I want to split 10 into an array of 4 random numbers, but neither can be 0 or higher than 4. For example [1,2,3,4], [1,4,4,1] or [4,2,3,1].
I think it's an easy question, but for some reason I can't think of how to do this. If someone has some instruction that would be very helpful!
Edit:
This is the code I have now, but I generates also a total number under 10:
let formation = [];
let total = 0;
for (let i = 0; i < 4; i ++) {
if (total < 9) {
formation[i] = Math.floor(Math.random() * 4) + 1;
} else {
formation[i] = 1;
}
}
You could create all possible combinations and pick a random array.
function get4() {
function iter(temp) {
return function (v) {
var t = temp.concat(v);
if (t.length === 4) {
if (t.reduce(add) === 10) {
result.push(t);
}
return;
}
values.forEach(iter(t));
};
}
const
add = (a, b) => a + b,
values = [1, 2, 3, 4],
result = [];
values.forEach(iter([]));
return result;
}
console.log(get4().map(a => a.join(' ')));
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An algorithm for getting random values without a list of all possible combinations
It works by using a factor for the random value and an offset, based on the actual sum, index, minimum sum which is needed for the next index, and the maximum sum.
The offset is usually the minimum sum, or the greater value of the difference of sum and maximum sum. For getting the factor, three values are taken for the minimum for multiplying the random value.
The table illustrates all possible values of the sum and the needed iterations, based on a given value and the iteration for getting all values.
At the beginning the sum is the value for distribution in small parts. The result is the second block with a rest sum of 14 ... 10, because it is possible to take a value of 1 ... 5. The third round follows the same rules. At the end, the leftover sum is taken as offset for the value.
An example with 1, ..., 5 values and 5 elements with a sum of 15 and all possibilities:
min: 1
max: 5
length: 5
sum: 15
smin = (length - index - 1) * min
smax = (length - index - 1) * max
offset = Math.max(sum - smax, min)
random = 1 + Math.min(sum - offset, max - offset, sum - smin - min)
index sum sum min sum max random offset
------- ------- ------- ------- ------- -------
_ 0 15 4 20 5 1
1 14 3 15 5 1
1 13 3 15 5 1
1 12 3 15 5 1
1 11 3 15 5 1
_ 1 10 3 15 5 1
2 13 2 10 3 3
2 12 2 10 4 2
2 11 2 10 5 1
2 10 2 10 5 1
2 9 2 10 5 1
2 8 2 10 5 1
2 7 2 10 5 1
2 6 2 10 4 1
_ 2 5 2 10 3 1
3 10 1 5 1 5
3 9 1 5 2 4
3 8 1 5 3 3
3 7 1 5 4 2
3 6 1 5 5 1
3 5 1 5 4 1
3 4 1 5 3 1
3 3 1 5 2 1
_ 3 2 1 5 1 1
4 5 0 0 1 5
4 4 0 0 1 4
4 3 0 0 1 3
4 2 0 0 1 2
4 1 0 0 1 1
The example code takes the target 1, ..., 4 with a length of 4 parts and a sum of 10.
function getRandom(min, max, length, sum) {
return Array.from(
{ length },
(_, i) => {
var smin = (length - i - 1) * min,
smax = (length - i - 1) * max,
offset = Math.max(sum - smax, min),
random = 1 + Math.min(sum - offset, max - offset, sum - smin - min),
value = Math.floor(Math.random() * random + offset);
sum -= value;
return value;
}
);
}
console.log(Array.from({ length: 10 }, _ => getRandom(1, 4, 4, 10).join(' ')));
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The simplest solution is brute force.
Make a while loop to nest your calculations in
In the loop, create an empty array and fill it with random values until length is reached
Check if the sum of the array is your desired value, and if it is then break the loop
The above should run until you have a result.
Two things worth considering though.
Your can easily test if a solution is at all possible by calculating, that length-of-array times minimum-value isn't more than the sum and length-of-array times maximum-value isn't less than the sum.
A loop based on random conditions could potentially run forever, so a maximum amount of iterations might be desirable.
Both of these points are considered in the snippet below:
function randomNumber(max, min) {
while (true) {
var r = Math.round(Math.random() * max);
if (r >= min) {
return r;
}
}
}
function splitXintoYComponentsBetweenMaxAndMin(numberToSplit, numberOfSplits, maxValue, minValue, onUpdate) {
if (minValue === void 0) {
minValue = 1;
}
//Test that a result can exist
if (maxValue * numberOfSplits < numberToSplit || minValue * numberOfSplits > numberToSplit) {
return new Promise(function(resolve, reject) {
resolve(false);
});
}
//Create returner array
var arr = [];
var accumulator = 0;
while (arr.length < numberOfSplits) {
var val = randomNumber(Math.floor(numberToSplit / numberOfSplits), minValue);
accumulator += val;
arr.push(val);
}
return new Promise(function(resolve, reject) {
function runTest() {
var d = Date.now();
var localMaxValue = Math.min(maxValue, Math.ceil((numberToSplit - accumulator) / 4));
//Combination loop
while (accumulator < numberToSplit && Date.now() - d < 17) {
var index = Math.round(Math.random() * (arr.length - 1));
if (arr[index] >= maxValue) {
continue;
}
var r = randomNumber(localMaxValue, minValue);
while (arr[index] + r > maxValue || accumulator + r > numberToSplit) {
if (Date.now() - d >= 17) {
break;
}
r = randomNumber(localMaxValue, minValue);
}
if (arr[index] + r > maxValue || accumulator + r > numberToSplit) {
continue;
}
arr[index] += r;
accumulator += r;
}
if (accumulator < numberToSplit) {
if (onUpdate !== void 0) {
onUpdate(arr);
}
requestAnimationFrame(runTest);
} else {
resolve(arr);
}
}
runTest();
});
}
//TEST
var table = document.body.appendChild(document.createElement('table'));
table.innerHTML = "<thead><tr><th>Number to split</th><th>Number of splits</th><th>Max value</th><th>Min value</th><th>Run</th></tr></thead>" +
"<tbody><tr><th><input id=\"number-to-split\" value=\"10\" type=\"number\" min=\"1\"/></th><th><input id=\"number-of-splits\" value=\"4\" type=\"number\" min=\"1\"/></th><th><input id=\"max-value\" type=\"number\" min=\"1\" value=\"4\"/></th><th><input id=\"min-value\" type=\"number\" min=\"1\" value=\"1\"/></th><th><input id=\"run\" type=\"button\" value=\"Run\"/></th></tr></tbody>";
var output = document.body.appendChild(document.createElement('pre'));
output.style.overflowX = "scroll";
document.getElementById("run").onclick = function() {
splitXintoYComponentsBetweenMaxAndMin(parseInt(document.getElementById("number-to-split").value, 10), parseInt(document.getElementById("number-of-splits").value, 10), parseInt(document.getElementById("max-value").value, 10), parseInt(document.getElementById("min-value").value, 10))
.then(function(data) {
if (data !== false) {
output.textContent += data.join("\t") + '\n';
} else {
output.textContent += 'Invalid data\n';
}
});
};
EDIT 1 - Big calculations
Using requestAnimationFrame and Promises the code can now execute asynchronously, which allows for longer calculation time without bothering the user.
I also made the random function scale with the remaining range, greatly reducing the amount of calculations needed for big numbers.
A litte late to the show, but I found this a fun task to think about so here you go. My approach does not need to create all partitions, it also does not rely on pure luck of finding a random match, it is compact and it should be unbiased.
It works efficiently even when large values are used, as long as max is not too limiting.
const len = 4;
const total = 10;
const max = 4;
let arr = new Array(len);
let sum = 0;
do {
// get some random numbers
for (let i = 0; i < len; i++) {
arr[i] = Math.random();
}
// get the total of the random numbers
sum = arr.reduce((acc, val) => acc + val, 0);
// compute the scale to use on the numbers
const scale = (total - len) / sum;
// scale the array
arr = arr.map(val => Math.min(max, Math.round(val * scale) + 1));
// re-compute the sum
sum = arr.reduce((acc, val) => acc + val, 0);
// loop if the sum is not exactly the expected total due to scale rounding effects
} while (sum - total);
console.log(arr);
Basically you need the partitions (See https://en.wikipedia.org/wiki/Partition_(number_theory)) of 10 and apply your conditions on the resulting set.
// Partition generator taken from
// https://gist.github.com/k-hamada/8aa85ac9b334fb89ac4f
function* partitions(n) {
if (n <= 0) throw new Error('positive integer only');
yield [n];
var x = new Array(n);
x[0] = n;
for (var i = 1; i < n; i++) x[i] = 1;
var m = 0, h = 0, r, t;
while (x[0] != 1) {
if (x[h] == 2) {
m += 1;
x[h] = 1;
h -= 1;
} else {
r = x[h] - 1;
x[h] = r;
t = m - h + 1;
while (t >= r) {
h += 1;
x[h] = r;
t -= r;
}
m = h + (t !== 0 ? 1 : 0);
if (t > 1) {
h += 1;
x[h] = t;
}
}
yield x.slice(0, m + 1);
}
}
results = [];
// Get all possible partitions for your number
for (var partition of partitions(10)) {
// Apply your conditions (must be 4 numbers, none of them greater than 4)
if(partition.length != 4 || partition.some((x) => x > 4)) continue;
results.push(partition);
}
console.log(results);
Given that:
In a collection of n positive numbers that sum up to S, at least one of them will be less than S divided by n (S/n)
and that you want a result set of exactly 4 numbers,
you could use the following algorithm:
Get a random number from range [1, floor(S/n)], in this case floor(10/4) = 2, so get a random number in the range of [1,2]. Lets mark it as x1.
Get a random number from range [1, floor((S - x1)/(n - 1))]. Lets mark it as x2.
Get a random number from range [1, floor((S - x1 - x2)/(n - 2))].
Continue until you get x(n-1).
Get the last number by doing S - x1 - x2 .... - x(n-1).
Finally, extend the above algorithm with a condition to limit the upper limit of the random numbers.
In n steps, you can get a collection.
function getRandomInt(min, max) {
return Math.floor(Math.random() * (max - min + 1)) + min;
}
function getRandomCollection(min, max, length, sum) {
var collection = [];
var leftSum = sum - (min - 1);
for(var i = 0; i < length - 1; i++) {
var number = getRandomInt(min, Math.min(Math.ceil(leftSum/(length - i)), max));
leftSum -= number;
collection.push(number);
}
leftSum += min - 1;
while(leftSum > max) {
var randomIndex = Math.floor(Math.random() * collection.length);
if(collection[randomIndex] < max) {
collection[randomIndex]++;
leftSum--;
}
}
collection.push(leftSum);
return collection;
}
console.log(getRandomCollection(1, 4, 4, 10).join(' + ') + ' = 10');
console.log(getRandomCollection(3, 20, 10, 100).join(' + ') + ' = 100');
Reference
My answer using the same algorithm for another question
Quick and simple but biased and nondeterministically terminating
function partition(sum, len, min, max) {
const a = Array(len).fill(min)
while (a.reduce((acc,val)=>acc+val) < sum) {
const i = Math.random()*len|0
if (a[i] < max) a[i]++
}
return a
}
console.log(Array(10).fill().map(_=>partition(10, 4, 1, 4).join(' ')))
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The while loop can loop forever with an infinitesimal probability. To prevent this, you can keep another array of "valid indexes" and delete keys of it when the value reaches max.
this calculates a random number from 1 to 4
wrap it on a function to your needs to generate the arrays
Math.floor(Math.random() * 4) + 1
var randomNumber = Math.floor(Math.random() * 4) + 1 ;
console.log(randomNumber);
It was too easy.
var values = null;
while(true) {
var currentSum = 0;
var expectedSum = 10;
values = [];
while(expectedSum !== currentSum) {
//var value = Math.floor(Math.random() * 9) + 1;
var value = Math.floor(Math.random() * 4) + 1;
if(value + currentSum > expectedSum) {
continue;
}
currentSum += value;
values.push(value);
}
if(values.length === 4) {
break;
} else {
console.log('false iteration')
}
}
console.log(values);
var x = 0;
var y = 1;
var z;
fib[0] = 0;
fib[1] = 1;
for (i = 2; i <= 10; i++) {
alert(x + y);
fib[i] = x + y;
x = y;
z = y;
}
I'm trying to get to generate a simple Fibonacci Sequence but there no output.
Can anybody let me know what's wrong?
You have never declared fib to be an array. Use var fib = []; to solve this.
Also, you're never modifying the y variable, neither using it.
The code below makes more sense, plus, it doesn't create unused variables:
var i;
var fib = [0, 1]; // Initialize array!
for (i = 2; i <= 10; i++) {
// Next fibonacci number = previous + one before previous
// Translated to JavaScript:
fib[i] = fib[i - 2] + fib[i - 1];
console.log(fib[i]);
}
According to the Interview Cake question, the sequence goes 0,1,1,2,3,5,8,13,21. If this is the case, this solution works and is recursive without the use of arrays.
function fibonacci(n) {
return n < 1 ? 0
: n <= 2 ? 1
: fibonacci(n - 1) + fibonacci(n - 2)
}
console.log(fibonacci(4))
Think of it like this.
fibonacci(4) .--------> 2 + 1 = 3
| / |
'--> fibonacci(3) + fibonacci(2)
| ^
| '----------- 2 = 1 + 1 <----------.
1st step -> | ^ |
| | |
'----> fibonacci(2) -' + fibonacci(1)-'
Take note, this solution is not very efficient though.
Yet another answer would be to use es6 generator functions.
function* fib() {
var current = a = b = 1;
yield 1;
while (true) {
current = b;
yield current;
b = a + b;
a = current;
}
}
sequence = fib();
sequence.next(); // 1
sequence.next(); // 1
sequence.next(); // 2
// ...
Here's a simple function to iterate the Fibonacci sequence into an array using arguments in the for function more than the body of the loop:
fib = function(numMax){
for(var fibArray = [0,1], i=0,j=1,k=0; k<numMax;i=j,j=x,k++ ){
x=i+j;
fibArray.push(x);
}
console.log(fibArray);
}
fib(10)
[ 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89 ]
You should've declared the fib variable to be an array in the first place (such as var fib = [] or var fib = new Array()) and I think you're a bit confused about the algorithm.
If you use an array to store the fibonacci sequence, you do not need the other auxiliar variables (x,y,z) :
var fib = [0, 1];
for(var i=fib.length; i<10; i++) {
fib[i] = fib[i-2] + fib[i-1];
}
console.log(fib);
Click for the demo
You should consider the recursive method too (note that this is an optimised version) :
function fib(n, undefined){
if(fib.cache[n] === undefined){
fib.cache[n] = fib(n-1) + fib(n-2);
}
return fib.cache[n];
}
fib.cache = [0, 1, 1];
and then, after you call the fibonacci function, you have all the sequence in the fib.cache field :
fib(1000);
console.log(fib.cache);
The golden ration "phi" ^ n / sqrt(5) is asymptotic to the fibonacci of n, if we round that value up, we indeed get the fibonacci value.
function fib(n) {
let phi = (1 + Math.sqrt(5))/2;
let asymp = Math.pow(phi, n) / Math.sqrt(5);
return Math.round(asymp);
}
fib(1000); // 4.346655768693734e+208 in just a few milliseconds
This runs faster on large numbers compared to the recursion based solutions.
You're not assigning a value to z, so what do you expect y=z; to do? Likewise you're never actually reading from the array. It looks like you're trying a combination of two different approaches here... try getting rid of the array entirely, and just use:
// Initialization of x and y as before
for (i = 2; i <= 10; i++)
{
alert(x + y);
z = x + y;
x = y;
y = z;
}
EDIT: The OP changed the code after I'd added this answer. Originally the last line of the loop was y = z; - and that makes sense if you've initialized z as per my code.
If the array is required later, then obviously that needs to be populated still - but otherwise, the code I've given should be fine.
Another easy way to achieve this:
function fibonacciGenerator(n) {
// declare the array starting with the first 2 values of the fibonacci sequence
// starting at array index 1, and push current index + previous index to the array
for (var fibonacci = [0, 1], i = 2; i < n; i++)
fibonacci.push(fibonacci[i-1] + fibonacci[i - 2])
return fibonacci
}
console.log( fibonacciGenerator(10) )
function fib(n) {
if (n <= 1) {
return n;
} else {
return fib(n - 1) + fib(n - 2);
}
}
fib(10); // returns 55
fibonacci 1,000 ... 10,000 ... 100,000
Some answers run into issues when trying to calculate large fibonacci numbers. Others are approximating numbers using phi. This answer will show you how to calculate a precise series of large fibonacci numbers without running into limitations set by JavaScript's floating point implementation.
Below, we generate the first 1,000 fibonacci numbers in a few milliseconds. Later, we'll do 100,000!
const { fromInt, toString, add } =
Bignum
const bigfib = function* (n = 0)
{
let a = fromInt (0)
let b = fromInt (1)
let _
while (n >= 0) {
yield toString (a)
_ = a
a = b
b = add (b, _)
n = n - 1
}
}
console.time ('bigfib')
const seq = Array.from (bigfib (1000))
console.timeEnd ('bigfib')
// 25 ms
console.log (seq.length)
// 1001
console.log (seq)
// [ 0, 1, 1, 2, 3, ... 995 more elements ]
Let's see the 1,000th fibonacci number
console.log (seq [1000])
// 43466557686937456435688527675040625802564660517371780402481729089536555417949051890403879840079255169295922593080322634775209689623239873322471161642996440906533187938298969649928516003704476137795166849228875
10,000
This solution scales quite nicely. We can calculate the first 10,000 fibonacci numbers in under 2 seconds. At this point in the sequence, the numbers are over 2,000 digits long – way beyond the capacity of JavaScript's floating point numbers. Still, our result includes precise values without making approximations.
console.time ('bigfib')
const seq = Array.from (bigfib (10000))
console.timeEnd ('bigfib')
// 1877 ms
console.log (seq.length)
// 10001
console.log (seq [10000] .length)
// 2090
console.log (seq [10000])
// 3364476487 ... 2070 more digits ... 9947366875
Of course all of that magic takes place in Bignum, which we will share now. To get an intuition for how we will design Bignum, recall how you added big numbers using pen and paper as a child...
1259601512351095520986368
+ 50695640938240596831104
---------------------------
?
You add each column, right to left, and when a column overflows into the double digits, remembering to carry the 1 over to the next column...
... <-001
1259601512351095520986368
+ 50695640938240596831104
---------------------------
... <-472
Above, we can see that if we had two 10-digit numbers, it would take approximately 30 simple additions (3 per column) to compute the answer. This is how we will design Bignum to work
const Bignum =
{ fromInt: (n = 0) =>
n < 10
? [ n ]
: [ n % 10, ...Bignum.fromInt (n / 10 >> 0) ]
, fromString: (s = "0") =>
Array.from (s, Number) .reverse ()
, toString: (b) =>
Array.from (b) .reverse () .join ('')
, add: (b1, b2) =>
{
const len = Math.max (b1.length, b2.length)
let answer = []
let carry = 0
for (let i = 0; i < len; i = i + 1) {
const x = b1[i] || 0
const y = b2[i] || 0
const sum = x + y + carry
answer.push (sum % 10)
carry = sum / 10 >> 0
}
if (carry > 0) answer.push (carry)
return answer
}
}
We'll run a quick test to verify our example above
const x =
fromString ('1259601512351095520986368')
const y =
fromString ('50695640938240596831104')
console.log (toString (add (x,y)))
// 1310297153289336117817472
And now a complete program demonstration. Expand it to calculate the precise 10,000th fibonacci number in your own browser! Note, the result is the same as the answer provided by wolfram alpha
const Bignum =
{ fromInt: (n = 0) =>
n < 10
? [ n ]
: [ n % 10, ...Bignum.fromInt (n / 10 >> 0) ]
, fromString: (s = "0") =>
Array.from (s, Number) .reverse ()
, toString: (b) =>
Array.from (b) .reverse () .join ('')
, add: (b1, b2) =>
{
const len = Math.max (b1.length, b2.length)
let answer = []
let carry = 0
for (let i = 0; i < len; i = i + 1) {
const x = b1[i] || 0
const y = b2[i] || 0
const sum = x + y + carry
answer.push (sum % 10)
carry = sum / 10 >> 0
}
if (carry > 0) answer.push (carry)
return answer
}
}
const { fromInt, toString, add } =
Bignum
const bigfib = function* (n = 0)
{
let a = fromInt (0)
let b = fromInt (1)
let _
while (n >= 0) {
yield toString (a)
_ = a
a = b
b = add (b, _)
n = n - 1
}
}
console.time ('bigfib')
const seq = Array.from (bigfib (10000))
console.timeEnd ('bigfib')
// 1877 ms
console.log (seq.length)
// 10001
console.log (seq [10000] .length)
// 2090
console.log (seq [10000])
// 3364476487 ... 2070 more digits ... 9947366875
100,000
I was just curious how far this little script could go. It seems like the only limitation is just time and memory. Below, we calculate the first 100,000 fibonacci numbers without approximation. Numbers at this point in the sequence are over 20,000 digits long, wow! It takes 3.18 minutes to complete but the result still matches the answer from wolfram alpha
console.time ('bigfib')
const seq = Array.from (bigfib (100000))
console.timeEnd ('bigfib')
// 191078 ms
console.log (seq .length)
// 100001
console.log (seq [100000] .length)
// 20899
console.log (seq [100000])
// 2597406934 ... 20879 more digits ... 3428746875
BigInt
JavaScript now has native support for BigInt. This allows for calculating huge integers very quickly -
function* fib (n)
{ let a = 0n
let b = 1n
let _
while (n >= 0) {
yield a.toString()
_ = a
a = b
b = b + _
n = n - 1
}
}
console.time("fib(1000)")
const result = Array.from(fib(1000))
console.timeEnd("fib(1000)")
document.body.textContent = JSON.stringify(result, null, 2)
body {
font-family: monospace;
white-space: pre;
}
I like the fact that there are so many ways to create a fibonacci sequence in JS. I will try to reproduce a few of them. The goal is to output a sequence to console (like {n: 6, fiboNum: 8})
Good ol' closure
// The IIFE form is purposefully omitted. See below.
const fiboGenClosure = () => {
let [a, b] = [0, 1];
let n = 0;
return (fiboNum = a) => {
[a, b] = [b, a + b];
return {
n: n++,
fiboNum: fiboNum
};
};
}
// Gets the sequence until given nth number. Always returns a new copy of the main function, so it is possible to generate multiple independent sequences.
const generateFiboClosure = n => {
const newSequence = fiboGenClosure();
for (let i = 0; i <= n; i++) {
console.log(newSequence());
}
}
generateFiboClosure(21);
Fancy ES6 generator
Similar to the closure pattern above, using the advantages of generator function and for..of loop.
// The 'n' argument is a substitute for index.
function* fiboGen(n = 0) {
let [a, b] = [0, 1];
while (true) {
yield [a, n++];
[a, b] = [b, a + b];
}
}
// Also gives a new sequence every time is invoked.
const generateFibonacci = n => {
const iterator = fiboGen();
for (let [value, index] of iterator) {
console.log({
n: index,
fiboNum: value
});
if (index >= n) break;
}
}
generateFibonacci(21);
Tail call recursion
This one is a little tricky, because, now in late 2018, TC optimization is still an issue. But honestly – if you don't use any smart tricks to allow the default JS engine to use a really big numbers, it will get dizzy and claims that the next fibonacci number is "Infinity" by iteration 1477. The stack would probably overflow somewhere around iteration 10 000 (vastly depends on browser, memory etc…). Could be probably padded by try… catch block or check if "Infinity" was reached.
const fibonacciRTC = (n, i = 0, a = 0, b = 1) => {
console.log({
n: i,
fibonacci: a
});
if (n === 0) return;
return fibonacciRTC(--n, ++i, b, a + b);
}
fibonacciRTC(21)
It can be written as a one-liner, if we throe away the console.log thing and simply return a number:
const fibonacciRTC2 = (n, a = 0, b = 1) => n === 0 ? a : fibonacciRTC2(n - 1, b, a + b);
console.log(fibonacciRTC2(21))
Important note!
As I found out reading this mathIsFun article, the fibonacci sequence is valid for negative numbers as well! I tried to implement that in the recursive tail call form above like that:
const fibonacciRTC3 = (n, a = 0, b = 1, sign = n >= 0 ? 1 : -1) => {
if (n === 0) return a * sign;
return fibonacciRTC3(n - sign, b, a + b, sign);
}
console.log(fibonacciRTC3(8)); // 21
console.log(fibonacciRTC3(-8)); // -21
There is also a generalization of Binet's formula for negative integers:
static float phi = (1.0f + sqrt(5.0f)) / 2.0f;
int generalized_binet_fib(int n) {
return round( (pow(phi, n) - cos(n * M_PI) * pow(phi, -n)) / sqrt(5.0f) );
}
...
for(int i = -10; i < 10; ++i)
printf("%i ", generalized_binet_fib(i));
A quick way to get ~75
ty #geeves for the catch, I replaced Math.floor for Math.round which seems to get it up to 76 where floating point issues come into play :/ ...
either way, I wouldn't want to be using recursion up and until that point.
/**
* Binet Fibonacci number formula for determining
* sequence values
* #param {int} pos - the position in sequence to lookup
* #returns {int} the Fibonacci value of sequence #pos
*/
var test = [0,1,1,2,3,5,8,13,21,34,55,89,144,233,377,610,987,1597,2584,4181,6765,10946,17711,28657,46368,75025,121393,196418,317811,514229,832040,1346269,2178309,3524578,5702887,9227465,14930352,24157817,39088169,63245986,102334155,165580141,267914296,433494437,701408733,1134903170,1836311903,2971215073,4807526976,7778742049,12586269025,20365011074,32951280099,53316291173,86267571272,139583862445,225851433717,365435296162,591286729879,956722026041,1548008755920,2504730781961,4052739537881,6557470319842,10610209857723,17167680177565,27777890035288,44945570212853,72723460248141,117669030460994,190392490709135,308061521170129,498454011879264,806515533049393,1304969544928657,2111485077978050,3416454622906707,5527939700884757,8944394323791464,14472334024676221,23416728348467685,37889062373143906,61305790721611591,99194853094755497,160500643816367088,259695496911122585,420196140727489673,679891637638612258,1100087778366101931,1779979416004714189,2880067194370816120,4660046610375530309,7540113804746346429,12200160415121876738,19740274219868223167,31940434634990099905,51680708854858323072,83621143489848422977,135301852344706746049,218922995834555169026];
var fib = function (pos) {
return Math.round((Math.pow( 1 + Math.sqrt(5), pos)
- Math.pow( 1 - Math.sqrt(5), pos))
/ (Math.pow(2, pos) * Math.sqrt(5)));
};
/* This is only for the test */
var max = test.length,
i = 0,
frag = document.createDocumentFragment(),
_div = document.createElement('div'),
_text = document.createTextNode(''),
div,
text,
err,
num;
for ( ; i < max; i++) {
div = _div.cloneNode();
text = _text.cloneNode();
num = fib(i);
if (num !== test[i]) {
err = i + ' == ' + test[i] + '; got ' + num;
div.style.color = 'red';
}
text.nodeValue = i + ': ' + num;
div.appendChild(text);
frag.appendChild(div);
}
document.body.appendChild(frag);
You can get some cache to speedup the algorithm...
var tools = {
fibonacci : function(n) {
var cache = {};
// optional seed cache
cache[2] = 1;
cache[3] = 2;
cache[4] = 3;
cache[5] = 5;
cache[6] = 8;
return execute(n);
function execute(n) {
// special cases 0 or 1
if (n < 2) return n;
var a = n - 1;
var b = n - 2;
if(!cache[a]) cache[a] = execute(a);
if(!cache[b]) cache[b] = execute(b);
return cache[a] + cache[b];
}
}
};
If using ES2015
const fib = (n, prev = 0, current = 1) => n
? fib(--n, current, prev + current)
: prev + current
console.log( fib(10) )
If you need to build a list of fibonacci numbers easily you can use array destructuring assignment to ease your pain:
function fibonacci(n) {
let fibList = [];
let [a, b] = [0, 1]; // array destructuring to ease your pain
while (a < n) {
fibList.push(a);
[a, b] = [b, a + b]; // less pain, more gain
}
return fibList;
}
console.log(fibonacci(10)); // prints [0, 1, 1, 2, 3, 5, 8]
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN" "http://www.w3.org/TR/html4/strict.dtd">
<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
<title>fibonacci series</title>
<script type="text/javascript">
function generateseries(){
var fno = document.getElementById("firstno").value;
var sno = document.getElementById("secondno").value;
var a = parseInt(fno);
var result = new Array();
result[0] = a;
var b = ++fno;
var c = b;
while (b <= sno) {
result.push(c);
document.getElementById("maindiv").innerHTML = "Fibonacci Series between "+fno+ " and " +sno+ " is " +result;
c = a + b;
a = b;
b = c;
}
}
function numeric(evt){
var theEvent = evt || window.event;
var key = theEvent.keyCode || theEvent.which;
key = String.fromCharCode(key);
var regex = /[0-9]|\./;
if (!regex.test(key)) {
theEvent.returnValue = false;
if (theEvent.preventDefault)
theEvent.preventDefault();
}
}
</script>
<h1 align="center">Fibonacci Series</h1>
</head>
<body>
<div id="resultdiv" align="center">
<input type="text" name="firstno" id="firstno" onkeypress="numeric(event)"><br>
<input type="text" name="secondno" id="secondno" onkeypress="numeric(event)"><br>
<input type="button" id="result" value="Result" onclick="generateseries();">
<div id="maindiv"></div>
</div>
</body>
</html>
I know this is a bit of an old question, but I realized that many of the answers here are utilizing for loops rather than while loops.
Sometimes, while loops are faster than for loops, so I figured I'd contribute some code that runs the Fibonacci sequence in a while loop as well! Use whatever you find suitable to your needs.
function fib(length) {
var fibArr = [],
i = 0,
j = 1;
fibArr.push(i);
fibArr.push(j);
while (fibArr.length <= length) {
fibArr.push(fibArr[j] + fibArr[i]);
j++;
i++;
}
return fibArr;
};
fib(15);
sparkida, found an issue with your method. If you check position 10, it returns 54 and causes all subsequent values to be incorrect. You can see this appearing here: http://jsfiddle.net/createanaccount/cdrgyzdz/5/
(function() {
function fib(n) {
var root5 = Math.sqrt(5);
var val1 = (1 + root5) / 2;
var val2 = 1 - val1;
var value = (Math.pow(val1, n) - Math.pow(val2, n)) / root5;
return Math.floor(value + 0.5);
}
for (var i = 0; i < 100; i++) {
document.getElementById("sequence").innerHTML += (0 < i ? ", " : "") + fib(i);
}
}());
<div id="sequence">
</div>
Here are examples how to write fibonacci using recursion, generator and reduce.
'use strict'
//------------- using recursion ------------
function fibonacciRecursion(n) {
return (n < 2) ? n : fibonacciRecursion(n - 2) + fibonacciRecursion(n - 1)
}
// usage
for (let i = 0; i < 10; i++) {
console.log(fibonacciRecursion(i))
}
//-------------- using generator -----------------
function* fibonacciGenerator() {
let a = 1,
b = 0
while (true) {
yield b;
[a, b] = [b, a + b]
}
}
// usage
const gen = fibonacciGenerator()
for (let i = 0; i < 10; i++) {
console.log(gen.next().value)
}
//------------- using reduce ---------------------
function fibonacciReduce(n) {
return new Array(n).fill(0)
.reduce((prev, curr) => ([prev[0], prev[1]] = [prev[1], prev[0] + prev[1]], prev), [0, 1])[0]
}
// usage
for (let i = 0; i < 10; i++) {
console.log(fibonacciReduce(i))
}
I just would like to contribute with a tail call optimized version by ES6. It's quite simple;
var fibonacci = (n, f = 0, s = 1) => n === 0 ? f : fibonacci(--n, s, f + s);
console.log(fibonacci(12));
There is no need for slow loops, generators or recursive functions (with or without caching). Here is a fast one-liner using Array and reduce.
ECMAScript 6:
var fibonacci=(n)=>Array(n).fill().reduce((a,b,c)=>a.concat(c<2?c:a[c-1]+a[c-2]),[])
ECMAScript 5:
function fibonacci(n){
return Array.apply(null,{length:n}).reduce(function(a,b,c){return a.concat((c<2)?c:a[c-1]+a[c-2]);},[]);
}
Tested in Chrome 59 (Windows 10):
fibonacci(10); // 0 ms -> (10) [0, 1, 1, 2, 3, 5, 8, 13, 21, 34]
JavaScript can handle numbers up to 1476 before reaching Infinity.
fibonacci(1476); // 11ms -> (1476) [0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ...]
Another implementation, while recursive is very fast and uses single inline function. It hits the javascript 64-bit number precision limit, starting 80th sequence (as do all other algorithms):
For example if you want the 78th term (78 goes in the last parenthesis):
(function (n,i,p,r){p=(p||0)+r||1;i=i?i+1:1;return i<=n?arguments.callee(n,i,r,p):r}(78));
will return: 8944394323791464
This is backwards compatible all the way to ECMASCRIPT4 - I tested it with IE7 and it works!
This script will take a number as parameter, that you want your Fibonacci sequence to go.
function calculateFib(num) {
var fibArray = [];
var counter = 0;
if (fibArray.length == 0) {
fibArray.push(
counter
);
counter++
};
fibArray.push(fibArray[fibArray.length - 1] + counter);
do {
var lastIndex = fibArray[fibArray.length - 1];
var snLastIndex = fibArray[fibArray.length - 2];
if (lastIndex + snLastIndex < num) {
fibArray.push(lastIndex + snLastIndex);
}
} while (lastIndex + snLastIndex < num);
return fibArray;
};
This is what I came up with
//fibonacci numbers
//0,1,1,2,3,5,8,13,21,34,55,89
//print out the first ten fibonacci numbers
'use strict';
function printFobonacciNumbers(n) {
var firstNumber = 0,
secondNumber = 1,
fibNumbers = [];
if (n <= 0) {
return fibNumbers;
}
if (n === 1) {
return fibNumbers.push(firstNumber);
}
//if we are here,we should have at least two numbers in the array
fibNumbers[0] = firstNumber;
fibNumbers[1] = secondNumber;
for (var i = 2; i <= n; i++) {
fibNumbers[i] = fibNumbers[(i - 1)] + fibNumbers[(i - 2)];
}
return fibNumbers;
}
var result = printFobonacciNumbers(10);
if (result) {
for (var i = 0; i < result.length; i++) {
console.log(result[i]);
}
}
Beginner, not too elegant, but shows the basic steps and deductions in JavaScript
/* Array Four Million Numbers */
var j = [];
var x = [1,2];
var even = [];
for (var i = 1;i<4000001;i++){
j.push(i);
}
// Array Even Million
i = 1;
while (i<4000001){
var k = j[i] + j[i-1];
j[i + 1] = k;
if (k < 4000001){
x.push(k);
}
i++;
}
var total = 0;
for (w in x){
if (x[w] %2 === 0){
even.push(x[w]);
}
}
for (num in even){
total += even[num];
}
console.log(x);
console.log(even);
console.log(total);
My 2 cents:
function fibonacci(num) {
return Array.apply(null, Array(num)).reduce(function(acc, curr, idx) {
return idx > 2 ? acc.concat(acc[idx-1] + acc[idx-2]) : acc;
}, [0, 1, 1]);
}
console.log(fibonacci(10));
I would like to add some more code as an answer :), Its never too late to code :P
function fibonacciRecursive(a, b, counter, len) {
if (counter <= len) {
console.log(a);
fibonacciRecursive(b, a + b, counter + 1, len);
}
}
fibonacciRecursive(0, 1, 1, 20);
Result
0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181
function fibo(count) {
//when count is 0, just return
if (!count) return;
//Push 0 as the first element into an array
var fibArr = [0];
//when count is 1, just print and return
if (count === 1) {
console.log(fibArr);
return;
}
//Now push 1 as the next element to the same array
fibArr.push(1);
//Start the iteration from 2 to the count
for(var i = 2, len = count; i < len; i++) {
//Addition of previous and one before previous
fibArr.push(fibArr[i-1] + fibArr[i-2]);
}
//outputs the final fibonacci series
console.log(fibArr);
}
Whatever count we need, we can give it to above fibo method and get the fibonacci series upto the count.
fibo(20); //output: [0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181]
Fibonacci (one-liner)
function fibonacci(n) {
return (n <= 1) ? n : fibonacci(n - 1) + fibonacci(n - 2);
}
Fibonacci (recursive)
function fibonacci(number) {
// n <= 1
if (number <= 0) {
return n;
} else {
// f(n) = f(n-1) + f(n-2)
return fibonacci(number - 1) + fibonacci(number - 2);
}
};
console.log('f(14) = ' + fibonacci(14)); // 377
Fibonacci (iterative)
function fibonacci(number) {
// n < 2
if (number <= 0) {
return number ;
} else {
var n = 2; // n = 2
var fn_1 = 0; // f(n-2), if n=2
var fn_2 = 1; // f(n-1), if n=2
// n >= 2
while (n <= number) {
var aa = fn_2; // f(n-1)
var fn = fn_1 + fn_2; // f(n)
// Preparation for next loop
fn_1 = aa;
fn_2 = fn;
n++;
}
return fn_2;
}
};
console.log('f(14) = ' + fibonacci(14)); // 377
Fibonacci (with Tail Call Optimization)
function fibonacci(number) {
if (number <= 1) {
return number;
}
function recursion(length, originalLength, previous, next) {
if (length === originalLength)
return previous + next;
return recursion(length + 1, originalLength, next, previous + next);
}
return recursion(1, number - 1, 0, 1);
}
console.log(`f(14) = ${fibonacci(14)}`); // 377