Algorithms: Number Theory Tutorials and Code Examples - Page 9

Sieve of Eratosthenes in JavaScript

The sieve identifies all primes up to a limit by marking multiples of smaller primes.

javascript

function sieve_count(n) {
    alg_require(Number.isInteger(n) && n >= -2147483648 && n <= 2147483647);
    alg_require(((n >= 0) && (n <= 1000000)));
    let composite = new Int32Array(alg_size(alg_add(n, 1)));
    let p = 2;
    let multiple = 0;
    let count = 0;
    while ((p <= Math.floor(n / p))) {
        if ((composite[p] == 0)) {
            multiple = alg_mul(p, p);
            while ((multiple <= n)) {
                composite[multiple] = 1;

Nov 15, 2026 javascript

Algorithms: Number Theory

Sieve of Eratosthenes in Java

The sieve identifies all primes up to a limit by marking multiples of smaller primes.

java

    static int sieve_count(int n) {
        alg_require(((n >= 0) && (n <= 1000000)));
        int[] composite = new int[alg_size(Math.addExact(n, 1))];
        int p = 2;
        int multiple = 0;
        int count = 0;
        while ((p <= (n / p))) {
            if ((composite[p] == 0)) {
                multiple = Math.multiplyExact(p, p);
                while ((multiple <= n)) {
                    composite[multiple] = 1;
                    multiple = Math.addExact(multiple, p);

Nov 15, 2026 Java

Algorithms: Number Theory

Iterative Factorial in PHP

Factorial counts permutations of n distinct objects.

php

function factorial(int $n): int {
    alg_require((($n >= 0) && ($n <= 1000000)));
    alg_require((($n >= 0) && ($n <= 12)));
    $result = 1;
    $i = 2;
    while (($i <= $n)) {
        $result = alg_mul($result, $i);
        $i = alg_add($i, 1);
    }
    return $result;
}

Nov 15, 2026 PHP

Algorithms: Number Theory

Iterative Factorial in C#

Factorial counts permutations of n distinct objects.

csharp

    static int factorial(int n) {
        checked {
            alg_require(((n >= 0) && (n <= 1000000)));
            alg_require(((n >= 0) && (n <= 12)));
            int result = 1;
            int i = 2;
            while ((i <= n)) {
                result = (result * i);
                i = (i + 1);
            }
            return result;
        }

Nov 15, 2026 csharp

Algorithms: Number Theory

Iterative Factorial in C++

Factorial counts permutations of n distinct objects.

cpp

int factorial(int n) {
    alg_require(((n >= 0) && (n <= 1000000)));
    alg_require(((n >= 0) && (n <= 12)));
    int result = 1;
    int i = 2;
    while ((i <= n)) {
        result = alg_mul(result, i);
        i = alg_add(i, 1);
    }
    return result;
}

Nov 15, 2026 C++