AdventOfCode-ts-2023/6/6_2.ts

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

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

const input = await LoadInput(6);

const theRace = ParseRaces(input);

FindWinningTimes(theRace);

console.log("The amount of possible race wins is:", theRace.WinningTimesQuantity);


/**
 * 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 {
    // The quote unquote times of the race
    const times = ExtractNumbers(inputLines.shift() || "");
    // The quote unquote distances of the race
    const distances = ExtractNumbers(inputLines.shift() || "");
    
    return {
        Duration: Number(times.join("")),
        RecordDistance: Number(distances.join("")),
        WinningTimesQuantity: -1,
    };
}

/**
 * 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);

    race.WinningTimesQuantity = upperBounds - lowerBounds + 1;
}

/**
 * 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,
    /** The amount of ways you hold the button in order to beat the RecordDistance */
    WinningTimesQuantity: number
};