have a preference from the available options
'c' gets 3
score: 200+149+147+16 = 512
While that's a good guess that's gathered without checking every permutation, it may be wrong. From here, ask, "If one cook traded with any one other cook, would the total increase?"
The answer is YES, a(0)+d(2) = 200+16 = 216, but a(2)+d(0) = 148+69 = 217.
I'll leave it to you to write the code for the "best guess" using the weighted approach, but after that, here's a good start for you:
// a totally uneducated guess...
$picks = array(0=>'a', 1=>'b', 2=>'c', 3=>'d');
do {
$best_change = false;
$best_change_weight = 0;
foreach ($picks as $dish1 => $cook1) {
foreach ($picks as $dish2 => $cook2) {
if (($array[$cook1][$dish1] + $array[$cook2][$dish2]) <
($array[$cook1][$dish2] + $array[$cook2][$dish1]))
{
$old_score = $array[$cook1][$dish1] + $array[$cook2][$dish2];
$new_score = $array[$cook1][$dish2] + $array[$cook2][$dish1];
if (($new_score - $old_score) > $best_change_weight) {
$best_change_weight = $new_score - $old_score;
$best_change = $dish2;
}
}
}
if ($best_change !== false) {
$cook2 = $picks[$best_change];
$picks[$dish1] = $cook2;
$picks[$dish2] = $cook1;
break;
}
}
} while ($best_change !== false);
I can't find a counter example to show that this doesn't work, but I'm suspicious of the case where
($array[$cook1][$dish1] + $array[$cook2][$dish2])
==
($array[$cook1][$dish2] + $array[$cook2][$dish1])
Maybe someone else will follow up with an answer to this "What if?"
Given this matrix, where the items in brackets are the "picks"
[a1] a2 a3
b1 [b2] b3
c1 c2 [c3]
If a1 + b2 == a2 + b1, then 'a' and 'b' will not switch dishes. The case I'm not 100% sure about is if there exists a matrix such that this is a better choice:
a1 [a2] a3
b1 b2 [b3]
[c1] c2 c3
Getting from the first state to the second requires two switches, the first of which seems arbitrary since it doesn't change the total. But, only by going through this arbitrary change can the last switch be made.
I tried to find an example 3x3 such that based on the "weighted preference" model I wrote about above, the first would be selected, but also such that the real optimum selection is given by the second. I wasn't able to find an example, but that doesn't mean that it doesn't exist. I don't feel like doing more matrix algebra right now, but maybe someone will pick up where I left off. Heck, maybe the case doesn't exist, but I thought I should point out the concern.
If it does work and you start with the correct pick, the above code will only loop through 64 times (8x8) for 8 cooks/dishes. If the pick is not correct and the first cook has a change, then it will go up to 72. If the 8th cook has a change, it's up to 128. It's possible that the do-while will loop several times, but I doubt it will get up near the CPU cycles required to sum all of the 40k combinations.
I may have a starting point for you with this algorithm that tries to choose cooks based on their ratio of max score to sum of scores (thus trying to choose chefs who are really good at one recipe but bad at the rest of the recipes to do that recipe)
$cooks = array(
array(1,2,3,4),
array(35,0,0,0),
array(36,33,1,1),
array(20,20,5,3)
);
$results = array();
while (count($cooks)) {
$curResult = array(
'cookId' => -1,
'recipe' => -1,
'score' => -1,
'ratio' => -1
);
foreach ($cooks as $cookId => $scores) {
$max = max($scores);
$ratio = $max / array_sum($scores);
if ($ratio > $curResult['ratio']) {
$curResult['cookId'] = $cookId;
$curResult['ratio'] = $ratio;
foreach ($scores as $recipe => $score) {
if ($score == $max) {
$curResult['recipe'] = $recipe;
$curResult['score'] = $score;
}
}
}
}
$results[$curResult['recipe']] = $curResult['score'];
unset($cooks[$curResult['cookId']]);
foreach ($cooks as &$cook) {
unset($cook[$curResult['recipe']]);
}
}
For the dataset provided, it does find what seems to be the optimum answer (35,33,5,4). However, it is still not perfect, for example, with the array:
$cooks = array(
array(1,2,3,4),
array(35,0,33,0),
array(36,33,1,1),
array(20,20,5,3)
);
The ideal answer would be (20,33,33,4), however this algorithm would return (35,33,5,4).
But since the question was asking for ideas of where to start, I guess this at least might suffice as something to start from :P
Try this
$mainArr = array(
array (1,2,3,4) ,
array (35,0,0,0) ,
array (36,33,1,1) ,
array (20,20,5,3)
);
$i = 0;
foreach( $mainArr as $subArray )
{
foreach( $subArray as $key => $value)
{
$newArr[$key][$i]=$value;
$i++;
}
}
$finalArr = array();
foreach( $newArr as $newSubArray )
{
$finalArr[] = max($newSubArray);
}
print_r( $finalArr );
OK here is a solution that allows you to find the best permutation of one cook to one recipe and no cook works twice and no recipe is made twice.
Thanks for the code to calculate perm of arrays goes to o'reilly...
http://docstore.mik.ua/orelly/webprog/pcook/ch04_26.htm
CONSIDERATIONS:
The number of cooks and the number of recipes are the same.
Going above a 5 by 5 matrix as here will get very big very fast. (see part 2 to be posted shortly)
The logic:
A permutation of an array assigns a place as well as just being included (ie what a combination does), so why not then assign each key of such an array to a recipe, the permutation guarantees no cook is repeated and the keys guarantee no recipe is repeated.
Please let me know if there are improvements or errors in my thinking or my code but here it is!
<?php
function pc_next_permutation($p, $size) {
//this is from http://docstore.mik.ua/orelly/webprog/pcook/ch04_26.htm
// slide down the array looking for where we're smaller than the next guy
for ($i = $size - 1; $p[$i] >= $p[$i+1]; --$i) { }
// if this doesn't occur, we've finished our permutations
// the array is reversed: (1, 2, 3, 4) => (4, 3, 2, 1)
if ($i == -1) { return false; }
// slide down the array looking for a bigger number than what we found before
for ($j = $size; $p[$j] <= $p[$i]; --$j) { }
// swap them
$tmp = $p[$i]; $p[$i] = $p[$j]; $p[$j] = $tmp;
// now reverse the elements in between by swapping the ends
for (++$i, $j = $size; $i < $j; ++$i, --$j) {
$tmp = $p[$i]; $p[$i] = $p[$j]; $p[$j] = $tmp;
}
return $p;
}
$cooks[441] = array(340=>5,342=>43,343=>50,344=>9,345=>0);
$cooks[442] = array(340=>5,342=>-33,343=>-30,344=>29,345=>0);
$cooks[443] = array(340=>5,342=>3,343=>0,344=>9,345=>10,);
$cooks[444] = array(340=>25,342=>23,343=>20,344=>19,345=>20,);
$cooks[445] = array(340=>27,342=>27,343=>26,344=>39,345=>50,);
//a consideration: this solution requires that the number of cooks equal the number of recipes
foreach ($cooks as $cooksCode => $cooksProfile){
$arrayOfCooks[]=$cooksCode;
$arrayOfRecipes = (array_keys($cooksProfile));
}
echo "<br/> here is the array of the different cooks<br/>";
print_r($arrayOfCooks);
echo "<br/> here is the array of the different recipes<br/>";
print_r($arrayOfRecipes);
$set = $arrayOfCooks;
$size = count($set) - 1;
$perm = range(0, $size);
$j = 0;
do {
foreach ($perm as $i) { $perms[$j][] = $set[$i]; }
} while ($perm = pc_next_permutation($perm, $size) and ++$j);
echo "<br/> here are all the permutations of the cooks<br/>";
print_r($perms);
$bestCombo = 0;
foreach($perms as $perm){
$thisScore =0;
foreach($perm as $key =>$cook){
$recipe= $arrayOfRecipes[$key];
$cookScore =$cooks[$cook][$recipe];
$thisScore = $thisScore+$cookScore;
}
if ($thisScore>$bestCombo){
$bestCombo=$thisScore;
$bestArray= $perm;
}
}
echo "<br/> here is the very best array<br/>";
print_r ($bestArray);
echo "<br/> best recipe assignment value is:".$bestCombo."<br/><br/>";
?>
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 have a fully-populated array of values, and I would like to arbitrarily remove elements from this array with more removed towards the far end.
For example, given input ( where a . signifies a populated index )
............................................
I would like something like
....... . ... .. . . .. . .
My first thought was to count the elements, then iterate over the array generating a random number somewhere between the current index and the total size of the array, eg:
if ( mt_rand( 0, $total ) > $total - $current_index )
//remove this element
however, as this entails making a random number each time the loop goes round it becomes very arduous.
Is there a better way of doing this?
One easy way is to flip a weighted coin for each entry with coin flips more weighted towards the end. For example, if the array is size n, for each entry you could choose a random number from 0 to n-1 and only keep the value if the index is less than or equal to the random number. (That is, keep each entry with probability 1 - index/total.) This has the nice advantage that if you're going to be compacting your array anyways, and you're using a good enough but efficient random number generator (could be a simple integer hash over a nonce), it's going to be rather fast for memory access.
On the other hand if you're only blanking out a few items and aren't rearranging the array, you can go with some sort of weighted random number generator that more often chooses numbers that are toward the end of the index. For example, if you have a random number generator that generates floats in the value of [0,1] (closed or open bounds not mattering that much likely), consider obtaining such a random float r and squaring it. This will tend to prefer lower values. You can fix this by flipping it around: 1-r^2. Of course, you need this to be in your index range of 0 to n - 1, so take floor(n * (1 - r^2)) and also round n down to n-1.
There's practically an infinite number of variations on both of these techniques.
This is quite probably not the best/most efficient way to do this, but it is the best I can come up with and it does work.
N.B. the codepad example takes a long time to execute, but this is because of the pretty-print loop I added to the end so you can see it visibly working. If you remove the inner loop, execution time drops to acceptable levels.
<?php
$array = range(0, 99);
for ($i = 0, $count = count($array); $i < $count; $i++) {
// Get array keys
$keys = array_keys($array);
// Get a random number between 0 and count($keys) - 1
$rand = mt_rand(0, count($keys) - 1);
// Cut $rand elements off the beginning of the keys
$keys = array_slice($keys, $rand);
// Unset a random key from the remaining keys
unset($array[$keys[array_rand($keys)]]);
}
This method isn't random- it works by you defining a function, and its inverse. Different functions, with different constant coefficients will have different distribution characteristics.
The results are very pattern like, as expected when mapping a continuous function to a discrete structure like an array.
Here's an example using a quadratic function. You could try varying the constant.
demo: http://codepad.org/ojU3s9xM
#as in y = x^2 / 7;
function y($x) {
return $x * $x / 7;
}
function x($y) {
return 7 * sqrt($y);
}
$theArray = range(0,100);
$size = count($theArray);
//use func inverse to find the max value we can input to $y() without going out of array bounds
$maximumX = x($size);
for ($i=0; $i<$maximumX; $i++) {
$index = (int) y($i);
//unset the index if it still exists, else, the next greatest index
while (!isset($theArray[$index]) && $index < $size) {
$index++;
}
unset($theArray[$index]);
}
for ($i=0; $i<$size; $i++) {
printf("[%-3s]", isset($theArray[$i]) ? $theArray[$i] : '');
}
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.