Add solution for 2015, day 20

2015/20/README.md

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+# Day 20: Infinite Elves and Infinite Houses
+To keep the Elves busy, Santa has them deliver some presents by hand, door-to-door. He sends them down a street with infinite houses numbered sequentially: `1`, `2`, `3`, `4`, `5`, and so on.
+
+Each Elf is assigned a number, too, and delivers presents to houses based on that number:
+
+- The first Elf (number `1`) delivers presents to every house: `1`, `2`, `3`, `4`, `5`, ....
+- The second Elf (number `2`) delivers presents to every second house: `2`, `4`, `6`, `8`, `10`, ....
+- Elf number `3` delivers presents to every third house: `3`, `6`, `9`, `12`, `15`, ....
+
+There are infinitely many Elves, numbered starting with `1`. Each Elf delivers presents equal to **ten times** his or her number at each house.
+
+So, the first nine houses on the street end up like this:
+
+```
+House 1 got 10 presents.
+House 2 got 30 presents.
+House 3 got 40 presents.
+House 4 got 70 presents.
+House 5 got 60 presents.
+House 6 got 120 presents.
+House 7 got 80 presents.
+House 8 got 150 presents.
+House 9 got 130 presents.
+```
+
+The first house gets `10` presents: it is visited only by Elf `1`, which delivers `1 * 10 = 10` presents. The fourth house gets `70` presents, because it is visited by Elves `1`, `2`, and `4`, for a total of `10 + 20 + 40 = 70` presents.
+
+What is the lowest house number of the house to get at least as many presents as the number in your puzzle input?
+
+## Part Two
+The Elves decide they don't want to visit an infinite number of houses. Instead, each Elf will stop after delivering presents to `50` houses. To make up for it, they decide to deliver presents equal to **eleven times** their number at each house.
+
+With these changes, what is the new **lowest house number** of the house to get at least as many presents as the number in your puzzle input?

2015/20/helpers/find-factors.test.ts

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+import { describe, expect, it } from 'vitest';
+
+import { findFactors } from './find-factors.js';
+
+/* ========================================================================== */
+
+describe('Calculate factors', () => {
+	it('should return the factors for any given number', () => {
+		expect(findFactors(25)).toEqual([1, 5, 25]);
+		expect(findFactors(45)).toEqual([1, 3, 5, 9, 15, 45]);
+		expect(findFactors(53)).toEqual([1, 53]);
+		expect(findFactors(64)).toEqual([1, 2, 4, 8, 16, 32, 64]);
+		expect(findFactors(100)).toEqual([1, 2, 4, 5, 10, 20, 25, 50, 100]);
+		expect(findFactors(102)).toEqual([1, 2, 3, 6, 17, 34, 51, 102]);
+		expect(findFactors(120)).toEqual([1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120]);
+		expect(findFactors(12345)).toEqual([1, 3, 5, 15, 823, 2469, 4115, 12345]);
+		expect(findFactors(32766)).toEqual([
+			1, 2, 3, 6, 43, 86, 127, 129, 254, 258, 381, 762, 5461, 10922, 16383, 32766
+		]);
+		expect(findFactors(32767)).toEqual([1, 7, 31, 151, 217, 1057, 4681, 32767]);
+	});
+});

2015/20/helpers/find-factors.ts

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+/**
+ * Finds the factors for a given number.
+ *
+ * @param value The number for which to find the the factors.
+ *
+ * @returns An array with all the factors, sorted from low to high.
+ *
+ * @see {@link https://courses.lumenlearning.com/mathforliberalartscorequisite/chapter/finding-all-the-factors-of-a-number/}
+ */
+export function findFactors(value: number): number[] {
+	const factors: number[] = [];
+	// We need to stop when the divisor becomes smaller than the quotient. We
+	// could do that be checking the result in the for loop or we calculate when
+	// it is. By taking the square root we know the tipping point and since we
+	// only deal with integers we need to round it down.
+	// E.g.: When factoring 72 the tipping point is 8. This because the square
+	//       root of 72, rounded down, is 8.
+	//       - 72 / 8 = 9, the divisor (8) is more than the quotient (9)
+	//       - 72 / 9 = 8, the divisor (9) has become more than the quotient (8)
+	const limit = Math.floor(Math.sqrt(value));
+
+	// Starting by 1 keep processing all the integers until the limit has been
+	// processed too.
+	for (let divisor = 1; divisor <= limit; divisor++) {
+		// When the quotient is not a whole number, the divisor and quotient
+		// are not factors.
+		if (value % divisor !== 0) continue;
+
+		factors.push(divisor);
+
+		// When the divisor and quotient are the same, there is no need to add
+		// the quotient the list of factors it has already been added when the
+		// divisor was added to the list.
+		if (value / divisor !== divisor) {
+			factors.push(value / divisor);
+		}
+	}
+
+	return factors.sort((a, b) => a - b);
+}

2015/20/part-1.ts

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+import { findFactors } from './helpers/find-factors.js';
+
+/* ========================================================================== */
+
+async function solver(input: string): Promise<number> {
+	// Each elf gives 10 times the number of presents as his/her number. If we
+	// divide the input by 10 each elf gives 1 time the number of presents as
+	// his/her number and we a lower target to find a solution to.
+	const presentsGoal = Number(input) / 10;
+
+	// Iterate over the houses, start with 1 house and keep increasing till the
+	// first house with the specified number of presents has been found.
+	for (let houseNumber = 1; houseNumber < Infinity; houseNumber++) {
+		const visitingElves = findFactors(houseNumber);
+		const numberOfPresents = visitingElves.reduce((sum, count) => sum + count, 0);
+
+		if (numberOfPresents >= presentsGoal) return houseNumber;
+	}
+
+	return -1;
+}
+
+/* ========================================================================== */
+
+export default {
+	prompt: 'lowest house number to receive specified number of presents',
+	solver
+} satisfies Solution;

2015/20/part-2.ts

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+import { findFactors } from './helpers/find-factors.js';
+
+/* ========================================================================== */
+
+async function solver(input: string): Promise<number> {
+	const presentsGoal = Number(input);
+
+	// Iterate over the houses, start with 1 house and keep increasing till the
+	// first house with the specified number of presents has been found.
+	for (let houseNumber = 1; houseNumber < Infinity; houseNumber++) {
+		// Get the number of the elves that will make a stop at the
+		// current house. Only elves for whom it is at most their fifth visit
+		// will visit this house. Elves which have already visited 50 houses
+		// will sit this one out.
+		const visitingElves = findFactors(houseNumber).filter(elf => houseNumber / elf <= 50);
+
+		// Count the number of presents which will be presented to the house.
+		const numberOfPresents = visitingElves.reduce((sum, elf) => sum + (elf * 11), 0);
+
+		if (numberOfPresents >= presentsGoal) return houseNumber;
+	}
+
+	return -1;
+}
+
+/* ========================================================================== */
+
+export default {
+	prompt: 'lowest house number to receive specified number of presents',
+	solver
+} satisfies Solution;