Aufgaben pro Durchlauf abwechslungsreich ziehen — keine direkte Wiederholung, max. 2x

src/lib/game/tasks.test.ts

@@ -1,21 +1,20 @@
 import { describe, it, expect } from 'vitest';
-import { generateTask, TARGETS, type Target } from './tasks';
+import { buildTask, createDeck, drawTask, TARGETS, type Target } from './tasks';
 
-describe('generateTask', () => {
+describe('buildTask', () => {
   it.each(TARGETS)('produces a valid decomposition for target %i', (target) => {
-    for (let i = 0; i < 50; i++) {
-      const task = generateTask(target);
+    for (let given = 0; given <= target; given++) {
+      const task = buildTask(target, given);
       expect(task.target).toBe(target);
-      expect(task.given).toBeGreaterThanOrEqual(0);
-      expect(task.given).toBeLessThanOrEqual(target);
+      expect(task.given).toBe(given);
       expect(task.given + task.answer).toBe(target);
     }
   });
 
   it('always includes the correct answer in choices', () => {
     for (const target of TARGETS) {
-      for (let i = 0; i < 30; i++) {
-        const task = generateTask(target);
+      for (let given = 0; given <= target; given++) {
+        const task = buildTask(target, given);
         expect(task.choices).toContain(task.answer);
       }
     }
@@ -23,34 +22,75 @@ describe('generateTask', () => {
 
   it('produces choices without duplicates', () => {
     for (const target of TARGETS) {
-      for (let i = 0; i < 30; i++) {
-        const task = generateTask(target);
-        const unique = new Set(task.choices);
-        expect(unique.size).toBe(task.choices.length);
+      for (let given = 0; given <= target; given++) {
+        const task = buildTask(target, given);
+        expect(new Set(task.choices).size).toBe(task.choices.length);
       }
     }
   });
 
-  it('returns 3 choices for targets >= 5', () => {
-    for (const target of [5, 6, 7, 8, 9, 10] as Target[]) {
-      const task = generateTask(target);
+  it('returns 3 choices for every target', () => {
+    for (const target of TARGETS) {
+      const task = buildTask(target, 1);
       expect(task.choices.length).toBe(3);
     }
   });
-
-  it('returns 3 choices for target 4 (3 possible answers total)', () => {
-    const task = generateTask(4);
-    expect(task.choices.length).toBe(3);
 });
 
-  it('avoids reusing the same given when possible', () => {
-    const target: Target = 7;
-    const prev = generateTask(target);
-    let differed = 0;
-    for (let i = 0; i < 50; i++) {
-      const t = generateTask(target, prev);
-      if (t.given !== prev.given) differed++;
+// Zieht n Aufgaben hintereinander aus einem frischen Deck.
+function drawSequence(target: Target, n: number): number[] {
+  let deck = createDeck(target);
+  const givens: number[] = [];
+  for (let i = 0; i < n; i++) {
+    const res = drawTask(deck);
+    givens.push(res.task.given);
+    deck = res.deck;
+  }
+  return givens;
+}
+
+describe('drawTask deck', () => {
+  it('never repeats the same given twice in a row', () => {
+    for (const target of TARGETS) {
+      // Lange Reihe über viele Beutel-Zyklen, auch über die Zyklusgrenzen hinweg.
+      const seq = drawSequence(target, 200);
+      for (let i = 1; i < seq.length; i++) {
+        expect(seq[i]).not.toBe(seq[i - 1]);
+      }
+    }
+  });
+
+  it('distributes givens as evenly as possible (counts differ by at most 1)', () => {
+    for (const target of TARGETS) {
+      const poolSize = target + 1;
+      const seq = drawSequence(target, poolSize * 7 + 3);
+      const counts = new Map<number, number>();
+      for (const g of seq) counts.set(g, (counts.get(g) ?? 0) + 1);
+      // Jede Vorgabe muss vorgekommen sein.
+      expect(counts.size).toBe(poolSize);
+      const values = [...counts.values()];
+      expect(Math.max(...values) - Math.min(...values)).toBeLessThanOrEqual(1);
+    }
+  });
+
+  it('uses each given at most twice over a full 10-task run', () => {
+    // Ein Spieldurchlauf zieht ~10 Aufgaben; der kleinste Pool (Zielzahl 4) hat 5.
+    for (const target of TARGETS) {
+      for (let trial = 0; trial < 50; trial++) {
+        const seq = drawSequence(target, 10);
+        const counts = new Map<number, number>();
+        for (const g of seq) counts.set(g, (counts.get(g) ?? 0) + 1);
+        expect(Math.max(...counts.values())).toBeLessThanOrEqual(2);
+      }
+    }
+  });
+
+  it('keeps every given within [0..target]', () => {
+    for (const target of TARGETS) {
+      for (const g of drawSequence(target, 60)) {
+        expect(g).toBeGreaterThanOrEqual(0);
+        expect(g).toBeLessThanOrEqual(target);
+      }
     }
-    expect(differed).toBe(50);
   });
 });

src/lib/game/tasks.ts

@@ -4,6 +4,11 @@
 //   given: vorgegebene Zerlegungszahl in [0..T] (inkl. der trivialen 0/T-Zerlegung)
 //   answer: T - given (das Kind muss diese tippen)
 //   choices: 3 große Buttons (richtige Antwort + 2 Distraktoren), gemischt
+//
+// Aufgabenfolge pro Spieldurchlauf: ein "Beutel" (TaskDeck) zieht alle möglichen
+// Vorgaben ohne Zurücklegen, mischt nach dem Leeren neu und verhindert direkte
+// Wiederholungen. So kommt nie 2x dieselbe Vorgabe hintereinander und die
+// Häufigkeiten bleiben über den Durchlauf maximal gleichmäßig.
 
 export type Target = 4 | 5 | 6 | 7 | 8 | 9 | 10;
 
@@ -18,10 +23,6 @@ export const TARGETS: Target[] = [4, 5, 6, 7, 8, 9, 10];
 
 const DESIRED_CHOICES = 3;
 
-function randInt(min: number, max: number): number {
-  return Math.floor(Math.random() * (max - min + 1)) + min;
-}
-
 function shuffle<T>(arr: T[]): T[] {
   const a = arr.slice();
   for (let i = a.length - 1; i > 0; i--) {
@@ -31,26 +32,46 @@ function shuffle<T>(arr: T[]): T[] {
   return a;
 }
 
-export function generateTask(target: Target, prev?: Task): Task {
-  // Mögliche given-Werte: 0..target (inkl. 0 und target selbst).
-  const candidates: number[] = [];
-  for (let i = 0; i <= target; i++) candidates.push(i);
+// Alle möglichen Vorgabe-Zahlen für eine Zielzahl: 0..target.
+export function givenPool(target: Target): number[] {
+  const pool: number[] = [];
+  for (let i = 0; i <= target; i++) pool.push(i);
+  return pool;
+}
 
-  // Vermeide identisches given wie zuletzt, wenn Auswahl groß genug.
-  const givenPool =
-    prev && prev.target === target && candidates.length > 1
-      ? candidates.filter((g) => g !== prev.given)
-      : candidates;
-
-  const given = givenPool[randInt(0, givenPool.length - 1)];
+// Baut die Aufgabe zu einer konkreten Vorgabe (richtige Antwort + 2 zufällige Distraktoren).
+export function buildTask(target: Target, given: number): Task {
   const answer = target - given;
-
-  // Distraktoren: alle möglichen Antworten außer der korrekten.
-  // Mögliche Antworten = 0..target (gleicher Wertebereich).
-  const distractorPool = candidates.filter((n) => n !== answer);
+  const distractorPool = givenPool(target).filter((n) => n !== answer);
   const numDistractors = Math.min(DESIRED_CHOICES - 1, distractorPool.length);
   const distractors = shuffle(distractorPool).slice(0, numDistractors);
-
   const choices = shuffle([answer, ...distractors]);
   return { target, given, answer, choices };
 }
+
+// Ziehbeutel pro Spieldurchlauf. `bag` = noch nicht gezogene Vorgaben des aktuellen
+// Zyklus, `lastGiven` = zuletzt gezogene Vorgabe (für den Schutz an der Zyklusgrenze).
+export type TaskDeck = {
+  target: Target;
+  bag: number[];
+  lastGiven: number | null;
+};
+
+export function createDeck(target: Target): TaskDeck {
+  return { target, bag: [], lastGiven: null };
+}
+
+// Zieht die nächste Aufgabe und liefert das fortgeschriebene Deck zurück (immutable).
+export function drawTask(deck: TaskDeck): { task: Task; deck: TaskDeck } {
+  let bag = deck.bag.slice();
+  if (bag.length === 0) {
+    bag = shuffle(givenPool(deck.target));
+    // Zyklusgrenze: erste Ziehung darf nicht der letzten des alten Beutels gleichen.
+    if (deck.lastGiven !== null && bag.length > 1 && bag[0] === deck.lastGiven) {
+      [bag[0], bag[1]] = [bag[1], bag[0]];
+    }
+  }
+  const given = bag.shift() as number;
+  const task = buildTask(deck.target, given);
+  return { task, deck: { target: deck.target, bag, lastGiven: given } };
+}

src/lib/stores/game.ts

@@ -1,5 +1,5 @@
 import { get, writable, derived } from 'svelte/store';
-import { generateTask, type Target, type Task } from '../game/tasks';
+import { createDeck, drawTask, type Target, type Task, type TaskDeck } from '../game/tasks';
 import { isWin, stageFor } from '../game/stages';
 import { settings } from './settings';
 import { recordResult } from './progress';
@@ -16,6 +16,7 @@ export type GameState = {
   totalMs: number;
   lastWasCorrect: boolean | null;
   stageBumpKey: number; // monoton wachsend → triggert FX-Animation
+  deck: TaskDeck | null; // Ziehbeutel für abwechslungsreiche Aufgabenfolge
 };
 
 const initial: GameState = {
@@ -28,6 +29,7 @@ const initial: GameState = {
   totalMs: 0,
   lastWasCorrect: null,
   stageBumpKey: 0,
+  deck: null,
 };
 
 export const game = writable<GameState>(initial);
@@ -75,7 +77,7 @@ function finalize() {
 export function startGame(target: Target): void {
   clearTick();
   const totalMs = get(settings).roundSeconds * 1000;
-  const firstTask = generateTask(target);
+  const { task: firstTask, deck } = drawTask(createDeck(target));
   game.set({
     status: 'running',
     target,
@@ -86,6 +88,7 @@ export function startGame(target: Target): void {
     totalMs,
     lastWasCorrect: null,
     stageBumpKey: 0,
+    deck,
   });
   lastTickAt = performance.now();
   tickHandle = requestAnimationFrame(tick);
@@ -112,12 +115,13 @@ export function answer(value: number): void {
       finalize();
       return;
     }
-    const nextTask = generateTask(g.target, g.task);
+    const { task: nextTask, deck } = drawTask(g.deck ?? createDeck(g.target));
     game.update((s) => ({
       ...s,
       correctCount: nextCount,
       prevTask: s.task,
       task: nextTask,
+      deck,
       lastWasCorrect: true,
       stageBumpKey: stageBump ? s.stageBumpKey + 1 : s.stageBumpKey,
     }));
@@ -126,13 +130,6 @@ export function answer(value: number): void {
   }
 }
 
-export function nextTaskAfterWrong(): void {
-  const g = get(game);
-  if (g.status !== 'running' || !g.task || g.target === null) return;
-  const nextTask = generateTask(g.target, g.task);
-  game.update((s) => ({ ...s, prevTask: s.task, task: nextTask, lastWasCorrect: null }));
-}
-
 export function abortGame(): void {
   clearTick();
   game.set(initial);