AdventOfCode-ts-2023/6/6_1.ts

import { ExtractNumbers, LoadInput } from "../common.ts";

const tests = [
    "Time:      7  15   30",
    "Distance:  9  40  200",
];

const input = await LoadInput(6);

const races = ParseRaces(input);

races.forEach((race) => FindWinningTimes(race));

// Get our output as a "checksum"
// The checksum is the number of ways each race could be won multiplied by each other
console.log("The race checksum is", races.reduce((accumulator, race) => accumulator *= race.WinningTimes.length, 1));


/**
 * Parse the input to get a list of races
 *
 * @param {string[]} inputLines The two lines of input
 * @returns {Race[]} A list of race details
 */
function ParseRaces(inputLines: string[]): Race[] {
    const races: Race[] = [];

    const times = ExtractNumbers(inputLines.shift() || "");
    const distances = ExtractNumbers(inputLines.shift() || "");

    do {
        races.push({
            Duration: times.shift() || -1,
            RecordDistance: distances.shift() || -1,
            WinningTimes: [],
        });
    } while (times.length);

    return races;
}

/**
 * Find all possible winning times for a given race
 *
 * @param {Race} race The race to find winning times for
 */
function FindWinningTimes(race: Race) {
    // For our sake, flip the sign on the RecordDistance to create a floor for the parabola
    let [lowerBounds, upperBounds] = FindQuadraticRoots(-1, race.Duration, (race.RecordDistance * -1));

    // Exclusively bind the two bounds to integers
    // Add/subtract 0.01 to force integer roots to their next whole number
    lowerBounds = Math.ceil(lowerBounds + 0.01);
    upperBounds = Math.floor(upperBounds - 0.01);

    for(let i = lowerBounds; i <= upperBounds; i++) { race.WinningTimes.push(i); }
}

/**
 * Find the quadratic roots of a parabola
 *
 * @param a 
 * @param b 
 * @param c 
 * @returns The quadratic roots of a parabola
 */
function FindQuadraticRoots(a: number, b: number, c: number): number[] {
    if (a == 0) { return []; }

    // Solve for the discriminant -- sqrt(b^2 - 4ac)
    const discriminant = Math.sqrt(Math.pow(b, 2) - (4 * a * c));
    
    return [
        ((b * -1) + discriminant) / (2 * a),
        ((b * -1) - discriminant) / (2 * a),
    ];
}

/**
 * Information regarding a boat race
 */
type Race = {
    /** The total duration of the race in milliseconds */
    Duration: number,
    /** The current record holder for boat distance */
    RecordDistance: number,
    /** A list of times the boat's button could be held that would beat the RecordDistance */
    WinningTimes: number[]
};