Related
I am trying to write an algorithm to calculate the sum of prime numbers less than or equal to a given number argument. Here is my code:
function sumPrimes(num) {
// populates the array with numbers uptp the given num
let prime = [], i = 2;
while (prime.indexOf(num) < 0){
prime.push(i)
i++;
}
// filters the array leaving only the prime numbers and sums all prime numbers
let result = prime
.filter(function (a){
if(a === 2 ||a === 3 || a === 5 || a === 7){
return a
} else {
return a % 2 > 0 && a % 3 > 0 && a % 5 > 0 && a % 7 > 0
}}).reduce((a,b) => a+b)
console.log(result)
return result
}
sumPrimes(977); //outputs 108789 instead of 73156
My filter function check if a given number divisible simultaneously by 2, 3, 5, 7 returns a remainder greater than zero if so such number is a prime number. However, when the supplied argument is 977, it falls apart and outputs the wrong sum. Can anyone figure out what is going on here?
As per my comment: your check for prime is faulty. Just because a number cannot be divided by 2, 3, 5 or 7 does not mean it is prime. You can simply recycle the prime checking logic from this answer: Number prime test in JavaScript, and optimize your loop so that you only perform iteration once.
You start a for loop from 2, the smallest prime, increment it until it reaches your target number. In the for loop, check the number if it is prime: if it, add it to the sum.
The advantage of this approach is that:
You don't store an arbitrary large array of prime numbers in the prime array, which is eventually reduced by summing it up. Of course, this is under the assumption that you don't need the primes for anything else.
You don't need to perform several iterations, compared to your old code, where you perform repeated iterations in: (1) the while loop to generate all numbers between 2 and your target number, (2) the filter check for prime, and (3) the reduce method
// Adapted from: https://stackoverflow.com/questions/40200089/number-prime-test-in-javascript
function isPrime(num) {
for (let i = 2, s = Math.sqrt(num); i <= s; i++)
if (num % i === 0) return false;
return num > 1;
}
function sumPrimes(num) {
let sum = 0;
for (let n = 2; n <= num; n++) {
if (isPrime(n)) {
sum += n;
}
}
console.log(sum);
return sum;
}
sumPrimes(977); // Outputs 73156 as expected
To check whether a number is prime it should not be divisible by any other prime. So while your logic is kind of correct, you need to expand your array of primes constantly. This could be achieves like this:
const primeArray = (n) => {
var p = [2];
if (n<2) return [];
if (n===2) return [2];
for (let i=3;i<=n;i+=2) if (p.every(x=>i%x)) p.push(i);
return p;
}
We start with the first prime and then we will check every second number starting from 3, as all even numbers are divisible by 2. While iterating through i+2, we simply check whether i is divisible by any already identified primes. If this is not the case (i%x), we expand the array of primes by i.
Here is another scalable minimalist and performance optimized version of the Erastostenes sieve with a cap for testing only up to the square root of the current number:
function primeArr(n){
for (var primes=[],i=1,j=0,cap=2; ++i<=n;){
if (i>2 && i==cap) cap=primes[j]*primes[j++];
if (primes.slice(0,j-1).every(p=>i%p)) primes.push(i)
}
return primes;
}
let pa=primeArr(977);
console.log("sum:", pa.reduce((a,c)=>a+=c));
console.log("all primes:", pa.join(" "));
Complete and fast solution via prime-lib:
import {generatePrimes, stopOnValue} from 'prime-lib';
const i = stopOnValue(generatePrimes(), 977);
let sum = 0;
for (let a of i) {
sum += a;
}
console.log(sum); //=> 73156
well this is problem number 12 on projecteuler website:
The sequence of triangle numbers is generated by adding the natural numbers. So the 7th triangle number would be 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28. The first ten terms would be:
1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...
Let us list the factors of the first seven triangle numbers:
1: 1
3: 1,3
6: 1,2,3,6
10: 1,2,5,10
15: 1,3,5,15
21: 1,3,7,21
28: 1,2,4,7,14,28
We can see that 28 is the first triangle number to have over five divisors.
What is the value of the first triangle number to have over five hundred divisors?
and here's my code (I'm new to Javascript)
let num = 1;
let add= 1;
let divisors = [];
while (divisors.length < 500){
divisors = []
for(let i = 1; i <= num; i++){
if(num % i == 0){
divisors.push(i);
}
}
add ++;
num += add;
}
console.log(num - add)
this code run fine when I change the while loop condition to 300 or less.
and this code running on Intel i7 Q740 1.75GHz.
when I try it nothing shows up on console and my question is that's because of my CPU and lack of power or my code has issue? I wait about 20 mins and still nothing as result.
This code is not very efficient as #Vasil Dininski pointed out but you won't reach the max Integer you just have to wait a while for your program to calculate.
I would recommend to optimize your code e.g. by writing a simple function which returns your number of divisors for your current number.
This could look similar to this:
function numberOfDivisors(num) {
var numOfDivisors = 0;
var sqrtOfNum = Math.sqrt(num);
for(var i = 1; i <= sqrtOfNum; i++) {
if(num % i == 0) {
numOfDivisors += 2;
}
}
// if your number is a perfect square you have to reduce it by one
if(sqrtOfNum * sqrtOfNum == num) {
numOfDivisors--;
}
return numOfDivisors;
}
Then you could use this method in your while loop like this:
var maxNumOfDivisors = 500;
var num = 0;
var i = 1;
while(numberOfDivisors(num) < maxNumOfDivisors) {
num += i;
i++;
}
which would return you the correct triangular number.
Please also note that triangular numbers start at 0 which is why my num is 0.
As you might have noticed, this algorithm might be a bit brute-force. A better one would be combine a few things. Let's assume the number we're looking for is "n":
Find all prime numbers in the range [1, square root of n]. You will
be iterating over n, so the sieve of
eratosthenes
will help in terms of efficiency (you can memoize primes you've already found)
Given that any number can be expressed as a prime number to some power, multiplied by a prime number to some power, etc. you can find all the combinations of those primes to a power, which are divisors of n.
This would be a more efficient, albeit a more complicated way to find them. You can take a look at this quora answer for more details: https://www.quora.com/What-is-an-efficient-algorithm-to-find-divisors-of-any-number
If my calculation is not wrong, you add one more to each next divisor from previous divisor and you get final result.
let prev = 0;
for(let i=0; i < 500; i++) {
prev = prev + i;
}
console.log("AA ", prev);
how much 0 at the end of 1*2*3*....*100?
for example1 zero 10,2 zero at the end of 10100,0 zero at 10001
The interviewer gave me 3 mins.
front-end develope intern was the job i went for.
i tried to solve it in JavaScript,it was wrong because 100! is so big for a JS variable.Here is my code.
var factorial = function(x){
if(x<0){
return error;
}else if (x ===1 || x ===0) {
return x;
}else if (x > 1) {
return (factorial(x - 1) * x);
}
}
var counter = 0;
var countZero = function(x){
while((x%10) === 0){
counter = counter + 1;
x = x/10;
}
return counter;
}
console.log(countZero(factorial(100)));
Any ideas?I solved it without computer in a pure-math way,but i want to know how to solve it in JS.
A number gets a zero at the end of it if the number has 10 as a factor. For instance, 10 is a factor of 50, 120, and 1234567890. So you need to find out how many times 10 is a factor in the expansion of 100!.
But since 5×2 = 10, we need to account for all the products of 5 and 2. Looking at the factors in the above expansion, there are many more numbers that are multiples of 2 (2, 4, 6, 8, 10, 12, 14,...) than are multiples of 5 (5, 10, 15,...). That is, if we take all the numbers with 5 as a factor, We'll have way more than enough even numbers to pair with them to get factors of 10 (and another trailing zero on my factorial). So to find the number of times 10 is a factor, all we really need to worry about is how many times 5 is a factor in all of the numbers between 1 and 100
Okay, how many multiples of 5 are there in the numbers from 1 to 100? There's 5, 10, 15, 20, 25,...
Let's do this the short way: 100 is the closest multiple of 5 below or equal to 100, and 100 ÷ 5 = 20, so there are twenty multiples of 5 between 1 and 100.
But wait: 25 is 5×5, so each multiple of 25 has an extra factor of 5 that we need to account for. How many multiples of 25 are between 1 and 100? Since 100 ÷ 25 = 4, there are four multiples of 25 between 1 and 100.
Adding these, We get 20 + 4 = 24 trailing zeroes in 100!
It was more of a math question that a Javascript specific question and you don't need to calculate the actual factorial to find the number of trailing zeros
More details here
Zeros at the end of a number result from 2s and 5s being multiplied together. So, one way to count up the total number of zeros would be to figure out how many total 2s and 5s go into 100! - don't calculate that number, just add up the number of factors - and then return whichever count (2s or 5s) is smallest.
let twos = 0;
let fives = 0;
for (let i = 1; i <= 100; i++) {
let num = i;
while (num % 2 === 0) {
twos++;
num /= 2;
}
while (num % 5 === 0) {
fives++;
num /= 5;
}
}
console.log(Math.min(twos, fives));
For the numbers less or equal than 1000000000 as your case here you could use the following algorithm :
function numberOfZeros(n) {
if (n == 0) return 0;
return parseInt(n * (n - 1) / (4 * n));
}
console.log(numberOfZeros(100));
So I am determining which is a prime number and which isn't, but I am just not understanding how it ends up with the correct output.
So the first starts at 2 and loops by 1 to 100. Easy.
But the second starts at 0, and loops by y + itself, this would make sense, but in determining the primes, it should mess up, atleast I thought
it's like: 1+3 = 4 or 2 + 4 = 6 or 3 + 5 = 8
and that works, but what happens to let's say the 15? that isn't a prime number.
How is numbers like that sorted in the loop?
var prim = [];
var notprim = [];
for(var x = 2; x <= 100; x++){
if(!notprim[x]){
prim.push(x);
for(var y = 0; y <= 100; y = y+x){
notprim[y] = true;
document.write(y);
}
}
}
You have an Array notprim that you can imagine as [undefined × 100], and !!undefined === false, i.e. undefined is falsy
If for some number n you have notprim[n] falsy, you assume it means n must be a prime number and add it to another Array, prim
Then you set all multiples of n to be truthy in notprim, i.e. if n is 3, you set notprim[n * x] = true;, i.e. 0, 3, 6, 9, 12, 15, etc
You then look for the next falsy index in notprim to start again
The reason the first loop starts at 2 is because 2 is the first prime number, starting from 1 or 0 would cause the assumption that "notprim[n] falsy means n is a prime number" to fail
Great, but what about the other loop? Well, one way of going through n * x is to add n to itself x times. When you're thinking of it this way, you can then limit how high you go without knowing a maximum multiplier in advance by looking at the running total, for example in a for loop
for (t = 0; t <= 100; t = t + n)
// t ∈ nℤ, 0 <= t <= 100
but what happens to lets say the 15?
When you've found the prime number 3, you then flag all multiples of 3 to be excluded from your search for primes. 15 is a multiple of 3 so gets flagged as not a prime. Hence your if (!notprim[x]) does not pass
You can reduce the number of iterations this code needs by excluding 0 and x from the second for loop; i.e. begin from the index y = 2 * x
I'm trying to generate a random number that must have a fixed length of exactly 6 digits.
I don't know if JavaScript has given below would ever create a number less than 6 digits?
Math.floor((Math.random()*1000000)+1);
I found this question and answer on StackOverflow here. But, it's unclear.
EDIT: I ran the above code a bunch of times, and Yes, it frequently creates numbers less than 6 digits. Is there a quick/fast way to make sure it's always exactly 6 digits?
console.log(Math.floor(100000 + Math.random() * 900000));
Will always create a number of 6 digits and it ensures the first digit will never be 0. The code in your question will create a number of less than 6 digits.
Only fully reliable answer that offers full randomness, without loss. The other ones prior to this answer all looses out depending on how many characters you want. The more you want, the more they lose randomness.
They achieve it by limiting the amount of numbers possible preceding the fixed length.
So for instance, a random number of fixed length 2 would be 10 - 99. For 3, 100 - 999. For 4, 1000 - 9999. For 5 10000 - 99999 and so on. As can be seen by the pattern, it suggests 10% loss of randomness because numbers prior to that are not possible. Why?
For really large numbers ( 18, 24, 48 ) 10% is still a lot of numbers to loose out on.
function generate(n) {
var add = 1, max = 12 - add; // 12 is the min safe number Math.random() can generate without it starting to pad the end with zeros.
if ( n > max ) {
return generate(max) + generate(n - max);
}
max = Math.pow(10, n+add);
var min = max/10; // Math.pow(10, n) basically
var number = Math.floor( Math.random() * (max - min + 1) ) + min;
return ("" + number).substring(add);
}
The generator allows for ~infinite length without lossy precision and with minimal performance cost.
Example:
generate(2)
"03"
generate(2)
"72"
generate(2)
"20"
generate(3)
"301"
generate(3)
"436"
generate(3)
"015"
As you can see, even the zero are included initially which is an additional 10% loss just that, besides the fact that numbers prior to 10^n are not possible.
That is now a total of 20%.
Also, the other options have an upper limit on how many characters you can actually generate.
Example with cost:
var start = new Date(); var num = generate(1000); console.log('Time: ', new Date() - start, 'ms for', num)
Logs:
Time: 0 ms for 7884381040581542028523049580942716270617684062141718855897876833390671831652069714762698108211737288889182869856548142946579393971303478191296939612816492205372814129483213770914444439430297923875275475120712223308258993696422444618241506074080831777597175223850085606310877065533844577763231043780302367695330451000357920496047212646138908106805663879875404784849990477942580056343258756712280958474020627842245866908290819748829427029211991533809630060693336825924167793796369987750553539230834216505824880709596544701685608502486365633618424746636614437646240783649056696052311741095247677377387232206206230001648953246132624571185908487227730250573902216708727944082363775298758556612347564746106354407311558683595834088577220946790036272364740219788470832285646664462382109714500242379237782088931632873392735450875490295512846026376692233811845787949465417190308589695423418373731970944293954443996348633968914665773009376928939207861596826457540403314327582156399232931348229798533882278769760
More hardcore:
generate(100000).length === 100000 -> true
I would go with this solution:
Math.floor(Math.random() * 899999 + 100000)
More generally, generating a random integer with fixed length can be done using Math.pow:
var randomFixedInteger = function (length) {
return Math.floor(Math.pow(10, length-1) + Math.random() * (Math.pow(10, length) - Math.pow(10, length-1) - 1));
}
To answer the question: randomFixedInteger(6);
You can use the below code to generate a random number that will always be 6 digits:
Math.random().toString().substr(2, 6)
Hope this works for everyone :)
Briefly how this works is Math.random() generates a random number between 0 and 1 which we convert to a string and using .toString() and take a 6 digit sample from said string using .substr() with the parameters 2, 6 to start the sample from the 2nd char and continue it for 6 characters.
This can be used for any length number.
If you want to do more reading on this here are some links to the docs to save you some googling:
Math.random(): https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Math/random
.toString(): https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Object/toString
.substr(): https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/String/substr
short with arbitrary precision
below code ALWAYS generate string with n digits - solution in snippet use it
[...Array(n)].map(_=>Math.random()*10|0).join``
let gen = n=> [...Array(n)].map(_=>Math.random()*10|0).join``
// TEST: generate 6 digit number
// first number can't be zero - so we generate it separatley
let sixDigitStr = (1+Math.random()*9|0) + gen(5)
console.log( +(sixDigitStr) ) // + convert to num
100000 + Math.floor(Math.random() * 900000);
will give a number from 100000 to 999999 (inclusive).
Based on link you've provided, right answer should be
Math.floor(Math.random()*899999+100000);
Math.random() returns float between 0 and 1, so minimum number will be 100000, max - 999999. Exactly 6 digits, as you wanted :)
Here is my function I use. n - string length you want to generate
function generateRandomNumber(n) {
return Math.floor(Math.random() * (9 * Math.pow(10, n - 1))) + Math.pow(10, n - 1);
}
This is another random number generator that i use often, it also prevent the first digit from been zero(0)
function randomNumber(length) {
var text = "";
var possible = "123456789";
for (var i = 0; i < length; i++) {
var sup = Math.floor(Math.random() * possible.length);
text += i > 0 && sup == i ? "0" : possible.charAt(sup);
}
return Number(text);
}
let length = 6;
("0".repeat(length) + Math.floor(Math.random() * 10 ** length)).slice(-length);
Math.random() - Returns floating point number between 0 - 1
10 ** length - Multiply it by the length so we can get 1 - 6 length numbers with decimals
Math.floor() - Returns above number to integer(Largest integer to the given number).
What if we get less than 6 digits number?
That's why you have to append 0s with it.
"0".repeat() repeats the given string which is 0
So we may get more than 6 digits right?
That's why we have to use "".slice() method. It returns the array within given indexes. By giving minus values, it counts from the last element.
I created the below function to generate random number of fix length:
function getRandomNum(length) {
var randomNum =
(Math.pow(10,length).toString().slice(length-1) +
Math.floor((Math.random()*Math.pow(10,length))+1).toString()).slice(-length);
return randomNum;
}
This will basically add 0's at the beginning to make the length of the number as required.
npm install --save randomatic
var randomize = require('randomatic');
randomize(pattern, length, options);
Example:
To generate a 10-character randomized string using all available characters:
randomize('*', 10);
//=> 'x2_^-5_T[$'
randomize('Aa0!', 10);
//=> 'LV3u~BSGhw'
a: Lowercase alpha characters (abcdefghijklmnopqrstuvwxyz'
A: Uppercase alpha characters (ABCDEFGHIJKLMNOPQRSTUVWXYZ')
0: Numeric characters (0123456789')
!: Special characters (~!##$%^&()_+-={}[];\',.)
*: All characters (all of the above combined)
?: Custom characters (pass a string of custom characters to the options)
NPM repo
I use randojs to make the randomness simpler and more readable. you can pick a random int between 100000 and 999999 like this with randojs:
console.log(rando(100000, 999999));
<script src="https://randojs.com/1.0.0.js"></script>
const generate = n => String(Math.ceil(Math.random() * 10**n)).padStart(n, '0')
// n being the length of the random number.
Use a parseInt() or Number() on the result if you want an integer.
If you don't want the first integer to be a 0 then you could use padEnd() instead of padStart().
I was thinking about the same today and then go with the solution.
var generateOTP = function(otpLength=6) {
let baseNumber = Math.pow(10, otpLength -1 );
let number = Math.floor(Math.random()*baseNumber);
/*
Check if number have 0 as first digit
*/
if (number < baseNumber) {
number += baseNumber;
}
return number;
};
Let me know if it has any bug. Thanks.
"To Generate Random Number Using JS"
console.log(
Math.floor(Math.random() * 1000000)
);
<!DOCTYPE html>
<html>
<body>
<h2>JavaScript Math.random()</h2>
<p id="demo"></p>
</body>
</html>
You can use this module https://www.npmjs.com/package/uid, it generates variable length unique id
uid(10) => "hbswt489ts"
uid() => "rhvtfnt" Defaults to 7
Or you can have a look at this module https://www.npmjs.com/package/shortid
const shortid = require('shortid');
console.log(shortid.generate());
// PPBqWA9
Hope it works for you :)
var number = Math.floor(Math.random() * 9000000000) + 1000000000;
console.log(number);
This can be simplest way and reliable one.
For the length of 6, recursiveness doesn't matter a lot.
function random(len) {
let result = Math.floor(Math.random() * Math.pow(10, len));
return (result.toString().length < len) ? random(len) : result;
}
console.log(random(6));
In case you also want the first digit to be able to be 0 this is my solution:
const getRange = (size, start = 0) => Array(size).fill(0).map((_, i) => i + start);
const getRandomDigit = () => Math.floor(Math.random() * 10);
const generateVerificationCode = () => getRange(6).map(getRandomDigit).join('');
console.log(generateVerificationCode())
generate a random number that must have a fixed length of exactly 6 digits:
("000000"+Math.floor((Math.random()*1000000)+1)).slice(-6)
Generate a random number that will be 6 digits:
console.log(Math.floor(Math.random() * 900000));
Result = 500229
Generate a random number that will be 4 digits:
console.log(Math.floor(Math.random() * 9000));
Result = 8751
This code provides nearly full randomness:
function generator() {
const ran = () => [1, 2, 3, 4, 5, 6, 7, 8, 9, 0].sort((x, z) => {
ren = Math.random();
if (ren == 0.5) return 0;
return ren > 0.5 ? 1 : -1
})
return Array(6).fill(null).map(x => ran()[(Math.random() * 9).toFixed()]).join('')
}
console.log(generator())
This code provides complete randomness:
function generator() {
const ran1 = () => [1, 2, 3, 4, 5, 6, 7, 8, 9, 0].sort((x, z) => {
ren = Math.random();
if (ren == 0.5) return 0;
return ren > 0.5 ? 1 : -1
})
const ran2 = () => ran1().sort((x, z) => {
ren = Math.random();
if (ren == 0.5) return 0;
return ren > 0.5 ? 1 : -1
})
return Array(6).fill(null).map(x => ran2()[(Math.random() * 9).toFixed()]).join('')
}
console.log(generator())
parseInt(Math.random().toString().slice(2,Math.min(length+2, 18)), 10); // 18 -> due to max digits in Math.random
Update:
This method has few flaws:
- Sometimes the number of digits might be lesser if its left padded with zeroes.