I want to get n
random numbers(e.g n=16)(whole numbers) between 1 to 5(including both) so that average is x.
x can be any value between (1, 1.5, 2, 2.5, 3,
If I got it right, I would suggest you to have the average, than generate a number below the average and then to add a number with the same distance from average to the other side. For example, average 4 has the maximum border distance of 1 from nearest limit 5, so you should generate between 3, 4, 5. If 3 is generated - put 5 next. If 5, then 3. If 4 - put 4 next. And so on 8 times.
The best way to solve it is to put it this way:
average = sum of all numbers / amount of numbers, therefor, average * amount = sum, as Michael said. Now, if your sum is not integer - you will have no solution for this one.
It means that no matter, which method to use - mine, or Michael's. The difference is Michael's method doubles randomness with larger execution time.
I would implement it like this:
Edit: I have re-written this to avoid having to call the function recursively.
<?php
/**
* Get an array of random numbers between the given range with a given average value
*
* @param integer $min
* @param integer $max
* @param integer $count
* @param integer|float $average
* @return boolean|array
*/
function getRandomNumbers($min = 1, $max = 5, $count = 16, $average = 3)
{
// Return FALSE if the range and/or the count are not all integers
if (!is_int($min) || !is_int($max) || !is_int($count))
{
return FALSE;
}
// Round the average if the target total would be impossible
if (!is_int($count * $average))
{
$average = round($average);
}
// Get the target total
$total = $count * $average;
// Return FALSE is the result is impossible
if ($min > $max || $min * $count > $total || $max * $count < $total)
{
return FALSE;
}
// Get the specified number of random integers
for ($i = 0; $i < $count; ++$i)
{
// Get a random number within the given range
$rand = mt_rand($min, $max);
// As a default do not continue
$cont = FALSE;
// Check to see if the random number is acceptable and if not change it until it is
while (!$cont)
{
// If the number is too high then decrease it by one
if (($total - $rand) - (($count - 1 - $i) * $min) < 0)
{
--$rand;
}
// Otherwise if the number is too low then increase it by one
elseif (($total - $rand) - (($count - 1 - $i) * $max) > 0)
{
++$rand;
}
// Otherwise we can continue
else
{
$cont = TRUE;
}
}
// Store the number and minus it from the total
$total -= $result[] = $rand;
}
// Return the result
return $result;
}
// Output an array of random numbers
print_r(getRandomNumbers());
This answer allows any value for the target average (regardless of whether n is odd or even) and avoids the use of recursion to optimize performance.
The Function
function getRandomNumbersWithAverage($target_average, $n, $min=1, $max=5)
{
if($min>$max) list($min, $max) = array($max, $min);
if($target_average<$min || $target_average>$max) return false;
else if($target_average==$min) return array_fill(0, $n, $min);
else if($target_average==$max) return array_fill(0, $n, $max);
if($n<1) return false;
else if($n==1) return array($target_average);
else
{
$numbers = array();
for($i=0;$i<$n;$i++)
{
$sum = array_sum($numbers);
$average = $i ? $sum/($i+1) : ($min+$max)/2;
$contrived_number = $target_average*($i+1) - $sum;
// Last one must be contrived
if($i==$n-1) $new_number = ceil($contrived_number); // Round up
else
{
// The tolerance gets smaller with iteration
$tolerance = ($max-$min)*(1-($i/($n-1)));
$temp_min = ($contrived_number-$tolerance);
if($temp_min<$min) $temp_min = $min;
$temp_max = ($contrived_number+$tolerance);
if($temp_max>$max) $temp_max = $max;
$new_number = mt_rand($temp_min, $temp_max);
}
if($new_number==0) $new_number = 0; // Handle -0
$numbers[] = $new_number;
}
// Since the numbers get more contrived towards the end, it might be nice to shuffle
shuffle($numbers);
return $numbers;
}
}
Example Output:
getRandomNumbersWithAverage(1, 12)
produced the numbers: (1,1,1,1,1,1,1,1,1,1,1,1) having an average of: 1
getRandomNumbersWithAverage(1.1, 13)
produced the numbers: (1,1,1,1,1,1,1,4,1,1,1,0,1) having an average of: 1.1538461538462
getRandomNumbersWithAverage(2.7, 14)
produced the numbers: (3,3,2,5,1,2,4,3,3,2,3,3,3,1) having an average of: 2.7142857142857
getRandomNumbersWithAverage(2.7, 15)
produced the numbers: (3,3,4,3,4,2,1,1,3,2,4,1,5,1,4) having an average of: 2.7333333333333
getRandomNumbersWithAverage(3.5, 16)
produced the numbers: (5,5,4,3,1,5,5,1,2,5,3,3,4,4,4,2) having an average of: 3.5
getRandomNumbersWithAverage(3.5, 17)
produced the numbers: (5,2,3,5,4,1,2,3,5,4,5,4,2,3,5,3,4) having an average of: 3.5294117647059
getRandomNumbersWithAverage(4, 18)
produced the numbers: (3,5,5,3,5,5,3,4,4,4,5,2,5,1,5,4,5,4) having an average of: 4
getRandomNumbersWithAverage(4.9, 19)
produced the numbers: (5,5,5,5,7,5,5,5,5,6,5,3,5,5,3,5,5,5,5) having an average of: 4.9473684210526
getRandomNumbersWithAverage(5, 20)
produced the numbers: (5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5) having an average of: 5
getRandomNumbersWithAverage(0.5, 10)
does not produce numbers
getRandomNumbersWithAverage(0, 9)
does not produce numbers
getRandomNumbersWithAverage(-1, 8)
does not produce numbers
getRandomNumbersWithAverage(5.5, 7)
does not produce numbers
getRandomNumbersWithAverage(6, 6)
does not produce numbers
getRandomNumbersWithAverage(6, 5, 1, 7)
produced the numbers: (7,7,2,7,7) having an average of: 6
getRandomNumbersWithAverage(6, 5, 1, 6)
produced the numbers: (6,6,6,6,6) having an average of: 6
getRandomNumbersWithAverage(3, 1)
produced the numbers: (3) having an average of: 3
I have written the JS implementation for this:
function getRandom(min, max) {
return Math.random() * (max - min) + min;
}
function getArr(size, avg, min, max) {
let arr = [];
let tmax = max;
let tmin = min;
while (arr.length < size) {
const variable1 = +getRandom(min, tmax).toFixed(1);
let variable2 = +(avg * 2 - variable1).toFixed(1);
if (variable2 < min) {
tmax = max - (min - variable2);
variable2 = min;
} else if (variable2 > max) {
tmin = min + (variable2 - max);
variable2 = max;
} else {
tmax = max;
tmin = min;
}
arr = arr.concat([variable1, variable2]);
}
let sumErr = arr.reduce((a, b) => a + b, 0) - avg * size;
if (sumErr > 0) {
arr = arr.map((x) => {
if (x > min && sumErr > 0.001) {
let maxReduce = x - min;
if (maxReduce > sumErr) {
const toReturn = +(x - sumErr).toFixed(1);
sumErr = 0;
return toReturn;
} else {
sumErr -= maxReduce;
return min;
}
}
return x;
});
} else {
arr = arr.map((x) => {
if (x < max && sumErr < -0.001) {
let maxAdd = max - x;
if (maxAdd > Math.abs(sumErr)) {
const toReturn = +(x + Math.abs(sumErr)).toFixed(1);
sumErr = 0;
return toReturn;
} else {
sumErr += maxAdd;
return max;
}
}
return x;
});
}
return arr.sort(() => Math.random() - 0.5);
}
const output = getArr(40, 2.01, 0.5, 2.5)
const outputAvg = output.reduce((a, b) => a + b, 0) / 40
console.log(`givenAvg: ${2.01} outputAvg: ${outputAvg}`)
console.log(output)