Related
I'm trying to devise a (good) way to choose a random number from a range of possible numbers where each number in the range is given a weight. To put it simply: given the range of numbers (0,1,2) choose a number where 0 has an 80% probability of being selected, 1 has a 10% chance and 2 has a 10% chance.
It's been about 8 years since my college stats class, so you can imagine the proper formula for this escapes me at the moment.
Here's the 'cheap and dirty' method that I came up with. This solution uses ColdFusion. Yours may use whatever language you'd like. I'm a programmer, I think I can handle porting it. Ultimately my solution needs to be in Groovy - I wrote this one in ColdFusion because it's easy to quickly write/test in CF.
public function weightedRandom( Struct options ) {
var tempArr = [];
for( var o in arguments.options )
{
var weight = arguments.options[ o ] * 10;
for ( var i = 1; i<= weight; i++ )
{
arrayAppend( tempArr, o );
}
}
return tempArr[ randRange( 1, arrayLen( tempArr ) ) ];
}
// test it
opts = { 0=.8, 1=.1, 2=.1 };
for( x = 1; x<=10; x++ )
{
writeDump( weightedRandom( opts ) );
}
I'm looking for better solutions, please suggest improvements or alternatives.
Rejection sampling (such as in your solution) is the first thing that comes to mind, whereby you build a lookup table with elements populated by their weight distribution, then pick a random location in the table and return it. As an implementation choice, I would make a higher order function which takes a spec and returns a function which returns values based on the distribution in the spec, this way you avoid having to build the table for each call. The downsides are that the algorithmic performance of building the table is linear by the number of items and there could potentially be a lot of memory usage for large specs (or those with members with very small or precise weights, e.g. {0:0.99999, 1:0.00001}). The upside is that picking a value has constant time, which might be desirable if performance is critical. In JavaScript:
function weightedRand(spec) {
var i, j, table=[];
for (i in spec) {
// The constant 10 below should be computed based on the
// weights in the spec for a correct and optimal table size.
// E.g. the spec {0:0.999, 1:0.001} will break this impl.
for (j=0; j<spec[i]*10; j++) {
table.push(i);
}
}
return function() {
return table[Math.floor(Math.random() * table.length)];
}
}
var rand012 = weightedRand({0:0.8, 1:0.1, 2:0.1});
rand012(); // random in distribution...
Another strategy is to pick a random number in [0,1) and iterate over the weight specification summing the weights, if the random number is less than the sum then return the associated value. Of course, this assumes that the weights sum to one. This solution has no up-front costs but has average algorithmic performance linear by the number of entries in the spec. For example, in JavaScript:
function weightedRand2(spec) {
var i, sum=0, r=Math.random();
for (i in spec) {
sum += spec[i];
if (r <= sum) return i;
}
}
weightedRand2({0:0.8, 1:0.1, 2:0.1}); // random in distribution...
Generate a random number R between 0 and 1.
If R in [0, 0.1) -> 1
If R in [0.1, 0.2) -> 2
If R in [0.2, 1] -> 3
If you can't directly get a number between 0 and 1, generate a number in a range that will produce as much precision as you want. For example, if you have the weights for
(1, 83.7%) and (2, 16.3%), roll a number from 1 to 1000. 1-837 is a 1. 838-1000 is 2.
I use the following
function weightedRandom(min, max) {
return Math.round(max / (Math.random() * max + min));
}
This is my go-to "weighted" random, where I use an inverse function of "x" (where x is a random between min and max) to generate a weighted result, where the minimum is the most heavy element, and the maximum the lightest (least chances of getting the result)
So basically, using weightedRandom(1, 5) means the chances of getting a 1 are higher than a 2 which are higher than a 3, which are higher than a 4, which are higher than a 5.
Might not be useful for your use case but probably useful for people googling this same question.
After a 100 iterations try, it gave me:
==================
| Result | Times |
==================
| 1 | 55 |
| 2 | 28 |
| 3 | 8 |
| 4 | 7 |
| 5 | 2 |
==================
Here are 3 solutions in javascript since I'm not sure which language you want it in. Depending on your needs one of the first two might work, but the the third one is probably the easiest to implement with large sets of numbers.
function randomSimple(){
return [0,0,0,0,0,0,0,0,1,2][Math.floor(Math.random()*10)];
}
function randomCase(){
var n=Math.floor(Math.random()*100)
switch(n){
case n<80:
return 0;
case n<90:
return 1;
case n<100:
return 2;
}
}
function randomLoop(weight,num){
var n=Math.floor(Math.random()*100),amt=0;
for(var i=0;i<weight.length;i++){
//amt+=weight[i]; *alternative method
//if(n<amt){
if(n<weight[i]){
return num[i];
}
}
}
weight=[80,90,100];
//weight=[80,10,10]; *alternative method
num=[0,1,2]
8 years late but here's my solution in 4 lines.
Prepare an array of probability mass function such that
pmf[array_index] = P(X=array_index):
var pmf = [0.8, 0.1, 0.1]
Prepare an array for the corresponding cumulative distribution function such that
cdf[array_index] = F(X=array_index):
var cdf = pmf.map((sum => value => sum += value)(0))
// [0.8, 0.9, 1]
3a) Generate a random number.
3b) Get an array of elements that are more than or equal to this number.
3c) Return its length.
var r = Math.random()
cdf.filter(el => r >= el).length
This is more or less a generic-ized version of what #trinithis wrote, in Java: I did it with ints rather than floats to avoid messy rounding errors.
static class Weighting {
int value;
int weighting;
public Weighting(int v, int w) {
this.value = v;
this.weighting = w;
}
}
public static int weightedRandom(List<Weighting> weightingOptions) {
//determine sum of all weightings
int total = 0;
for (Weighting w : weightingOptions) {
total += w.weighting;
}
//select a random value between 0 and our total
int random = new Random().nextInt(total);
//loop thru our weightings until we arrive at the correct one
int current = 0;
for (Weighting w : weightingOptions) {
current += w.weighting;
if (random < current)
return w.value;
}
//shouldn't happen.
return -1;
}
public static void main(String[] args) {
List<Weighting> weightings = new ArrayList<Weighting>();
weightings.add(new Weighting(0, 8));
weightings.add(new Weighting(1, 1));
weightings.add(new Weighting(2, 1));
for (int i = 0; i < 100; i++) {
System.out.println(weightedRandom(weightings));
}
}
How about
int [ ] numbers = { 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 1 , 2 } ;
then you can randomly select from numbers and 0 will have an 80% chance, 1 10%, and 2 10%
This one is in Mathematica, but it's easy to copy to another language, I use it in my games and it can handle decimal weights:
weights = {0.5,1,2}; // The weights
weights = N#weights/Total#weights // Normalize weights so that the list's sum is always 1.
min = 0; // First min value should be 0
max = weights[[1]]; // First max value should be the first element of the newly created weights list. Note that in Mathematica the first element has index of 1, not 0.
random = RandomReal[]; // Generate a random float from 0 to 1;
For[i = 1, i <= Length#weights, i++,
If[random >= min && random < max,
Print["Chosen index number: " <> ToString#i]
];
min += weights[[i]];
If[i == Length#weights,
max = 1,
max += weights[[i + 1]]
]
]
(Now I'm talking with a lists first element's index equals 0) The idea behind this is that having a normalized list weights there is a chance of weights[n] to return the index n, so the distances between the min and max at step n should be weights[n]. The total distance from the minimum min (which we put it to be 0) and the maximum max is the sum of the list weights.
The good thing behind this is that you don't append to any array or nest for loops, and that increases heavily the execution time.
Here is the code in C# without needing to normalize the weights list and deleting some code:
int WeightedRandom(List<float> weights) {
float total = 0f;
foreach (float weight in weights) {
total += weight;
}
float max = weights [0],
random = Random.Range(0f, total);
for (int index = 0; index < weights.Count; index++) {
if (random < max) {
return index;
} else if (index == weights.Count - 1) {
return weights.Count-1;
}
max += weights[index+1];
}
return -1;
}
I suggest to use a continuous check of the probability and the rest of the random number.
This function sets first the return value to the last possible index and iterates until the rest of the random value is smaller than the actual probability.
The probabilities have to sum to one.
function getRandomIndexByProbability(probabilities) {
var r = Math.random(),
index = probabilities.length - 1;
probabilities.some(function (probability, i) {
if (r < probability) {
index = i;
return true;
}
r -= probability;
});
return index;
}
var i,
probabilities = [0.8, 0.1, 0.1],
count = probabilities.map(function () { return 0; });
for (i = 0; i < 1e6; i++) {
count[getRandomIndexByProbability(probabilities)]++;
}
console.log(count);
.as-console-wrapper { max-height: 100% !important; top: 0; }
Thanks all, this was a helpful thread. I encapsulated it into a convenience function (Typescript). Tests below (sinon, jest). Could definitely be a bit tighter, but hopefully it's readable.
export type WeightedOptions = {
[option: string]: number;
};
// Pass in an object like { a: 10, b: 4, c: 400 } and it'll return either "a", "b", or "c", factoring in their respective
// weight. So in this example, "c" is likely to be returned 400 times out of 414
export const getRandomWeightedValue = (options: WeightedOptions) => {
const keys = Object.keys(options);
const totalSum = keys.reduce((acc, item) => acc + options[item], 0);
let runningTotal = 0;
const cumulativeValues = keys.map((key) => {
const relativeValue = options[key]/totalSum;
const cv = {
key,
value: relativeValue + runningTotal
};
runningTotal += relativeValue;
return cv;
});
const r = Math.random();
return cumulativeValues.find(({ key, value }) => r <= value)!.key;
};
Tests:
describe('getRandomWeightedValue', () => {
// Out of 1, the relative and cumulative values for these are:
// a: 0.1666 -> 0.16666
// b: 0.3333 -> 0.5
// c: 0.5 -> 1
const values = { a: 10, b: 20, c: 30 };
it('returns appropriate values for particular random value', () => {
// any random number under 0.166666 should return "a"
const stub1 = sinon.stub(Math, 'random').returns(0);
const result1 = randomUtils.getRandomWeightedValue(values);
expect(result1).toEqual('a');
stub1.restore();
const stub2 = sinon.stub(Math, 'random').returns(0.1666);
const result2 = randomUtils.getRandomWeightedValue(values);
expect(result2).toEqual('a');
stub2.restore();
// any random number between 0.166666 and 0.5 should return "b"
const stub3 = sinon.stub(Math, 'random').returns(0.17);
const result3 = randomUtils.getRandomWeightedValue(values);
expect(result3).toEqual('b');
stub3.restore();
const stub4 = sinon.stub(Math, 'random').returns(0.3333);
const result4 = randomUtils.getRandomWeightedValue(values);
expect(result4).toEqual('b');
stub4.restore();
const stub5 = sinon.stub(Math, 'random').returns(0.5);
const result5 = randomUtils.getRandomWeightedValue(values);
expect(result5).toEqual('b');
stub5.restore();
// any random number above 0.5 should return "c"
const stub6 = sinon.stub(Math, 'random').returns(0.500001);
const result6 = randomUtils.getRandomWeightedValue(values);
expect(result6).toEqual('c');
stub6.restore();
const stub7 = sinon.stub(Math, 'random').returns(1);
const result7 = randomUtils.getRandomWeightedValue(values);
expect(result7).toEqual('c');
stub7.restore();
});
});
Shortest solution in modern JavaScript
Note: all weights need to be integers
function weightedRandom(items){
let table = Object.entries(items)
.flatMap(([item, weight]) => Array(item).fill(weight))
return table[Math.floor(Math.random() * table.length)]
}
const key = weightedRandom({
"key1": 1,
"key2": 4,
"key3": 8
}) // returns e.g. "key1"
here is the input and ratios : 0 (80%), 1(10%) , 2 (10%)
lets draw them out so its easy to visualize.
0 1 2
-------------------------------------________+++++++++
lets add up the total weight and call it TR for total ratio. so in this case 100.
lets randomly get a number from (0-TR) or (0 to 100 in this case) . 100 being your weights total. Call it RN for random number.
so now we have TR as the total weight and RN as the random number between 0 and TR.
so lets imagine we picked a random # from 0 to 100. Say 21. so thats actually 21%.
WE MUST CONVERT/MATCH THIS TO OUR INPUT NUMBERS BUT HOW ?
lets loop over each weight (80, 10, 10) and keep the sum of the weights we already visit.
the moment the sum of the weights we are looping over is greater then the random number RN (21 in this case), we stop the loop & return that element position.
double sum = 0;
int position = -1;
for(double weight : weight){
position ++;
sum = sum + weight;
if(sum > 21) //(80 > 21) so break on first pass
break;
}
//position will be 0 so we return array[0]--> 0
lets say the random number (between 0 and 100) is 83. Lets do it again:
double sum = 0;
int position = -1;
for(double weight : weight){
position ++;
sum = sum + weight;
if(sum > 83) //(90 > 83) so break
break;
}
//we did two passes in the loop so position is 1 so we return array[1]---> 1
I have a slotmachine and I used the code below to generate random numbers. In probabilitiesSlotMachine the keys are the output in the slotmachine, and the values represent the weight.
const probabilitiesSlotMachine = [{0 : 1000}, {1 : 100}, {2 : 50}, {3 : 30}, {4 : 20}, {5 : 10}, {6 : 5}, {7 : 4}, {8 : 2}, {9 : 1}]
var allSlotMachineResults = []
probabilitiesSlotMachine.forEach(function(obj, index){
for (var key in obj){
for (var loop = 0; loop < obj[key]; loop ++){
allSlotMachineResults.push(key)
}
}
});
Now to generate a random output, I use this code:
const random = allSlotMachineResults[Math.floor(Math.random() * allSlotMachineResults.length)]
Enjoy the O(1) (constant time) solution for your problem.
If the input array is small, it can be easily implemented.
const number = Math.floor(Math.random() * 99); // Generate a random number from 0 to 99
let element;
if (number >= 0 && number <= 79) {
/*
In the range of 0 to 99, every number has equal probability
of occurring. Therefore, if you gather 80 numbers (0 to 79) and
make a "sub-group" of them, then their probabilities will get added.
Hence, what you get is an 80% chance that the number will fall in this
range.
So, quite naturally, there is 80% probability that this code will run.
Now, manually choose / assign element of your array to this variable.
*/
element = 0;
}
else if (number >= 80 && number <= 89) {
// 10% chance that this code runs.
element = 1;
}
else if (number >= 90 && number <= 99) {
// 10% chance that this code runs.
element = 2;
}
For example: There are four items in an array. I want to get one randomly, like this:
array items = [
"bike" //40% chance to select
"car" //30% chance to select
"boat" //15% chance to select
"train" //10% chance to select
"plane" //5% chance to select
]
Both answers above rely on methods that will get slow quickly, especially the accepted one.
function weighted_random(items, weights) {
var i;
for (i = 1; i < weights.length; i++)
weights[i] += weights[i - 1];
var random = Math.random() * weights[weights.length - 1];
for (i = 0; i < weights.length; i++)
if (weights[i] > random)
break;
return items[i];
}
I replaced my older ES6 solution with this one as of December 2020, as ES6 isn't supported in older browsers, and I personally think this one is more readable.
If you'd rather use objects with the properties item and weight:
function weighted_random(options) {
var i;
var weights = [options[0].weight];
for (i = 1; i < options.length; i++)
weights[i] = options[i].weight + weights[i - 1];
var random = Math.random() * weights[weights.length - 1];
for (i = 0; i < weights.length; i++)
if (weights[i] > random)
break;
return options[i].item;
}
Explanation:
I've made this diagram that shows how this works:
This diagram shows what happens when an input with the weights [5, 2, 8, 3] is given. By taking partial sums of the weights, you just need to find the first one that's as large as a random number, and that's the randomly chosen item.
If a random number is chosen right on the border of two weights, like with 7 and 15 in the diagram, we go with the longer one. This is because 0 can be chosen by Math.random but 1 can't, so we get a fair distribution. If we went with the shorter one, A could be chosen 6 out of 18 times (0, 1, 2, 3, 4), giving it a higher weight than it should have.
Some es6 approach, with wildcard handling:
const randomizer = (values) => {
let i, pickedValue,
randomNr = Math.random(),
threshold = 0;
for (i = 0; i < values.length; i++) {
if (values[i].probability === '*') {
continue;
}
threshold += values[i].probability;
if (threshold > randomNr) {
pickedValue = values[i].value;
break;
}
if (!pickedValue) {
//nothing found based on probability value, so pick element marked with wildcard
pickedValue = values.filter((value) => value.probability === '*');
}
}
return pickedValue;
}
Example usage:
let testValues = [{
value : 'aaa',
probability: 0.1
},
{
value : 'bbb',
probability: 0.3
},
{
value : 'ccc',
probability: '*'
}]
randomizer(testValues); // will return "aaa" in 10% calls,
//"bbb" in 30% calls, and "ccc" in 60% calls;
Here's a faster way of doing that then other answers suggested...
You can achieve what you want by:
dividing the 0-to-1 segment into sections for each element based on their probability (For example, an element with probability 60% will take 60% of the segment).
generating a random number and checking in which segment it lands.
STEP 1
make a prefix sum array for the probability array, each value in it will signify where its corresponding section ends.
For example:
If we have probabilities: 60% (0.6), 30%, 5%, 3%, 2%. the prefix sum array will be: [0.6,0.9,0.95,0.98,1]
so we will have a segment divided like this (approximately): [ | | ||]
STEP 2
generate a random number between 0 and 1, and find it's lower bound in the prefix sum array. the index you'll find is the index of the segment that the random number landed in
Here's how you can implement this method:
let obj = {
"Common": "60",
"Uncommon": "25",
"Rare": "10",
"Legendary": "0.01",
"Mythical": "0.001"
}
// turning object into array and creating the prefix sum array:
let sums = [0]; // prefix sums;
let keys = [];
for(let key in obj) {
keys.push(key);
sums.push(sums[sums.length-1] + parseFloat(obj[key])/100);
}
sums.push(1);
keys.push('NONE');
// Step 2:
function lowerBound(target, low = 0, high = sums.length - 1) {
if (low == high) {
return low;
}
const midPoint = Math.floor((low + high) / 2);
if (target < sums[midPoint]) {
return lowerBound(target, low, midPoint);
} else if (target > sums[midPoint]) {
return lowerBound(target, midPoint + 1, high);
} else {
return midPoint + 1;
}
}
function getRandom() {
return lowerBound(Math.random());
}
console.log(keys[getRandom()], 'was picked!');
hope you find this helpful.
Note:
(In Computer Science) the lower bound of a value in a list/array is the smallest element that is greater or equal to it. for example, array:[1,10,24,99] and value 12. the lower bound will be the element with value 24.
When the array is sorted from smallest to biggest (like in our case) finding the lower bound of every value can be done extremely quickly with binary searching (O(log(n))).
Here is a O(1) (constant time) algo to solve your problem.
Generate a random number from 0 to 99 (100 total numbers). If there are 40 numbers (0 to 39) in a given sub-range, then there is a 40% probability that the randomly chosen number will fall in this range. See the code below.
const number = Math.floor(Math.random() * 99); // 0 to 99
let element;
if (number >= 0 && number <= 39) {
// 40% chance that this code runs. Hence, it is a bike.
element = "bike";
}
else if (number >= 40 && number <= 69) {
// 30% chance that this code runs. Hence, it is a car.
element = "car";
}
else if (number >= 70 && number <= 84) {
// 15% chance that this code runs. Hence, it is a boat.
element = "boat";
}
else if (number >= 85 && number <= 94) {
// 10% chance that this code runs. Hence, it is a train.
element = "train";
}
else if (number >= 95 && number <= 99) {
// 5% chance that this code runs. Hence, it is a plane.
element = "plane";
}
Remember this, one Mathematical principle from elementary school? "All the numbers in a specified distribution have equal probability of being chosen randomly."
This tells us that each of the random numbers have equal probability of occurring in a specific range, no matter how large or small that range might be.
That's it. This should work!
I added my solution as a method that works well on smaller arrays (no caching):
static weight_random(arr, weight_field){
if(arr == null || arr === undefined){
return null;
}
const totals = [];
let total = 0;
for(let i=0;i<arr.length;i++){
total += arr[i][weight_field];
totals.push(total);
}
const rnd = Math.floor(Math.random() * total);
let selected = arr[0];
for(let i=0;i<totals.length;i++){
if(totals[i] > rnd){
selected = arr[i];
break;
}
}
return selected;
}
Run it like this (provide the array and the weight property):
const wait_items = [
{"w" : 20, "min_ms" : "5000", "max_ms" : "10000"},
{"w" : 20, "min_ms" : "10000", "max_ms" : "20000"},
{"w" : 20, "min_ms" : "40000", "max_ms" : "80000"}
]
const item = weight_random(wait_items, "w");
console.log(item);
ES2015 version of Radvylf Programs's answer
function getWeightedRandomItem(items) {
const weights = items.reduce((acc, item, i) => {
acc.push(item.weight + (acc[i - 1] || 0));
return acc;
}, []);
const random = Math.random() * weights[weights.length - 1];
return items[weights.findIndex((weight) => weight > random)];
}
And ES2022
function getWeightedRandomItem(items) {
const weights = items.reduce((acc, item, i) => {
acc.push(item.weight + (acc[i - 1] ?? 0));
return acc;
}, []);
const random = Math.random() * weights.at(-1);
return items[weights.findIndex((weight) => weight > random)];
}
Sure you can. Here's a simple code to do it:
// Object or Array. Which every you prefer.
var item = {
bike:40, // Weighted Probability
care:30, // Weighted Probability
boat:15, // Weighted Probability
train:10, // Weighted Probability
plane:5 // Weighted Probability
// The number is not really percentage. You could put whatever number you want.
// Any number less than 1 will never occur
};
function get(input) {
var array = []; // Just Checking...
for(var item in input) {
if ( input.hasOwnProperty(item) ) { // Safety
for( var i=0; i<input[item]; i++ ) {
array.push(item);
}
}
}
// Probability Fun
return array[Math.floor(Math.random() * array.length)];
}
console.log(get(item)); // See Console.
I've been going over this question now for a couple of days and I'm still no closer to getting it right or understanding as to how to get it to run properly.
This is the current code I have:
let waterPay = prompt("Please enter the amount of water you use to get a price you need to pay, thank you!");
if (waterPay < 6000) {
console.log("The number is below 6000");
console.log (waterPay / 1000); //The outcome of this must be saved as a different let
console.log (waterPay * 15.73);// outcome of the above times by this amount
}
else if (waterPay > 6000 && waterPay <= 10500) {
console.log("The number is between 6000 and 10500");
}
else if (waterPay > 10500 && waterPay <= 35000) {
console.log("The number is between 10500 and 35000");
}
else if (waterPay > 35000) {
console.log("The number is above 35000");
}
What my code needs to do is take an input from the user stating how many litres of water they use, you can see in the code that depending on the amount of litres they use it should print out how much they owe.
The table above states that the first 6 000 litres will cost R15.73 per kilolitre.
Next, water consumption above 6 000 litres but below 10 500 litres will be
charged at R22.38 per kilolitre. Therefore, a household that has used 8000
litres will pay R139.14 (15.73 x 6 + 22.38 x 2). The table carries on in this
manner.
Im battling to figure out how I should go about working this out. Any help would be appreciated.
The data structure needed is something that pairs rates with usage thresholds. The last threshold is effectively infinite, to catch any usage above the highest. The logic is to find() the right rate object and multiply that rate tier's rate by the usage.
let rateData = [{
upTo: 6000,
rate: 15.73
},
{
upTo: 10500,
rate: 22.38
},
{
upTo: 35000,
rate: 34.0. // made this one up, not in the OP
},
{
upTo: Number.MAX_SAFE_INTEGER,
rate: 50.0. // made this one up, not in the OP
}
];
function rateDatumForUsage(usage) {
return rateData.find(r => usage <= r.upTo);
}
function costForUsage(usage) {
const rateDatum = rateDatumForUsage(usage);
return usage * rateDatum.rate;
}
console.log(`The cost of using 5000 units is (15.73*5000) ${costForUsage(5000)}`)
console.log(`The cost of using 10000 units is (22.38*10000) ${costForUsage(10000)}`)
console.log(`The cost of using 100000 units is (50*100000) ${costForUsage(100000)}`)
Total cost should be calculated by steps.
This means that, for example, if the first 10 liters cost USD 2, the following 10 liters (from 10 to 20) cost USD 1 and from 20 cost will be USD 0.5, then the total cost for 30 liters will be: 10*2 + 10*1 + 10*0.5 = 35.
This can only be achieved generically by looping. Here is the code:
const steps = [
6000,
10500,
35000
];
const rates = [
10,
20,
30
];
function calculate(used) {
let output = 0;
for (let i = 0; i < steps.length; i++) {
if (used >= steps[i]) {
output += steps[i] * rates[i];
} else {
output += (used - (steps[i - 1] || 0)) * rates[i];
break;
}
}
return output;
}
console.log(calculate(3000));
console.log(calculate(6000));
console.log(calculate(9000));
console.log(calculate(50000));
I have a question I have a value that I need to divide and make the values without infinite decimals when divided by an odd number
example:
5 values that add up to 200 divided by three people
this result is: 66.66666666666667
I want to avoid this, so that an approximation is made like:
2 people would stay with 65
and one person with 70
my code:
const test = [
{ price: 5, quantity: 10 },
{ price: 10, quantity: 10 },
{ price: 5, quantity: 10 },
];
const persons = ['person 1', 'person 2', 'person 3']
const total = testList
.map((test ) => test .unitPrice * test .quantity)
.reduce((sum, current) => sum + current);
const division = total/persons.length
I need a way that in the end the total is 200 divided for 3 people, without having decimal numbers
You need to figure out how many will remain. Remove them, divide it, than loop to add the remaining to the other buckets until you run out.
const total = 200
const numParts = 3
let extras = total % numParts;
const base = (total - extras) / numParts
const portions = new Array(numParts).fill(base)
for (let i = 0; i < numParts && extras > 0; i++) {
portions[i]++;
extras--;
}
console.log(portions);
For example: There are four items in an array. I want to get one randomly, like this:
array items = [
"bike" //40% chance to select
"car" //30% chance to select
"boat" //15% chance to select
"train" //10% chance to select
"plane" //5% chance to select
]
Both answers above rely on methods that will get slow quickly, especially the accepted one.
function weighted_random(items, weights) {
var i;
for (i = 1; i < weights.length; i++)
weights[i] += weights[i - 1];
var random = Math.random() * weights[weights.length - 1];
for (i = 0; i < weights.length; i++)
if (weights[i] > random)
break;
return items[i];
}
I replaced my older ES6 solution with this one as of December 2020, as ES6 isn't supported in older browsers, and I personally think this one is more readable.
If you'd rather use objects with the properties item and weight:
function weighted_random(options) {
var i;
var weights = [options[0].weight];
for (i = 1; i < options.length; i++)
weights[i] = options[i].weight + weights[i - 1];
var random = Math.random() * weights[weights.length - 1];
for (i = 0; i < weights.length; i++)
if (weights[i] > random)
break;
return options[i].item;
}
Explanation:
I've made this diagram that shows how this works:
This diagram shows what happens when an input with the weights [5, 2, 8, 3] is given. By taking partial sums of the weights, you just need to find the first one that's as large as a random number, and that's the randomly chosen item.
If a random number is chosen right on the border of two weights, like with 7 and 15 in the diagram, we go with the longer one. This is because 0 can be chosen by Math.random but 1 can't, so we get a fair distribution. If we went with the shorter one, A could be chosen 6 out of 18 times (0, 1, 2, 3, 4), giving it a higher weight than it should have.
Some es6 approach, with wildcard handling:
const randomizer = (values) => {
let i, pickedValue,
randomNr = Math.random(),
threshold = 0;
for (i = 0; i < values.length; i++) {
if (values[i].probability === '*') {
continue;
}
threshold += values[i].probability;
if (threshold > randomNr) {
pickedValue = values[i].value;
break;
}
if (!pickedValue) {
//nothing found based on probability value, so pick element marked with wildcard
pickedValue = values.filter((value) => value.probability === '*');
}
}
return pickedValue;
}
Example usage:
let testValues = [{
value : 'aaa',
probability: 0.1
},
{
value : 'bbb',
probability: 0.3
},
{
value : 'ccc',
probability: '*'
}]
randomizer(testValues); // will return "aaa" in 10% calls,
//"bbb" in 30% calls, and "ccc" in 60% calls;
Here's a faster way of doing that then other answers suggested...
You can achieve what you want by:
dividing the 0-to-1 segment into sections for each element based on their probability (For example, an element with probability 60% will take 60% of the segment).
generating a random number and checking in which segment it lands.
STEP 1
make a prefix sum array for the probability array, each value in it will signify where its corresponding section ends.
For example:
If we have probabilities: 60% (0.6), 30%, 5%, 3%, 2%. the prefix sum array will be: [0.6,0.9,0.95,0.98,1]
so we will have a segment divided like this (approximately): [ | | ||]
STEP 2
generate a random number between 0 and 1, and find it's lower bound in the prefix sum array. the index you'll find is the index of the segment that the random number landed in
Here's how you can implement this method:
let obj = {
"Common": "60",
"Uncommon": "25",
"Rare": "10",
"Legendary": "0.01",
"Mythical": "0.001"
}
// turning object into array and creating the prefix sum array:
let sums = [0]; // prefix sums;
let keys = [];
for(let key in obj) {
keys.push(key);
sums.push(sums[sums.length-1] + parseFloat(obj[key])/100);
}
sums.push(1);
keys.push('NONE');
// Step 2:
function lowerBound(target, low = 0, high = sums.length - 1) {
if (low == high) {
return low;
}
const midPoint = Math.floor((low + high) / 2);
if (target < sums[midPoint]) {
return lowerBound(target, low, midPoint);
} else if (target > sums[midPoint]) {
return lowerBound(target, midPoint + 1, high);
} else {
return midPoint + 1;
}
}
function getRandom() {
return lowerBound(Math.random());
}
console.log(keys[getRandom()], 'was picked!');
hope you find this helpful.
Note:
(In Computer Science) the lower bound of a value in a list/array is the smallest element that is greater or equal to it. for example, array:[1,10,24,99] and value 12. the lower bound will be the element with value 24.
When the array is sorted from smallest to biggest (like in our case) finding the lower bound of every value can be done extremely quickly with binary searching (O(log(n))).
Here is a O(1) (constant time) algo to solve your problem.
Generate a random number from 0 to 99 (100 total numbers). If there are 40 numbers (0 to 39) in a given sub-range, then there is a 40% probability that the randomly chosen number will fall in this range. See the code below.
const number = Math.floor(Math.random() * 99); // 0 to 99
let element;
if (number >= 0 && number <= 39) {
// 40% chance that this code runs. Hence, it is a bike.
element = "bike";
}
else if (number >= 40 && number <= 69) {
// 30% chance that this code runs. Hence, it is a car.
element = "car";
}
else if (number >= 70 && number <= 84) {
// 15% chance that this code runs. Hence, it is a boat.
element = "boat";
}
else if (number >= 85 && number <= 94) {
// 10% chance that this code runs. Hence, it is a train.
element = "train";
}
else if (number >= 95 && number <= 99) {
// 5% chance that this code runs. Hence, it is a plane.
element = "plane";
}
Remember this, one Mathematical principle from elementary school? "All the numbers in a specified distribution have equal probability of being chosen randomly."
This tells us that each of the random numbers have equal probability of occurring in a specific range, no matter how large or small that range might be.
That's it. This should work!
I added my solution as a method that works well on smaller arrays (no caching):
static weight_random(arr, weight_field){
if(arr == null || arr === undefined){
return null;
}
const totals = [];
let total = 0;
for(let i=0;i<arr.length;i++){
total += arr[i][weight_field];
totals.push(total);
}
const rnd = Math.floor(Math.random() * total);
let selected = arr[0];
for(let i=0;i<totals.length;i++){
if(totals[i] > rnd){
selected = arr[i];
break;
}
}
return selected;
}
Run it like this (provide the array and the weight property):
const wait_items = [
{"w" : 20, "min_ms" : "5000", "max_ms" : "10000"},
{"w" : 20, "min_ms" : "10000", "max_ms" : "20000"},
{"w" : 20, "min_ms" : "40000", "max_ms" : "80000"}
]
const item = weight_random(wait_items, "w");
console.log(item);
ES2015 version of Radvylf Programs's answer
function getWeightedRandomItem(items) {
const weights = items.reduce((acc, item, i) => {
acc.push(item.weight + (acc[i - 1] || 0));
return acc;
}, []);
const random = Math.random() * weights[weights.length - 1];
return items[weights.findIndex((weight) => weight > random)];
}
And ES2022
function getWeightedRandomItem(items) {
const weights = items.reduce((acc, item, i) => {
acc.push(item.weight + (acc[i - 1] ?? 0));
return acc;
}, []);
const random = Math.random() * weights.at(-1);
return items[weights.findIndex((weight) => weight > random)];
}
Sure you can. Here's a simple code to do it:
// Object or Array. Which every you prefer.
var item = {
bike:40, // Weighted Probability
care:30, // Weighted Probability
boat:15, // Weighted Probability
train:10, // Weighted Probability
plane:5 // Weighted Probability
// The number is not really percentage. You could put whatever number you want.
// Any number less than 1 will never occur
};
function get(input) {
var array = []; // Just Checking...
for(var item in input) {
if ( input.hasOwnProperty(item) ) { // Safety
for( var i=0; i<input[item]; i++ ) {
array.push(item);
}
}
}
// Probability Fun
return array[Math.floor(Math.random() * array.length)];
}
console.log(get(item)); // See Console.