From 691c98f86237ab0fbf6d37e5f1ccbbe055ab057a Mon Sep 17 00:00:00 2001
From: Rene Luria <rene.luria@infomaniak.com>
Date: Mon, 31 Aug 2026 09:35:11 +0200
Subject: [PATCH] =?UTF-8?q?feat:=20g=C3=A9n=C3=A9ration=20pond=C3=A9r?=
 =?UTF-8?q?=C3=A9e=20des=20questions=20(les=20grands=20facteurs=20sortent?=
 =?UTF-8?q?=20plus=20souvent)?=
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---
 ...8-28-livrets-multiplication-game-design.md |  2 +-
 .../com/livrets/game/QuestionGenerator.kt     | 14 ++++++-
 .../com/livrets/game/QuestionGeneratorTest.kt | 39 +++++++++++++++++++
 3 files changed, 52 insertions(+), 3 deletions(-)

diff --git a/docs/superpowers/specs/2026-08-28-livrets-multiplication-game-design.md b/docs/superpowers/specs/2026-08-28-livrets-multiplication-game-design.md
index 33de278..99b890b 100644
--- a/docs/superpowers/specs/2026-08-28-livrets-multiplication-game-design.md
+++ b/docs/superpowers/specs/2026-08-28-livrets-multiplication-game-design.md
@@ -84,7 +84,7 @@ data class GameResult(
 Événements : `AnswerSubmitted(n)`, `Timeout`, `Tick`, `FeedbackElapsed`.
 
 Règles :
-- Génération : `a`, `b` tirés uniformément dans 1..`config.maxTable` (le joueur limite la difficulté en réduisant la table max) ; forme `Direct` ou `MissingFactor` au hasard (~50/50) ; interdiction de répéter exactement la même question deux fois de suite.
+- Génération : `a`, `b` tirés dans 1..`config.maxTable` avec poids ∝ facteur (amendé le 2026-08-31 : cf. spec « Génération pondérée des questions ») ; forme `Direct` ou `MissingFactor` au hasard (~50/50) ; interdiction de répéter exactement la même question deux fois de suite.
 - Pour `MissingFactor(a, b)` : la question s'affiche `a × ? = a*b`, la réponse attendue est `b`.
 - Réponse correcte → `Feedback` vert 1,5 s → question suivante.
 - Réponse fausse → `Feedback` rouge 1,5 s (bonne réponse affichée) → question suivante.
diff --git a/sharedUI/src/commonMain/kotlin/com/livrets/game/QuestionGenerator.kt b/sharedUI/src/commonMain/kotlin/com/livrets/game/QuestionGenerator.kt
index 282e77c..9b1d436 100644
--- a/sharedUI/src/commonMain/kotlin/com/livrets/game/QuestionGenerator.kt
+++ b/sharedUI/src/commonMain/kotlin/com/livrets/game/QuestionGenerator.kt
@@ -9,11 +9,21 @@ fun interface QuestionSource {
 class QuestionGenerator(private val random: Random = Random.Default) : QuestionSource {
     override fun next(previous: Question?, maxTable: Int): Question {
         while (true) {
-            val a = random.nextInt(1, maxTable + 1)
-            val b = random.nextInt(1, maxTable + 1)
+            val a = nextFactor(maxTable)
+            val b = nextFactor(maxTable)
             val question =
                 if (random.nextBoolean()) Question.Direct(a, b) else Question.MissingFactor(a, b)
             if (question != previous) return question
         }
     }
+
+    private fun nextFactor(maxTable: Int): Int {
+        val totalWeight = maxTable * (maxTable + 1) / 2
+        var roll = random.nextDouble() * totalWeight
+        for (k in 1..maxTable) {
+            roll -= k
+            if (roll < 0) return k
+        }
+        return maxTable
+    }
 }
diff --git a/sharedUI/src/commonTest/kotlin/com/livrets/game/QuestionGeneratorTest.kt b/sharedUI/src/commonTest/kotlin/com/livrets/game/QuestionGeneratorTest.kt
index 235b55d..6bbde8e 100644
--- a/sharedUI/src/commonTest/kotlin/com/livrets/game/QuestionGeneratorTest.kt
+++ b/sharedUI/src/commonTest/kotlin/com/livrets/game/QuestionGeneratorTest.kt
@@ -58,4 +58,43 @@ class QuestionGeneratorTest {
         assertEquals("7 × 8 = ?", Question.Direct(7, 8).toString())
         assertEquals("7 × ? = 56", Question.MissingFactor(7, 8).toString())
     }
+
+    private fun factors(q: Question): Pair<Int, Int> = when (q) {
+        is Question.Direct -> q.a to q.b
+        is Question.MissingFactor -> q.a to q.b
+    }
+
+    @Test
+    fun `biais progressif - les facteurs eleves reviennent plus souvent`() {
+        val generator = QuestionGenerator(Random(42))
+        var with1 = 0
+        var with10 = 0
+        repeat(5000) {
+            val (a, b) = factors(generator.next(previous = null, maxTable = 10))
+            if (a == 1 || b == 1) with1++
+            if (a == 10 || b == 10) with10++
+        }
+        assertTrue(with1 < with10 / 5, "with1=$with1, with10=$with10")
+    }
+
+    @Test
+    fun `les petits facteurs restent possibles`() {
+        val generator = QuestionGenerator(Random(42))
+        var with1 = 0
+        repeat(5000) {
+            val (a, b) = factors(generator.next(previous = null, maxTable = 10))
+            if (a == 1 || b == 1) with1++
+        }
+        assertTrue(with1 > 0, "with1=$with1")
+    }
+
+    @Test
+    fun `maxTable egale a 1 - seule question possible sans boucle infinie`() {
+        val generator = QuestionGenerator(Random(42))
+        repeat(200) {
+            val (a, b) = factors(generator.next(previous = null, maxTable = 1))
+            assertEquals(1, a)
+            assertEquals(1, b)
+        }
+    }
 }