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feat: add prime sieve and generator #50

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feat: add prime sieve and generator #50

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57 changes: 57 additions & 0 deletions Maths/Prime.ts
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Original file line number Diff line number Diff line change
@@ -0,0 +1,57 @@
const assert = (condition: boolean, message: string) => {
if (!condition) throw Error(message);
};

/**
* https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes
* @param limit An integer _n_ > 1
* @returns All prime numbers from 2 through {@linkcode limit}
*/
export function sieveOfEratosthenes(limit: number): number[] {
assert(limit > 1, "limit should be an integer greater than 1");

@appgurueu appgurueu Oct 11, 2022

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Suggestion: Replace all of this - including the assert def. - with if (!Number.isInteger(limit) || limit <= 1) throw new Error("limit should be an integer greater than 1");.

assert(Number.isInteger(limit), "limit should be an integer greater than 1");

const maybePrime: boolean[] = new Array(limit + 1).fill(true);
for (let i = 2; i * i <= limit; i++) {
if (!maybePrime[i]) continue;
for (let j = i * i; j <= limit; j += i) {
maybePrime[j] = false;
}
}

return maybePrime
.reduce(
(primes, isPrime, number) => (isPrime ? [...primes, number] : primes),

@appgurueu appgurueu Oct 11, 2022 •
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This seems horribly inefficient (and also unreadable) to me: It always copies the entire primes array so far just to append a single value. This implies quadratic runtime in the number of primes. Please write it out imperatively:

const primes = [];
for (let i = 2; i < primes.length; i++) if (maybePrime[i]) primes.push(i);

which seems more concise, performant, and readable to me.

@zFl4wless zFl4wless Jul 9, 2023 •
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I'm currently finishing this PR. There is a little spelling mistake in your suggestion. In the condition of the for-loop you typed primes instead of maybePrime :)

@appgurueu appgurueu Jul 9, 2023

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I'm currently finishing this PR. There is a little spelling mistake in your suggestion. In the condition of the for-loop you typed primes instead of maybePrime :)

Indeed, that ought to be maybePrime.

[] as number[]
)
.slice(2);
}

/**
* Generator that yields primes.
*
* Inspired by https://gist.github.com/e-nikolov/cd94db0de2a6b70da144124ae93a6458
*/
export function* primeGenerator() {
type NumberGen = Generator<number, void, any>;

function* filter(input: NumberGen, prime: number): NumberGen {
while (true) {
const { done, value } = input.next();
if (done) break;
if (value % prime !== 0) yield value;
}
}

let chain: NumberGen = (function* () {
let i = 2;
while (true) yield i++;
})();

while (true) {
const { done, value } = chain.next();
if (done) break;
yield value;
chain = filter(chain, value);
}
}
35 changes: 35 additions & 0 deletions Maths/test/Prime.test.ts
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Original file line number Diff line number Diff line change
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import { primeGenerator, sieveOfEratosthenes } from "../Prime";

describe(sieveOfEratosthenes, () => {
test.each([-1, 0, 1, 2.123, 1337.80085])(
"should throw an error when given an invalid limit=%d",
(invalidLimit) => {
expect(() => sieveOfEratosthenes(invalidLimit)).toThrow();
}
);
test.each([
[2, [2]],
[3, [2, 3]],
[4, [2, 3]],
[5, [2, 3, 5]],
[6, [2, 3, 5]],
[7, [2, 3, 5, 7]],
[8, [2, 3, 5, 7]],
[9, [2, 3, 5, 7]],
])(
"should return the expected list of primes for limit=%i",
(limit, expected) => {
expect(sieveOfEratosthenes(limit)).toEqual(expected);
}
);
});

describe(primeGenerator, () => {
it("should generate prime numbers", () => {
const expectedPrimes = sieveOfEratosthenes(123);
const primeGen = primeGenerator();
for (const prime of expectedPrimes) {
expect(primeGen.next().value).toBe(prime);
}
});
});