Develop Reference

Which algorithm should be used to find the point?

You need to find some unknown, predetermined point in three-dimensional space, in the smallest number of attempts, using only a function that can return the distance from
any point you pass to it to the desired unknown point.
To solve the problem, first implement a function f that, by taking the coordinates of any point s(x, y, z), return the distance between that point and a conditionally unknown, randomly generated point
point you arbitrarily generate r(x, y, z), where x, y, z can be integers between
0 и 100.
For example, for an arbitrarily generated point r(0, 0, 10) and a point passed to the function
s(0, 0, 0), the result of the function would be as follows:
f(s) = 10 // the distance between s(0, 0, 0) and r(0, 0, 10) is 10
Next, implement the algorithm itself for the assignment. The algorithm should find the coordinates of
of an arbitrarily generated point with the least number of calls to the function f.
I have a randomizer instead of an algorithm, that's all I got. Help.
const pointToFound = {
x: 12,
y: 9,
z: 76,
};
let attemts = 0;
let isXFound = false;
let isYFound = false;
let isZFound = false;
const pointHistory = [];
const getRandomPoint = () => {
return {
x: isXFound ? isXFound : Math.floor(Math.random() * 101),
y: isYFound ? isYFound : Math.floor(Math.random() * 101),
z: isZFound ? isZFound : Math.floor(Math.random() * 101),
};
};
const getDifference = (point, pointToCompare) => {
return {
x:
Math.max(point.x, pointToCompare.x) - Math.min(point.x, pointToCompare.x),
y:
Math.max(point.y, pointToCompare.y) - Math.min(point.y, pointToCompare.y),
z:
Math.max(point.z, pointToCompare.z) - Math.min(point.z, pointToCompare.z),
};
};
const condition = !isXFound && !isYFound && !isZFound;
while (condition) {
const point = getRandomPoint();
const difference = getDifference(point, pointToFound);
pointHistory.push(point);
attemts += 1;
if (isXFound && isYFound && isZFound) {
console.log("Total attempts: ", attemts);
console.log(point);
break;
}
if (difference.x === 0 && !isXFound) {
isXFound = point.x;
}
if (difference.y === 0 && !isYFound) {
isYFound = point.y;
}
if (difference.z === 0 && !isZFound) {
isZFound = point.z;
}
}
console.log(pointHistory);
I have a randomizer instead of an algorithm, that's all I got. Help.

This can be done with at most 3 guesses and often with 2 guesses:
Let the first guess be [0, 0, 0], and ask for the distance
Find in the 100x100x100 cube all points that have that distance to [0, 0, 0]. There might be around 100-200 points that have that distance: consider all of these candidates.
Take the first candidate as the second guess and ask for the distance
Find among the other candidates the ones that have exactly that distance to the first candidate. Often there will be only one point that satisfies this condition. In that case we can return that candidate and only 2 guesses were necessary.
Otherwise (when there is more than one candidate remaining) repeat the previous step which will now certainly lead to a single point.
Here is an implementation that provides a blackbox function which chooses the secret point in a local variable, and which returns two functions: f for the caller to submit a guess, and report for the caller to verify the result of the algorithm and report on the number of guesses. This is not part of the algorithm itself, which is provided in the findPoint function.
const rnd = () => Math.floor(Math.random() * 101);
const distance = (a, b) =>
a.reduce((acc, x, i) => acc + (x - b[i]) ** 2, 0) ** 0.5;
function findPoint(f) {
// First guess is always the zero-point
let guess = [0, 0, 0];
let dist = f(guess);
if (dist === 0) return guess; // Extremely lucky!
// Find the points in the cube that have this distance to [0,0,0]
let candidates = [];
const limit = Math.min(100, Math.round(dist));
for (let x = 0; x <= limit; x++) {
const p = [x, limit, 0];
// Follow circle in X=x plane
while (p[1] >= 0 && p[2] <= limit) {
const d = distance(p, guess);
const diff = d - dist;
if (Math.abs(diff) < 1e-7) candidates.push([...p]);
if (diff >= 0) p[1]--;
else p[2]++;
}
}
// As long there are multiple candidates, continue with a guess
while (candidates.length > 1) {
const candidates2 = [];
// These guesses are taking the first candidate as guess
guess = candidates[0];
dist = f(guess);
if (dist === 0) return guess; // lucky!
for (const p of candidates) {
let d = distance(p, guess);
let diff = d - dist;
if (Math.abs(diff) < 1e-7) candidates2.push(p);
}
candidates = candidates2;
}
return candidates[0]; // Don't call f as we are sure!
}
function blackbox() {
const secret = [rnd(), rnd(), rnd()];
console.log("Secret", JSON.stringify(secret));
let guessCount = 0;
const f = guess => {
guessCount++;
const dist = distance(secret, guess);
console.log("Submitted guess " + JSON.stringify(guess) + " is at distance " + dist);
return dist;
};
const report = (result) => {
console.log("Number of guesses: " + guessCount);
console.log("The provided result is " + (distance(secret, result) ? "not" : "") + "correct");
}
return {f, report};
}
// Example run
const {f, report} = blackbox();
const result = findPoint(f);
console.log("Algorithm says the secret point is: " + JSON.stringify(result));
report(result);
Each run will generate a new secret point. When running this thousands of times it turns out that there is 1/9 probability that the algorithm needs a third guess. In the other 8/9 cases, the algorithm needs two guesses.

One idea is as follows:
You pick an initial random point, and for each dimension, find the exact value. How? For the sake of symmetry, suppose that you desire to find x of the target point. Increase by one the x, and compute the distance of the new point from the target point. If it goes further, it means that you should move in the opposite direction. Hence, you can run a binary search and get the distance to find the exact x of the target point. Otherwise, it means that you are going in the right direction along X-axis. So, do a binary search between all points with the same y and z such that their x values can change from x+1 to 100. A more formal solution comes in the following (just a pseudo-code).
You should also ask about the complexity of this solution. As the dimension of the point is constant (3) and checking these conditions take a constant time, the complexity of number of calling getDifference function is O(log(n)). What is n here? the length of valid range for coordinates (here is 100).
1. p: (x,y,z) <- Pick a random coordinate
2. dist: (dist_x, dist_y, dist_z) <- getDifference(p, TargetPoint)
3. For each dimension, do the following (i can be 0 (x), 1 (y), 2 (3)):
4. if(dist == 0):
5. isFound[i] <- p[i]
6. continue
7. new_i <- p[i] + 1
8. new_point <- p
9. new_point[i] <- new_i
10. new_dist <- getDifference(new_point, pointToFound)
11. if(new_dist == 0):
12. isFound[i] <- new_point[i];
13. continue
14. if(new_dist[i] > dist[i]):
15. isFound[i] <- binary_search for range [0, p[i]-1] to find the exact value of the pointToFound in dimension i
15. continue
16. else:
17. isFound[i] <- binary_search for range [p[i] + 1, 100] to find the exact value of the pointToFound in dimension i
18. continue

Following method will work for coordinates with positive or negative real values as well.
Let's say you are searching for the coordinates of point P. As the first query point, use origin O. Let the distance to the origin O be |PO|. At this point, you know that P is on the surface of sphere
(P.x)^2 + (P.y)^2 + (P.z)^2 = |PO|^2 (1)
As the second query point, use Q = (|PO|, 0, 0). Not likely but if you find the distance |PQ| zero, Q is the point you are looking for. Otherwise, you get another sphere equation, and you know that P is on the surface of this sphere as well:
(P.x - |PO|)^2 + (P.y)^2 + (P.z)^2 = |PQ|^2 (2)
Now, if you subtract (1) from (2), you get
(P.x - |PO|)^2 - (P.x)^2 = |PQ|^2 - |PO|^2 (3)
Since the only unknown in this equation is P.x you can get its value:
P.x = (((-|PQ|^2 + |PO|^2) / |PO|) + |PO|)/2)
Following similar steps, you can get P.y with R = (0, |PO|, 0) and P.z with S = (0, 0, |PO|). So, by using four query points O, Q, R, and S you can get the coordinates of P.

Get a random number focused on center

Is it possible to get a random number between 1-100 and keep the results mainly within the 40-60 range? I mean, it will go out of that range rarely, but I want it to be mainly within that range... Is it possible with JavaScript/jQuery?
Right now I'm just using the basic Math.random() * 100 + 1.

The simplest way would be to generate two random numbers from 0-50 and add them together.
This gives a distribution biased towards 50, in the same way rolling two dice biases towards 7.
In fact, by using a larger number of "dice" (as #Falco suggests), you can make a closer approximation to a bell-curve:
function weightedRandom(max, numDice) {
let num = 0;
for (let i = 0; i < numDice; i++) {
num += Math.random() * (max/numDice);
}
return num;
}
JSFiddle: http://jsfiddle.net/797qhcza/1/

You have some good answers here that give specific solutions; let me describe for you the general solution. The problem is:
I have a source of more-or-less uniformly distributed random numbers between 0 and 1.
I wish to produce a sequence of random numbers that follow a different distribution.
The general solution to this problem is to work out the quantile function of your desired distribution, and then apply the quantile function to the output of your uniform source.
The quantile function is the inverse of the integral of your desired distribution function. The distribution function is the function where the area under a portion of the curve is equal to the probability that the randomly-chosen item will be in that portion.
I give an example of how to do so here:
http://ericlippert.com/2012/02/21/generating-random-non-uniform-data/
The code in there is in C#, but the principles apply to any language; it should be straightforward to adapt the solution to JavaScript.

Taking arrays of numbers, etc. isn't efficient. You should take a mapping which takes a random number between 0 to 100 and maps to the distribution you need. So in your case, you could take f(x)=-(1/25)x2+4x to get a distribution with the most values in the middle of your range.

I might do something like setup a "chance" for the number to be allowed to go "out of bounds". In this example, a 20% chance the number will be 1-100, otherwise, 40-60:
$(function () {
$('button').click(function () {
var outOfBoundsChance = .2;
var num = 0;
if (Math.random() <= outOfBoundsChance) {
num = getRandomInt(1, 100);
} else {
num = getRandomInt(40, 60);
}
$('#out').text(num);
});
function getRandomInt(min, max) {
return Math.floor(Math.random() * (max - min + 1)) + min;
}
});
<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.11.1/jquery.min.js"></script>
<button>Generate</button>
<div id="out"></div>
fiddle: http://jsfiddle.net/kbv39s9w/

I needed to solve this problem a few years ago and my solution was easier than any of the other answers.
I generated 3 randoms between the bounds and averaged them. This pulls the result towards the centre but leaves it completely possible to reach the extremities.

It looks stupid but you can use rand twice:
var choice = Math.random() * 3;
var result;
if (choice < 2){
result = Math.random() * 20 + 40; //you have 2/3 chance to go there
}
else {
result = Math.random() * 100 + 1;
}

Sure it is possible. Make a random 1-100. If the number is <30 then generate number in range 1-100 if not generate in range 40-60.

There is a lot of different ways to generate such random numbers. One way to do it is to compute the sum of multiple uniformly random numbers. How many random numbers you sum and what their range is will determine how the final distribution will look.
The more numbers you sum up, the more it will be biased towards the center. Using the sum of 1 random number was already proposed in your question, but as you notice is not biased towards the center of the range. Other answers have propose using the sum of 2 random numbers or the sum of 3 random numbers.
You can get even more bias towards the center of the range by taking the sum of more random numbers. At the extreme you could take the sum of 99 random numbers which each were either 0 or 1. That would be a binomial distribution. (Binomial distributions can in some sense be seen as the discrete version of normal distributions). This can still in theory cover the full range, but it has so much bias towards the center that you should never expect to see it reach the endpoints.
This approach means you can tweak just how much bias you want.

What about using something like this:
var loops = 10;
var tries = 10;
var div = $("#results").html(random());
function random() {
var values = "";
for(var i=0; i < loops; i++) {
var numTries = tries;
do {
var num = Math.floor((Math.random() * 100) + 1);
numTries--;
}
while((num < 40 || num >60) && numTries > 1)
values += num + "<br/>";
}
return values;
}
<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.11.1/jquery.min.js"></script>
<div id="results"></div>
The way I've coded it allows you to set a couple of variables:
loops = number of results
tries = number of times the function will try to get a number between 40-60 before it stops running through the while loop
Added bonus: It uses do while!!! Awesomeness at its best

You can write a function that maps random values between [0, 1) to [1, 100] according to weight. Consider this example:
Here, the value 0.95 maps to value between [61, 100].
In fact we have .05 / .1 = 0.5, which, when mapped to [61, 100], yields 81.
Here is the function:
/*
* Function that returns a function that maps random number to value according to map of probability
*/
function createDistributionFunction(data) {
// cache data + some pre-calculations
var cache = [];
var i;
for (i = 0; i < data.length; i++) {
cache[i] = {};
cache[i].valueMin = data[i].values[0];
cache[i].valueMax = data[i].values[1];
cache[i].rangeMin = i === 0 ? 0 : cache[i - 1].rangeMax;
cache[i].rangeMax = cache[i].rangeMin + data[i].weight;
}
return function(random) {
var value;
for (i = 0; i < cache.length; i++) {
// this maps random number to the bracket and the value inside that bracket
if (cache[i].rangeMin <= random && random < cache[i].rangeMax) {
value = (random - cache[i].rangeMin) / (cache[i].rangeMax - cache[i].rangeMin);
value *= cache[i].valueMax - cache[i].valueMin + 1;
value += cache[i].valueMin;
return Math.floor(value);
}
}
};
}
/*
* Example usage
*/
var distributionFunction = createDistributionFunction([
{ weight: 0.1, values: [1, 40] },
{ weight: 0.8, values: [41, 60] },
{ weight: 0.1, values: [61, 100] }
]);
/*
* Test the example and draw results using Google charts API
*/
function testAndDrawResult() {
var counts = [];
var i;
var value;
// run the function in a loop and count the number of occurrences of each value
for (i = 0; i < 10000; i++) {
value = distributionFunction(Math.random());
counts[value] = (counts[value] || 0) + 1;
}
// convert results to datatable and display
var data = new google.visualization.DataTable();
data.addColumn("number", "Value");
data.addColumn("number", "Count");
for (value = 0; value < counts.length; value++) {
if (counts[value] !== undefined) {
data.addRow([value, counts[value]]);
}
}
var chart = new google.visualization.ColumnChart(document.getElementById("chart"));
chart.draw(data);
}
google.load("visualization", "1", { packages: ["corechart"] });
google.setOnLoadCallback(testAndDrawResult);
<script src="https://www.google.com/jsapi"></script>
<div id="chart"></div>

Here's a weighted solution at 3/4 40-60 and 1/4 outside that range.
function weighted() {
var w = 4;
// number 1 to w
var r = Math.floor(Math.random() * w) + 1;
if (r === 1) { // 1/w goes to outside 40-60
var n = Math.floor(Math.random() * 80) + 1;
if (n >= 40 && n <= 60) n += 40;
return n
}
// w-1/w goes to 40-60 range.
return Math.floor(Math.random() * 21) + 40;
}
function test() {
var counts = [];
for (var i = 0; i < 2000; i++) {
var n = weighted();
if (!counts[n]) counts[n] = 0;
counts[n] ++;
}
var output = document.getElementById('output');
var o = "";
for (var i = 1; i <= 100; i++) {
o += i + " - " + (counts[i] | 0) + "\n";
}
output.innerHTML = o;
}
test();
<pre id="output"></pre>

Ok, so I decided to add another answer because I felt like my last answer, as well as most answers here, use some sort of half-statistical way of obtaining a bell-curve type result return. The code I provide below works the same way as when you roll a dice. Therefore, it is hardest to get 1 or 99, but easiest to get 50.
var loops = 10; //Number of numbers generated
var min = 1,
max = 50;
var div = $("#results").html(random());
function random() {
var values = "";
for (var i = 0; i < loops; i++) {
var one = generate();
var two = generate();
var ans = one + two - 1;
var num = values += ans + "<br/>";
}
return values;
}
function generate() {
return Math.floor((Math.random() * (max - min + 1)) + min);
}
<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.11.1/jquery.min.js"></script>
<div id="results"></div>

I'd recommend using the beta distribution to generate a number between 0-1, then scale it up. It's quite flexible and can create many different shapes of distributions.
Here's a quick and dirty sampler:
rbeta = function(alpha, beta) {
var a = 0
for(var i = 0; i < alpha; i++)
a -= Math.log(Math.random())
var b = 0
for(var i = 0; i < beta; i++)
b -= Math.log(Math.random())
return Math.ceil(100 * a / (a+b))
}

var randNum;
// generate random number from 1-5
var freq = Math.floor(Math.random() * (6 - 1) + 1);
// focus on 40-60 if the number is odd (1,3, or 5)
// this should happen %60 of the time
if (freq % 2){
randNum = Math.floor(Math.random() * (60 - 40) + 40);
}
else {
randNum = Math.floor(Math.random() * (100 - 1) + 1);
}

The best solution targeting this very problem is the one proposed by BlueRaja - Danny Pflughoeft but I think a somewhat faster and more general solution is also worth mentioning.
When I have to generate random numbers (strings, coordinate pairs, etc.) satisfying the two requirements of
The result set is quite small. (not larger than 16K numbers)
The result set is discreet. (like integer numbers only)
I usually start by creating an array of numbers (strings, coordinate pairs, etc.) fulfilling the requirement (In your case: an array of numbers containing the more probable ones multiple times.), then choose a random item of that array. This way, you only have to call the expensive random function once per item.

Distribution
5% for [ 0,39]
90% for [40,59]
5% for [60,99]
Solution
var f = Math.random();
if (f < 0.05) return random(0,39);
else if (f < 0.95) return random(40,59);
else return random(60,99);
Generic Solution
random_choose([series(0,39),series(40,59),series(60,99)],[0.05,0.90,0.05]);
function random_choose (collections,probabilities)
{
var acc = 0.00;
var r1 = Math.random();
var r2 = Math.random();
for (var i = 0; i < probabilities.length; i++)
{
acc += probabilities[i];
if (r1 < acc)
return collections[i][Math.floor(r2*collections[i].length)];
}
return (-1);
}
function series(min,max)
{
var i = min; var s = [];
while (s[s.length-1] < max) s[s.length]=i++;
return s;
}

You can use a helper random number to whether generate random numbers in 40-60 or 1-100:
// 90% of random numbers should be between 40 to 60.
var weight_percentage = 90;
var focuse_on_center = ( (Math.random() * 100) < weight_percentage );
if(focuse_on_center)
{
// generate a random number within the 40-60 range.
alert (40 + Math.random() * 20 + 1);
}
else
{
// generate a random number within the 1-100 range.
alert (Math.random() * 100 + 1);
}

If you can use the gaussian function, use it. This function returns normal number with average 0 and sigma 1.
95% of this number are within average +/- 2*sigma. Your average = 50, and sigma = 5 so
randomNumber = 50 + 5*gaussian()

The best way to do that is generating a random number that is distributed equally in a certain set of numbers, and then apply a projection function to the set between 0 and a 100 where the projection is more likely to hit the numbers you want.
Typically the mathematical way of achieving this is plotting a probability function of the numbers you want. We could use the bell curve, but let's for the sake of easier calculation just work with a flipped parabola.
Let's make a parabola such that its roots are at 0 and 100 without skewing it. We get the following equation:
f(x) = -(x-0)(x-100) = -x * (x-100) = -x^2 + 100x
Now, all the area under the curve between 0 and 100 is representative of our first set where we want the numbers generated. There, the generation is completely random. So, all we need to do is find the bounds of our first set.
The lower bound is, of course, 0. The upper bound is the integral of our function at 100, which is
F(x) = -x^3/3 + 50x^2
F(100) = 500,000/3 = 166,666.66666 (let's just use 166,666, because rounding up would make the target out of bounds)
So we know that we need to generate a number somewhere between 0 and 166,666. Then, we simply need to take that number and project it to our second set, which is between 0 and 100.
We know that the random number we generated is some integral of our parabola with an input x between 0 and 100. That means that we simply have to assume that the random number is the result of F(x), and solve for x.
In this case, F(x) is a cubic equation, and in the form F(x) = ax^3 + bx^2 + cx + d = 0, the following statements are true:
a = -1/3
b = 50
c = 0
d = -1 * (your random number)
Solving this for x yields you the actual random number your are looking for, which is guaranteed to be in the [0, 100] range and a much higher likelihood to be close to the center than the edges.

This answer is really good. But I would like to post implementation instructions (I'm not into JavaScript, so I hope you will understand) for different situation.
Assume you have ranges and weights for every range:
ranges - [1, 20], [21, 40], [41, 60], [61, 100]
weights - {1, 2, 100, 5}
Initial Static Information, could be cached:
Sum of all weights (108 in sample)
Range selection boundaries. It basically this formula: Boundary[n] = Boundary[n - 1] + weigh[n - 1] and Boundary[0] = 0. Sample has Boundary = {0, 1, 3, 103, 108}
Number generation:
Generate random number N from range [0, Sum of all weights).
for (i = 0; i < size(Boundary) && N > Boundary[i + 1]; ++i)
Take ith range and generate random number in that range.
Additional note for performance optimizations. Ranges don't have to be ordered neither ascending nor descending order, so for faster range look-up range that has highest weight should go first and one with lowest weight should go last.

Combinations Of Numbers To Equal One Total

In javascript I get two numbers let's call them x & y and an array of integers with random int's from 0 - 10 arrayints.
x is the number I'm trying to get by combining y with any of the numbers in arrayints.
for example: lets say x = 8 and y = 3 and arrayints consists of numbers arrayints(1,7,2,7,4,5)
so x could equal = y + 5
or
x = y + 1 + 4
All the values in x, y and arrayints will be random and always <= 10.
Please advise if more information is needed and everything will be in javascript or jquery no fuss as far as my code goes I will copy and paste but it will just be one blob of incromprehensible letters which are giving me an headache.
function makex(x,y) {
//this is how I get the array of random ints <=10
$("#div").children().each(function(n, i) {
var id = parseInt(this.id+"");
});
}

Here's a recursive solution that returns an array of the integers that add up to x, including y (or an empty array if it doesn't exist). If you want to exclude y, then feel free to make a wrapper for this.
function make(x, y, intOptions) {
var z = x - y
if (intOptions.indexOf(z) !== -1) {
return [y, z];
} else if (intOptions.length > 1){
var i = intOptions.length;
var ans;
while (i--) {
ans = make(z, intOptions[i], intOptions.slice(0, i))
if (ans.length) {
return [y].concat(ans);
}
}
}
return [];
}

Compute the closest point from a specific point

I create a panorama has a compass in the middle, the compass is pointing towards the top center of the image, initially.
Now I want to move the compass with respect to this point, since it is a 360 panorama, it creates an adjacent duplicate. So what I wanted is to point the compass to the point to whichever point is closer as you move from left to right or right to left.
Here is the what I have done so far, which doesn't behave like what I wanted.
So here is the code for that: https://gist.github.com/joeyhipolito/8678bf35dba7795de4d5
What I did is that I created two points:
points.push({
x: target.offset().left + (windowWidth) / 2,
y: target.offset().top
});
points.push({
x: (target.offset().left + (windowWidth) / 2) + (common.width / 2),
y: target.offset().top
});
And then try to calculate which points is closer to the reference by pythagorean theorem
var closestPoint = points[0];
var closestValue = Math.sqrt(Math.pow(points[0].x, 2) + Math.pow(points[0].y, 2));
for (var i = 1; i >= points.length; i++) {
var z = Math.sqrt(Math.pow(points[i].x, 2) + Math.pow(points[i].y, 2));
if(z < closestValue) {
closestPoint = points[i];
closestValue = z;
}
};
What do you think I am missing out?

You seem to have an issue with the control of your for loop. This loop:
for (var i = 1; i >= points.length; i++) {
};
(note the exit condition) does not run, because 1 (initial value of i) is immediately below the array's length, which is presumably at least 2. On the other hand, if the array length was at most 1, then this loop will never terminate, as i will keep increasing, and the i>=length statement remains true.
You probably want to change that exit condition to i<=length, then the minimum-finding logic should be fine.

Change
// ↓↓
for ( var i = 1; i >= points.length; i++ ) {
// ...
};
to
// ↓
for ( var i = 1; i < points.length; i++ ) {
// ...
};
Another way to do this is using Array.reduce(). It may not be as quick, but it may be more semantic:
function distFromOrigin( point ) {
return Math.sqrt( Math.pow( point, 2 ) + Math.pow( point, 2 ) );
}
var closestPoint = points.reduce(
function( closestPoint, currPoint, index, array ) {
var currDist = distFromOrigin( currPoint ),
closestDist = distFromOrigin( closestDist );
if ( currDist < closestDist ) {
return currPoint;
} else {
return closestPoint;
}
}
);

Different probability for ranges of random numbers

I'm looking for the best way of implementing random number generator, that will allow me to have control over probability from what range the generated number will be returned. To visualize what I'm trying to achieve I have a picture :
So to summarize :
Let's say that my range is 400. At the beginning I'd like to have 5% probability of getting number 0-20. But at some moment in time I'd like to have this probability increased up to 50%. Hope you get the idea.

Hmm, working on your original I had a pretty simple algorithm to generate ranges in an array in the appropriate proportion, then randomly select a range and generate a random number within that range. No doubt it can be optimised if necessary, but it works for me.
It looks like a lot of code, but 3/4 of it is comments, test data and function, the actual randomRange function is only 17 lines of code.
<script type="text/javascript">
function randomRange(dataArray) {
// Helper function
function getRandomInRange(s, f) {
return (Math.random() * (f-s+1) | 0) + s
}
// Generate new data array based on probability
var i, j = dataArray.length;
var oArray = [];
var o;
while (j--) {
o = dataArray[j];
// Make sure probability is an integer
for (i=0, iLen=o.probability|0; i<iLen; i++) {
oArray.push([o.rangeStart, o.rangeEnd]);
}
}
// Randomly select a range from new data array and
// generate a random number in that range
var oEnd = oArray.length;
var range = oArray[getRandomInRange(0, oArray.length - 1)];
return getRandomInRange(range[0], range[1]);
}
// Test data set. Probability just has to be
// representative, so 50/50 === 1/1
var dataArray = [
{
rangeStart: 0,
rangeEnd : 20,
probability: 1
},
{
rangeStart: 21,
rangeEnd : 400,
probability: 1
}
];
// Test function to show range and number is randomly
// selected for given probability
function testIt() {
var el0 = document.getElementById('div0');
var el1 = document.getElementById('div1');
function run() {
var n = randomRange(dataArray);
if (n <= 20) {
el0.innerHTML += '*';
} else {
el1.innerHTML += '*';
}
}
setInterval(run, 500);
}
</script>
<button onclick="testIt();">Generate random number</button>
<div>Numbers 0 - 20</div>
<div id="div0"></div>
<div>Numbers 21 - 400</div>
<div id="div1"></div>

It sounds to me like what you're looking for is a way to generate numbers on a normal (or Gaussian) distribution (take a look at the Wikipedia page if you don't know what that means).
The Box-Muller transformation can be used to generate pairs of normally distributed numbers.
Here is a c++ implementation of the polar form of the Box-Muller transformation that shouldn't be hard to translate to javascript.
// Return a real number from a normal (Gaussian) distribution with given
// mean and standard deviation by polar form of Box-Muller transformation
double x, y, r;
do
{
x = 2.0 * rand() - 1.0;
y = 2.0 * rand() - 1.0;
r = x * x + y * y;
}
while ( r >= 1.0 || r == 0.0 );
double s = sqrt( -2.0 * log(r) / r );
return mean + x * s * stddev;
Where mean is the mean of the normal distribution and stddev is the Standard Deviation of the distribution. This code is from a MersesenneTwister C++ class that I've been using recently that you can find on Rick Wagner's page. You can find some more useful information about the Box-Muller transformation on this page.