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ok, lcm was the missing piece
+23
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+23
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2023/day08/part2.ts
+23
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2023/day08/part2.ts
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type Node = { L: string; R: string };
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type Network = Record<string, Node>;
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type Path = {
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start: string;
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current: string;
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history: string[];
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};
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export function answer(input: string): number {
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export function answer(input: string) {
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const [instructionsRaw, , ...networkRaw] = input.split("\n");
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const network: Network = networkRaw.reduce((network, line) => {
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return { ...network, [id]: { L, R } };
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}, {});
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const instructions = instructionsRaw.split("");
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const instructions = instructionsRaw.split("") as ("L" | "R")[];
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const next = (node: string, i: number): string =>
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network[node][instructions[i] as "L" | "R"];
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const paths = Object.keys(network).filter((n) => n.endsWith("A"));
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const startNodes = Object.keys(network).filter((n) => n.endsWith("A"));
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const endNodes = Object.keys(network).filter((n) => n.endsWith("Z"));
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const paths: Path[] = startNodes.map((n) => ({
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start: n,
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current: n,
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history: [],
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}));
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const stepsToZCache: Record<string, number> = {};
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const stepPath = (p: Path, instIdx: number, step: number) => {
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p.history.push(p.current);
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p.current = next(p.current, instIdx);
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if (p.current.endsWith("Z")) {
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p.history.forEach((prev, i) => {
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console.log(`${instIdx}.${prev}.${p.current} = ${step - i + 1}`);
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stepsToZCache[`${instIdx}.${prev}.${p.current}`] = step - i + 1;
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});
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const stepsToZ = (node: string) => {
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let step = 0;
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while (!node.endsWith("Z")) {
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for (const dir of instructions) {
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node = network[node][dir];
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step++;
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if (node.endsWith("Z")) break;
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}
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}
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return step;
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};
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let step = 0;
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while (true) {
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for (let instIdx = 0; instIdx < instructions.length; instIdx++) {
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const stepsToZFromCurrent: number[] = [];
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paths.forEach((p) => {
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stepPath(p, instIdx, step);
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for (const en of endNodes) {
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const steps = stepsToZCache[`${instIdx}.${p.current}.${en}`];
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if (steps) stepsToZFromCurrent.push(steps);
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}
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});
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const pathsToZ = paths.map((p) =>
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endNodes
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.map((en) => stepsToZCache[`${instIdx}.${p.current}.${en}`])
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.filter((s) => s !== undefined),
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);
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return lcm(paths.map((p) => stepsToZ(p)));
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}
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if (pathsToZ.every((p) => p.length > 0)) {
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return pathsToZ.reduce((product, x) => (product *= x[x.length - 1]), 1);
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}
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function lcm(nums: number[]): number {
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const [a, b, ...rest] = nums;
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const c = (a * b) / gcf(a, b);
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if (rest.length === 0) return c;
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return lcm([c, ...rest]);
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}
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step++;
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}
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}
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function gcf(a: number, b: number): number {
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if (b === 0) return a;
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return gcf(b, a % b);
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}
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if (import.meta.main) {