feat: add daily challenges system

Three PST-midnight-resetting challenges generated deterministically per
day from click, boss, quest, and prestige types. Progress tracked
server-side for bosses and prestige, client-side for clicks and quests.
Crystal rewards awarded on completion and preserved through prestige resets.

apps/api/src/services/dailyChallenges.ts

@@ -0,0 +1,103 @@
+import type {
+  DailyChallenge,
+  DailyChallengeState,
+  DailyChallengeType,
+  GameState,
+} from "@elysium/types";
+import { DAILY_CHALLENGE_TEMPLATES } from "../data/dailyChallenges.js";
+
+// Use the server's PST/PDT timezone so challenges roll over at PST midnight
+const getTodayString = (): string =>
+  new Intl.DateTimeFormat("en-CA", { timeZone: "America/Los_Angeles" }).format(new Date());
+
+/** Simple deterministic pseudo-random based on a numeric seed. */
+const seededRandom = (seed: number): number => {
+  const x = Math.sin(seed + 1) * 10_000;
+  return x - Math.floor(x);
+};
+
+/** Converts a date string into a stable numeric seed. */
+const dateSeed = (dateStr: string): number =>
+  dateStr.split("").reduce((acc, char, i) => acc + char.charCodeAt(0) * (i + 1), 0);
+
+/** Deterministically shuffles an array using a numeric seed. */
+const shuffleWithSeed = <T>(arr: T[], seed: number): T[] => {
+  const result = [...arr];
+  for (let i = result.length - 1; i > 0; i--) {
+    const j = Math.floor(seededRandom(seed + i) * (i + 1));
+    [result[i], result[j]] = [result[j], result[i]];
+  }
+  return result;
+};
+
+const CHALLENGE_TYPES: DailyChallengeType[] = [
+  "clicks",
+  "bossesDefeated",
+  "questsCompleted",
+  "prestige",
+];
+
+/**
+ * Generates 3 daily challenges for the given date string, deterministically.
+ * Picks one challenge from 3 different randomly-selected types.
+ */
+export const generateDailyChallenges = (dateStr: string): DailyChallenge[] => {
+  const seed = dateSeed(dateStr);
+  const selectedTypes = shuffleWithSeed([...CHALLENGE_TYPES], seed).slice(0, 3);
+
+  return selectedTypes.map((type, index) => {
+    const templates = DAILY_CHALLENGE_TEMPLATES.filter((t) => t.type === type);
+    const templateIndex = Math.floor(seededRandom(seed + index * 100) * templates.length);
+    const template = templates[templateIndex];
+
+    return {
+      id: `${dateStr}_${type}`,
+      type: template.type,
+      label: template.label,
+      target: template.target,
+      progress: 0,
+      completed: false,
+      rewardCrystals: template.rewardCrystals,
+    };
+  });
+};
+
+/**
+ * Returns the current daily challenge state, generating fresh challenges if
+ * the stored date doesn't match today (i.e. a new day has begun).
+ */
+export const getOrResetDailyChallenges = (state: GameState): DailyChallengeState => {
+  const today = getTodayString();
+  if (state.dailyChallenges?.date === today) {
+    return state.dailyChallenges;
+  }
+  return { date: today, challenges: generateDailyChallenges(today) };
+};
+
+/**
+ * Increments progress for challenges matching the given type.
+ * Returns the updated challenge state and total crystals awarded for newly completed challenges.
+ */
+export const updateChallengeProgress = (
+  challengeState: DailyChallengeState,
+  type: DailyChallengeType,
+  amount: number,
+): { updatedChallenges: DailyChallengeState; crystalsAwarded: number } => {
+  let crystalsAwarded = 0;
+
+  const updatedChallenges: DailyChallengeState = {
+    ...challengeState,
+    challenges: challengeState.challenges.map((challenge) => {
+      if (challenge.type !== type || challenge.completed) return challenge;
+
+      const newProgress = Math.min(challenge.progress + amount, challenge.target);
+      const nowCompleted = newProgress >= challenge.target;
+
+      if (nowCompleted) crystalsAwarded += challenge.rewardCrystals;
+
+      return { ...challenge, progress: newProgress, completed: nowCompleted };
+    }),
+  };
+
+  return { updatedChallenges, crystalsAwarded };
+};