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GenerationTrace,
GenerationTraceStep,
SkillMasteryDisplay,
} from '@/db/schema/session-plans'
import type { PracticeStep, SkillSet } from '../types/tutorial'
import { getBaseComplexity, type SkillCostCalculator } from './skillComplexity'
import {
extractSkillsFromProblem,
extractSkillsFromSequence,
flattenProblemSkills,
} from './skillExtraction'
import { generateUnifiedInstructionSequence } from './unifiedStepGenerator'
// Re-export trace types for consumers that import from this file
export type { GenerationTrace, GenerationTraceStep }
// =============================================================================
// MEMOIZATION CACHE FOR SKILL ANALYSIS
// =============================================================================
//
// The analyzeStepSkills function is called hundreds of thousands of times during
// problem generation (e.g., 60 problems × 100 attempts × 4 terms × 18 candidates).
// Since the result depends only on (currentValue, term), we can memoize it.
//
// The cache key is `${currentValue}:${term}` because:
// - targetValue = currentValue + term (deterministic)
// - The third parameter (_newValue) is unused
// - Skill detection is pure functional (no side effects, no randomness)
const stepSkillsCache = new Map<string, string[]>()
/** Cache statistics for monitoring/testing */
interface CacheStats {
size: number
hits: number
misses: number
}
let cacheHits = 0
let cacheMisses = 0
/**
* Get the cache key for a given step.
* Uses currentValue and term only (newValue is computed from these).
*/
function getStepSkillsCacheKey(currentValue: number, term: number): string {
return `${currentValue}:${term}`
}
/**
* Clear the step skills cache.
* Useful for testing or when you want to force recomputation.
*/
export function clearStepSkillsCache(): void {
stepSkillsCache.clear()
cacheHits = 0
cacheMisses = 0
}
/**
* Get cache statistics for monitoring and testing.
*/
export function getStepSkillsCacheStats(): CacheStats {
return {
size: stepSkillsCache.size,
hits: cacheHits,
misses: cacheMisses,
}
}
/**
* Memoized version of analyzeStepSkills.
*
* This function returns cached results when available, avoiding expensive
* abacus simulation for repeated (currentValue, term) pairs.
*
* @param currentValue - Current abacus value
* @param term - Term to add (positive) or subtract (negative)
* @param _newValue - Expected result (unused, kept for API compatibility)
* @returns Array of unique skill identifiers required for this step
*/
export function analyzeStepSkillsMemoized(
currentValue: number,
term: number,
_newValue: number
): string[] {
const key = getStepSkillsCacheKey(currentValue, term)
const cached = stepSkillsCache.get(key)
if (cached !== undefined) {
cacheHits++
return cached
}
cacheMisses++
const result = analyzeStepSkills(currentValue, term, _newValue)
stepSkillsCache.set(key, result)
return result
}
export interface GeneratedProblem {
id: string
terms: number[]
answer: number
/** Skills that this problem exercises (output, not input constraint) */
skillsUsed: string[]
difficulty: 'easy' | 'medium' | 'hard'
explanation?: string
/** Step-by-step trace from the generator showing skills used at each step */
generationTrace?: GenerationTrace
}
export interface ProblemConstraints {
numberRange: { min: number; max: number }
maxSum?: number
minSum?: number
minTerms?: number
maxTerms: number
problemCount: number
/**
* Maximum complexity budget per term.
*
* Each term's skills are costed using the SkillCostCalculator,
* which factors in both base skill complexity and student mastery.
*
* If set, terms with total cost > budget are rejected during generation.
*/
maxComplexityBudgetPerTerm?: number
/**
* Minimum complexity budget per term.
*
* If set, terms with total cost < budget are rejected during generation.
* This ensures every term exercises real skills (no trivial direct additions).
*/
minComplexityBudgetPerTerm?: number
}
/**
* Analyzes which skills are required during sequential computation.
* Uses the unified step generator's actual abacus simulation to determine skills,
* ensuring consistency with the tutorial/help system.
*
* @param terms - Array of terms (positive for addition, negative for subtraction)
* @param _finalSum - Final sum (unused, kept for API compatibility)
* @returns Array of unique skill identifiers required for this problem
*/
export function analyzeRequiredSkills(terms: number[], _finalSum: number): string[] {
// Use the unified step generator to extract skills via actual abacus simulation
const skillsByTerm = extractSkillsFromProblem(terms, generateUnifiedInstructionSequence)
const allSkills = flattenProblemSkills(skillsByTerm)
return [...new Set(allSkills.map((s) => s.skillId))]
}
// GenerationTrace and GenerationTraceStep are imported from @/db/schema/session-plans
// and re-exported above for backward compatibility
/**
* Generates a human-readable explanation for a single step
*/
function generateStepExplanation(
before: number,
term: number,
after: number,
skills: string[],
isSubtraction: boolean = false
): string {
if (skills.length === 0) {
return isSubtraction
? `Subtract ${term} directly (no skill needed)`
: `Add ${term} directly (no skill needed)`
}
const explanations: string[] = []
for (const skill of skills) {
// Addition skills
if (skill === 'basic.directAddition') {
explanations.push(`direct addition of ${term}`)
} else if (skill === 'basic.heavenBead') {
explanations.push('use heaven bead (5)')
} else if (skill === 'basic.simpleCombinations') {
explanations.push('simple combination (5+n)')
} else if (skill.startsWith('fiveComplements.')) {
// e.g., "fiveComplements.4=5-1" -> "+4 = +5-1"
const match = skill.match(/fiveComplements\.(\d)=5-(\d)/)
if (match) {
explanations.push(`five complement: +${match[1]} = +5-${match[2]}`)
}
} else if (skill.startsWith('tenComplements.')) {
// e.g., "tenComplements.9=10-1" -> "+9 = +10-1"
const match = skill.match(/tenComplements\.(\d)=10-(\d)/)
if (match) {
explanations.push(`ten complement: +${match[1]} = +10-${match[2]} (carry)`)
}
}
// Subtraction skills
else if (skill === 'basic.directSubtraction') {
explanations.push(`direct subtraction of ${term}`)
} else if (skill === 'basic.heavenBeadSubtraction') {
explanations.push('remove heaven bead (5)')
} else if (skill === 'basic.simpleCombinationsSub') {
explanations.push('simple subtraction combination')
} else if (skill.startsWith('fiveComplementsSub.')) {
// e.g., "fiveComplementsSub.-4=-5+1" -> "-4 = -5+1"
const match = skill.match(/fiveComplementsSub\.-(\d)=-5\+(\d)/)
if (match) {
explanations.push(`five complement: -${match[1]} = -5+${match[2]}`)
}
} else if (skill.startsWith('tenComplementsSub.')) {
// e.g., "tenComplementsSub.-9=+1-10" -> "-9 = +1-10"
const match = skill.match(/tenComplementsSub\.-(\d)=\+(\d)-10/)
if (match) {
explanations.push(`ten complement: -${match[1]} = +${match[2]}-10 (borrow)`)
}
}
}
const beforeOnes = before % 10
const termOnes = term % 10
const op = isSubtraction ? '-' : '+'
const resultOnes = isSubtraction ? (before - term) % 10 : (before + term) % 10
const carryBorrow = isSubtraction
? beforeOnes < termOnes
? ' (borrow)'
: ''
: before + term >= 10
? ' (carry)'
: ''
return `${before} ${op} ${term}: ones column ${beforeOnes}${op}${termOnes}=${resultOnes}${carryBorrow} → ${explanations.join(', ')}`
}
/**
* Analyzes skills needed for a single step: currentValue + term = newValue
* Uses the unified step generator's actual abacus simulation to determine skills.
*
* @param currentValue - Current abacus value
* @param term - Term to add (positive) or subtract (negative)
* @param _newValue - Expected result (unused, kept for API compatibility)
* @returns Array of unique skill identifiers required for this step
*/
export function analyzeStepSkills(currentValue: number, term: number, _newValue: number): string[] {
const targetValue = currentValue + term
try {
const sequence = generateUnifiedInstructionSequence(currentValue, targetValue)
const skills = extractSkillsFromSequence(sequence)
return [...new Set(skills.map((s) => s.skillId))]
} catch {
// If sequence generation fails, return empty skills
return []
}
}
/**
* Helper to check if a skill is enabled in a skill set category
*/
function isSkillEnabled(skillPath: string, skillSet: SkillSet | Partial<SkillSet>): boolean {
const [category, skill] = skillPath.split('.')
if (category === 'basic' && skillSet.basic) {
return skillSet.basic[skill as keyof typeof skillSet.basic] || false
} else if (category === 'fiveComplements' && skillSet.fiveComplements) {
return skillSet.fiveComplements[skill as keyof typeof skillSet.fiveComplements] || false
} else if (category === 'tenComplements' && skillSet.tenComplements) {
return skillSet.tenComplements[skill as keyof typeof skillSet.tenComplements] || false
} else if (category === 'fiveComplementsSub' && skillSet.fiveComplementsSub) {
return skillSet.fiveComplementsSub[skill as keyof typeof skillSet.fiveComplementsSub] || false
} else if (category === 'tenComplementsSub' && skillSet.tenComplementsSub) {
return skillSet.tenComplementsSub[skill as keyof typeof skillSet.tenComplementsSub] || false
} else if (category === 'advanced' && skillSet.advanced) {
return skillSet.advanced[skill as keyof typeof skillSet.advanced] || false
}
return false
}
/**
* Checks if a problem matches the skill constraints
*/
export function problemMatchesSkills(
problem: GeneratedProblem,
allowedSkills: SkillSet,
targetSkills?: Partial<SkillSet>,
forbiddenSkills?: Partial<SkillSet>
): boolean {
// Check allowed skills - problem must use at least one enabled allowed skill
const hasAllowedSkill = problem.skillsUsed.some((skillPath) =>
isSkillEnabled(skillPath, allowedSkills)
)
if (!hasAllowedSkill) return false
// Check forbidden skills - problem must not use any forbidden skills
if (forbiddenSkills) {
const usesForbiddenSkill = problem.skillsUsed.some((skillPath) =>
isSkillEnabled(skillPath, forbiddenSkills)
)
if (usesForbiddenSkill) return false
}
// Check target skills - if specified, problem should use at least one target skill
if (targetSkills) {
const hasTargetSkill = problem.skillsUsed.some((skillPath) =>
isSkillEnabled(skillPath, targetSkills)
)
// If target skills are specified but none match, reject
const hasAnyTargetSkill =
Object.values(targetSkills.basic || {}).some(Boolean) ||
Object.values(targetSkills.fiveComplements || {}).some(Boolean) ||
Object.values(targetSkills.tenComplements || {}).some(Boolean) ||
Object.values(targetSkills.fiveComplementsSub || {}).some(Boolean) ||
Object.values(targetSkills.tenComplementsSub || {}).some(Boolean) ||
Object.values(targetSkills.advanced || {}).some(Boolean)
if (hasAnyTargetSkill && !hasTargetSkill) return false
}
return true
}
/**
* Options for generating a single problem
*/
export interface GenerateProblemOptions {
constraints: ProblemConstraints
allowedSkills: SkillSet
targetSkills?: Partial<SkillSet>
forbiddenSkills?: Partial<SkillSet>
/** Student-aware cost calculator for budget enforcement */
costCalculator?: SkillCostCalculator
/** Number of attempts before giving up (default: 100) */
attempts?: number
}
/**
* Diagnostic info about why problem generation failed
*/
export interface GenerationDiagnostics {
/** Total generation attempts made */
totalAttempts: number
/** How many attempts failed at sequence generation */
sequenceFailures: number
/** How many attempts failed sum constraints */
sumConstraintFailures: number
/** How many attempts failed skill matching */
skillMatchFailures: number
/** Skills the problem is allowed to use (whitelist) */
enabledAllowedSkills: string[]
/** Target skills the problem should preferentially use (if any) */
enabledTargetSkills: string[]
/** Last generated problem's skills (if any got that far) */
lastGeneratedSkills?: string[]
/** How many terms had to use lower complexity because minBudget was impossible */
termsWithForcedLowerComplexity?: number
/**
* True if we fell back to a problem that didn't match target skills.
* This happens when target skills are unreachable with the current allowed skills.
* E.g., heavenBeadSubtraction can't be used if heavenBead isn't enabled to reach state 5+.
*/
targetSkillsFallback?: boolean
}
/**
* Helper to extract enabled skill paths from a SkillSet
*/
function getEnabledSkillPaths(skillSet: SkillSet | Partial<SkillSet>): string[] {
const paths: string[] = []
for (const [category, skills] of Object.entries(skillSet)) {
if (skills && typeof skills === 'object') {
for (const [skill, enabled] of Object.entries(skills)) {
if (enabled) {
paths.push(`${category}.${skill}`)
}
}
}
}
return paths
}
/**
* Result from generateSingleProblemWithDiagnostics
*/
export interface GenerationResult {
problem: GeneratedProblem | null
diagnostics: GenerationDiagnostics
}
/**
* Check if a problem matches allowed and forbidden skills (ignoring target skills).
* Used to find fallback candidates when target skills are unreachable.
*/
function problemMatchesAllowedSkillsOnly(
problem: GeneratedProblem,
allowedSkills: SkillSet,
forbiddenSkills?: Partial<SkillSet>
): boolean {
// Check allowed skills - problem must use at least one enabled allowed skill
const hasAllowedSkill = problem.skillsUsed.some((skillPath) =>
isSkillEnabled(skillPath, allowedSkills)
)
if (!hasAllowedSkill) return false
// Check forbidden skills - problem must not use any forbidden skills
if (forbiddenSkills) {
const usesForbiddenSkill = problem.skillsUsed.some((skillPath) =>
isSkillEnabled(skillPath, forbiddenSkills)
)
if (usesForbiddenSkill) return false
}
return true
}
/**
* Generates a single problem with detailed diagnostics about what happened
*/
export function generateSingleProblemWithDiagnostics(
options: GenerateProblemOptions
): GenerationResult {
const { constraints, allowedSkills, targetSkills, forbiddenSkills, costCalculator } = options
const maxAttempts = options.attempts ?? 100
const diagnostics: GenerationDiagnostics = {
totalAttempts: 0,
sequenceFailures: 0,
sumConstraintFailures: 0,
skillMatchFailures: 0,
enabledAllowedSkills: getEnabledSkillPaths(allowedSkills),
enabledTargetSkills: targetSkills ? getEnabledSkillPaths(targetSkills) : [],
}
// Track the best "fallback" candidate - a problem that matches allowed/forbidden
// but not target skills. Used when target skills are unreachable.
let fallbackCandidate: GeneratedProblem | null = null
for (let attempt = 0; attempt < maxAttempts; attempt++) {
diagnostics.totalAttempts++
// Generate random number of terms within the specified range
const minTerms = constraints.minTerms ?? 3
const maxTerms = constraints.maxTerms
const termCount = Math.floor(Math.random() * (maxTerms - minTerms + 1)) + minTerms
// Generate the sequence of numbers to add
const sequenceResult = generateSequence(
constraints,
termCount,
allowedSkills,
targetSkills,
forbiddenSkills,
costCalculator
)
if (!sequenceResult) {
diagnostics.sequenceFailures++
continue
}
const { terms, trace } = sequenceResult
const sum = trace.answer
// Check sum constraints
if (constraints.maxSum && sum > constraints.maxSum) {
diagnostics.sumConstraintFailures++
continue
}
if (constraints.minSum && sum < constraints.minSum) {
diagnostics.sumConstraintFailures++
continue
}
const problemSkills = trace.allSkills
diagnostics.lastGeneratedSkills = problemSkills
// Determine difficulty
let difficulty: 'easy' | 'medium' | 'hard' = 'easy'
if (problemSkills.some((skill) => skill.startsWith('tenComplements'))) {
difficulty = 'hard'
} else if (problemSkills.some((skill) => skill.startsWith('fiveComplements'))) {
difficulty = 'medium'
}
const problem: GeneratedProblem = {
id: `problem_${Date.now()}_${Math.random().toString(36).substr(2, 9)}`,
terms,
answer: sum,
skillsUsed: problemSkills,
difficulty,
explanation: generateSequentialExplanation(terms, sum, problemSkills),
generationTrace: trace,
}
// Check full match (including target skills)
if (problemMatchesSkills(problem, allowedSkills, targetSkills, forbiddenSkills)) {
return { problem, diagnostics }
}
// If it matches allowed/forbidden but not target, save as fallback
if (
targetSkills &&
!fallbackCandidate &&
problemMatchesAllowedSkillsOnly(problem, allowedSkills, forbiddenSkills)
) {
fallbackCandidate = problem
}
diagnostics.skillMatchFailures++
}
// If we have a fallback candidate (matched required/forbidden but not target),
// return it with a warning. This handles cases where target skills are
// unreachable with the current required skills (e.g., heavenBeadSubtraction
// requires heavenBead to first reach state 5+).
if (fallbackCandidate) {
diagnostics.targetSkillsFallback = true
return { problem: fallbackCandidate, diagnostics }
}
return { problem: null, diagnostics }
}
/**
* Generates a single sequential addition problem that matches the given constraints and skills
*/
export function generateSingleProblem(
constraintsOrOptions: ProblemConstraints | GenerateProblemOptions,
allowedSkills?: SkillSet,
targetSkills?: Partial<SkillSet>,
forbiddenSkills?: Partial<SkillSet>,
attempts: number = 100
): GeneratedProblem | null {
// Support both old and new API
let constraints: ProblemConstraints
let _allowedSkills: SkillSet
let _targetSkills: Partial<SkillSet> | undefined
let _forbiddenSkills: Partial<SkillSet> | undefined
let _attempts: number
let costCalculator: SkillCostCalculator | undefined
if ('constraints' in constraintsOrOptions) {
// New options-based API
constraints = constraintsOrOptions.constraints
_allowedSkills = constraintsOrOptions.allowedSkills
_targetSkills = constraintsOrOptions.targetSkills
_forbiddenSkills = constraintsOrOptions.forbiddenSkills
_attempts = constraintsOrOptions.attempts ?? 100
costCalculator = constraintsOrOptions.costCalculator
} else {
// Old positional API (backward compatibility)
constraints = constraintsOrOptions
_allowedSkills = allowedSkills!
_targetSkills = targetSkills
_forbiddenSkills = forbiddenSkills
_attempts = attempts
}
// Use the diagnostics version internally
const result = generateSingleProblemWithDiagnostics({
constraints,
allowedSkills: _allowedSkills,
targetSkills: _targetSkills,
forbiddenSkills: _forbiddenSkills,
costCalculator,
attempts: _attempts,
})
return result.problem
}
/** Result from generating a sequence, includes provenance trace */
interface SequenceResult {
terms: number[]
trace: GenerationTrace
}
/**
* Checks if any subtraction skills are enabled in a skill set
*/
function hasSubtractionSkills(skillSet: SkillSet): boolean {
return (
skillSet.basic.directSubtraction ||
skillSet.basic.heavenBeadSubtraction ||
skillSet.basic.simpleCombinationsSub ||
Object.values(skillSet.fiveComplementsSub).some(Boolean) ||
Object.values(skillSet.tenComplementsSub).some(Boolean)
)
}
/**
* Generates a sequence of numbers that can be computed using only the specified skills.
* Supports both addition and subtraction operations.
* Also builds a trace showing what skills were computed at each step.
*/
function generateSequence(
constraints: ProblemConstraints,
termCount: number,
allowedSkills: SkillSet,
targetSkills?: Partial<SkillSet>,
forbiddenSkills?: Partial<SkillSet>,
costCalculator?: SkillCostCalculator
): SequenceResult | null {
const terms: number[] = []
const steps: GenerationTraceStep[] = []
let currentValue = 0
// Check if we can use subtraction
const canSubtract = hasSubtractionSkills(allowedSkills)
// Track previous term for no-immediate-inverse rule
let previousTerm: PreviousTerm | undefined
for (let i = 0; i < termCount; i++) {
// Try to find a valid next term (returns term + skills it computed)
// For first term, always add (can't subtract from 0)
const allowSubtraction = canSubtract && i > 0 && currentValue > 0
const result = findValidNextTermWithTrace(
currentValue,
constraints,
allowedSkills,
targetSkills,
forbiddenSkills,
i === termCount - 1, // isLastTerm
allowSubtraction,
costCalculator,
previousTerm // Pass previous term to avoid immediate inverses
)
if (result === null) return null // Couldn't find valid term
const { term, skillsUsed, isSubtraction, complexityCost } = result
// Update previous term for next iteration
previousTerm = { term, isSubtraction }
const newValue = isSubtraction ? currentValue - term : currentValue + term
// Build trace step with the skills the generator computed
const explanation = generateStepExplanation(
currentValue,
term,
newValue,
skillsUsed,
isSubtraction
)
const operation = isSubtraction
? `${currentValue} - ${term} = ${newValue}`
: `${currentValue} + ${term} = ${newValue}`
steps.push({
stepNumber: i + 1,
operation,
accumulatedBefore: currentValue,
termAdded: isSubtraction ? -term : term,
accumulatedAfter: newValue,
skillsUsed,
explanation,
complexityCost,
})
// Store the signed term for the problem
terms.push(isSubtraction ? -term : term)
currentValue = newValue
}
// Calculate total complexity cost from all steps
// Note: Use explicit NaN check since ?? only catches null/undefined, not NaN
const totalComplexityCost = steps.reduce((sum, step) => {
const cost = step.complexityCost
if (cost === undefined || cost === null || Number.isNaN(cost)) return sum
return sum + cost
}, 0)
// Build skill mastery context if cost calculator is available
const allSkills = [...new Set(steps.flatMap((s) => s.skillsUsed))]
let skillMasteryContext: Record<string, SkillMasteryDisplay> | undefined
if (costCalculator) {
skillMasteryContext = {}
for (const skillId of allSkills) {
const isPracticing = costCalculator.getIsPracticing(skillId)
skillMasteryContext[skillId] = {
isPracticing,
practiceLevel: isPracticing ? 'visual' : 'none',
baseCost: getBaseComplexity(skillId),
effectiveCost: costCalculator.calculateSkillCost(skillId),
}
}
}
return {
terms,
trace: {
terms,
answer: currentValue,
steps,
allSkills,
budgetConstraint: constraints.maxComplexityBudgetPerTerm,
minBudgetConstraint: constraints.minComplexityBudgetPerTerm,
totalComplexityCost: totalComplexityCost > 0 ? totalComplexityCost : undefined,
skillMasteryContext,
},
}
}
/** Info about the previous term for inverse checking */
interface PreviousTerm {
term: number
isSubtraction: boolean
}
/**
* State-dependent skills and their setup requirements.
*
* Some skills can only be triggered when the abacus is in a specific state.
* This map defines:
* - skillId: the skill that needs setup
* - canUse: function to check if current state enables the skill
* - setupPredicate: function to check if a term would set up the state for this skill
*
* For example, heavenBeadSubtraction requires ones digit 5-9 (heaven bead active)
* so we need to add terms that result in ones digit 5-9 before we can subtract 5.
*/
interface StateDependentSkill {
skillId: string
/** Check if the current value enables this skill */
canUse: (currentValue: number) => boolean
/** Check if applying this term would set up the state for this skill */
wouldSetupState: (currentValue: number, term: number, isSubtraction: boolean) => boolean
}
const STATE_DEPENDENT_SKILLS: StateDependentSkill[] = [
{
// heavenBeadSubtraction: requires ones digit 5-9, then subtract 5
skillId: 'basic.heavenBeadSubtraction',
canUse: (currentValue: number) => {
const onesDigit = currentValue % 10
return onesDigit >= 5 // Heaven bead is active when ones digit is 5-9
},
wouldSetupState: (currentValue: number, term: number, isSubtraction: boolean) => {
const newValue = isSubtraction ? currentValue - term : currentValue + term
if (newValue < 0) return false
const newOnesDigit = newValue % 10
return newOnesDigit >= 5 // Result has heaven bead active
},
},
{
// heavenBead (addition): requires ones digit 0-4 to add 5 directly
skillId: 'basic.heavenBead',
canUse: (currentValue: number) => {
const onesDigit = currentValue % 10
return onesDigit <= 4 // Can add 5 directly when ones is 0-4
},
wouldSetupState: (currentValue: number, term: number, isSubtraction: boolean) => {
const newValue = isSubtraction ? currentValue - term : currentValue + term
if (newValue < 0) return false
const newOnesDigit = newValue % 10
return newOnesDigit <= 4 // Result allows adding 5 directly
},
},
]
/**
* Check if a candidate term moves CLOSER to enabling a state-dependent skill.
*
* Unlike `wouldSetupState` which requires the state to be fully enabled,
* this checks if we're making progress toward the target state.
*
* For heavenBeadSubtraction (needs ones >= 5):
* - If current ones is 0 and new ones is 3, we're closer (progress)
* - If current ones is 0 and new ones is 5, we're there (setup complete)
*/
function movesTowardSetup(
depSkill: StateDependentSkill,
currentValue: number,
term: number,
isSubtraction: boolean
): boolean {
if (depSkill.skillId === 'basic.heavenBeadSubtraction') {
const currentOnes = currentValue % 10
const newValue = isSubtraction ? currentValue - term : currentValue + term
if (newValue < 0) return false
const newOnes = newValue % 10
// Progress if we're moving toward 5+ without overshooting
return newOnes > currentOnes && newOnes <= 9
}
if (depSkill.skillId === 'basic.heavenBead') {
const currentOnes = currentValue % 10
const newValue = isSubtraction ? currentValue - term : currentValue + term
if (newValue < 0) return false
const newOnes = newValue % 10
// Progress if we're moving toward 0-4
return newOnes < currentOnes && newOnes >= 0
}
return false
}
/**
* Find state-dependent skills that are in the target skills set
*/
function findStateDependentTargetSkills(
targetSkills: Partial<SkillSet> | undefined
): StateDependentSkill[] {
if (!targetSkills) return []
return STATE_DEPENDENT_SKILLS.filter((depSkill) => isSkillEnabled(depSkill.skillId, targetSkills))
}
/** Result from findValidNextTermWithTrace */
interface TermWithSkills {
term: number
skillsUsed: string[]
isSubtraction: boolean
/** Complexity cost (if calculator was provided) */
complexityCost?: number
/** Whether this term met the minBudget requirement (used for diagnostics) */
metMinBudget?: boolean
}
/**
* Collects all valid terms from a given state, categorized by complexity.
*
* This is the core of the state-aware generation algorithm. Instead of
* filtering by minBudget during collection (which can result in empty candidates),
* we collect ALL valid terms and categorize them for intelligent selection.
*/
function collectValidTerms(
currentValue: number,
constraints: ProblemConstraints,
allowedSkills: SkillSet,
forbiddenSkills: Partial<SkillSet> | undefined,
allowSubtraction: boolean,
costCalculator?: SkillCostCalculator
): { meetsMinBudget: TermWithSkills[]; belowMinBudget: TermWithSkills[] } {
const { min, max } = constraints.numberRange
const maxBudget = constraints.maxComplexityBudgetPerTerm
const minBudget = constraints.minComplexityBudgetPerTerm
const meetsMinBudget: TermWithSkills[] = []
const belowMinBudget: TermWithSkills[] = []
// Helper to check if a term is valid and categorize it
const processTerm = (term: number, isSubtraction: boolean) => {
const newValue = isSubtraction ? currentValue - term : currentValue + term
// Skip if result would be negative (for subtraction)
if (isSubtraction && newValue < 0) return
// Get skills for this operation (memoized for performance)
const signedTerm = isSubtraction ? -term : term
const stepSkills = analyzeStepSkillsMemoized(currentValue, signedTerm, newValue)
// Check if the step uses only allowed skills (and no forbidden skills)
const usesValidSkills = stepSkills.every((skillPath) => {
if (!isSkillEnabled(skillPath, allowedSkills)) return false
if (forbiddenSkills && isSkillEnabled(skillPath, forbiddenSkills)) return false
return true
})
if (!usesValidSkills) return
// Calculate complexity cost
const termCost = costCalculator ? costCalculator.calculateTermCost(stepSkills) : undefined
// Check max budget - skip if too complex for this student
if (termCost !== undefined && maxBudget !== undefined && termCost > maxBudget) return
// Determine if this term meets the min budget requirement
const meetsMin = minBudget === undefined || termCost === undefined || termCost >= minBudget
const candidate: TermWithSkills = {
term,
skillsUsed: stepSkills,
isSubtraction,
complexityCost: termCost,
metMinBudget: meetsMin,
}
if (meetsMin) {
meetsMinBudget.push(candidate)
} else {
belowMinBudget.push(candidate)
}
}
// Try each possible ADDITION term value
for (let term = min; term <= max; term++) {
processTerm(term, false)
}
// Try each possible SUBTRACTION term value (if allowed)
if (allowSubtraction) {
for (let term = min; term <= max; term++) {
processTerm(term, true)
}
}
return { meetsMinBudget, belowMinBudget }
}
/**
* Finds a valid next term in the sequence and returns both the term and
* the skills that were computed for it (provenance).
* Supports both addition and subtraction operations.
*
* KEY ALGORITHM: State-aware complexity selection
*
* The complexity of a skill depends on the current abacus state:
* - Adding +4 to currentValue=0 uses basic.directAddition (cost 0)
* - Adding +4 to currentValue=7 uses fiveComplements.4=5-1 (cost 1)
*
* This function:
* 1. Collects ALL valid terms (skills allowed, max budget OK)
* 2. Categorizes them: meets minBudget vs. below minBudget
* 3. Prefers terms that meet minBudget
* 4. Falls back to lower-cost terms if no term can meet minBudget
*
* This ensures generation never fails due to impossible budget constraints
* while still preferring appropriately challenging problems.
*/
function findValidNextTermWithTrace(
currentValue: number,
constraints: ProblemConstraints,
allowedSkills: SkillSet,
targetSkills?: Partial<SkillSet>,
forbiddenSkills?: Partial<SkillSet>,
isLastTerm: boolean = false,
allowSubtraction: boolean = false,
costCalculator?: SkillCostCalculator,
previousTerm?: PreviousTerm
): TermWithSkills | null {
// Step 1: Collect all valid terms, categorized by min budget
const { meetsMinBudget, belowMinBudget } = collectValidTerms(
currentValue,
constraints,
allowedSkills,
forbiddenSkills,
allowSubtraction,
costCalculator
)
// Step 2: Choose the best candidate pool
// Prefer terms that meet minBudget, fall back to lower-cost if needed
let candidates: TermWithSkills[]
if (meetsMinBudget.length > 0) {
candidates = meetsMinBudget
} else {
// Graceful fallback: accept lower complexity when budget can't be met
// This handles cases like first term from 0, or states where no term triggers high-cost skills
candidates = belowMinBudget
}
if (candidates.length === 0) return null
// Step 3: Filter out immediate inverses of the previous term
// e.g., if previous was +5, don't allow -5; if previous was -3, don't allow +3
if (previousTerm) {
const nonInverseCandidates = candidates.filter((candidate) => {
if (
candidate.term === previousTerm.term &&
candidate.isSubtraction !== previousTerm.isSubtraction
) {
return false
}
return true
})
// Only use filtered list if it's not empty
if (nonInverseCandidates.length > 0) {
candidates = nonInverseCandidates
}
}
if (candidates.length === 0) return null
// Step 4: If we have target skills and this is not the last term,
// prefer terms that use target skills
if (targetSkills && !isLastTerm) {
const targetCandidates = candidates.filter((candidate) =>
candidate.skillsUsed.some((skillPath) => isSkillEnabled(skillPath, targetSkills))
)
if (targetCandidates.length > 0) {
return targetCandidates[Math.floor(Math.random() * targetCandidates.length)]
}
// Step 4b: No candidates directly use target skills.
// Check if any target skills are state-dependent (need setup).
// If so, prefer terms that SET UP the state for those skills.
const stateDependentTargets = findStateDependentTargetSkills(targetSkills)
if (stateDependentTargets.length > 0) {
// Find candidates that would FULLY set up the state for state-dependent target skills
const setupCandidates = candidates.filter((candidate) =>
stateDependentTargets.some(
(depSkill) =>
!depSkill.canUse(currentValue) && // Not currently usable
depSkill.wouldSetupState(currentValue, candidate.term, candidate.isSubtraction)
)
)
if (setupCandidates.length > 0) {
return setupCandidates[Math.floor(Math.random() * setupCandidates.length)]
}
// Step 4c: No single term can complete the setup.
// Find candidates that PROGRESS toward the setup state (multi-term setup).
// E.g., for heavenBeadSubtraction, prefer terms that increase ones digit toward 5+
const progressCandidates = candidates.filter((candidate) =>
stateDependentTargets.some(
(depSkill) =>
!depSkill.canUse(currentValue) && // Not currently usable
movesTowardSetup(depSkill, currentValue, candidate.term, candidate.isSubtraction)
)
)
if (progressCandidates.length > 0) {
return progressCandidates[Math.floor(Math.random() * progressCandidates.length)]
}
}
}
// Step 5: Return random valid candidate
return candidates[Math.floor(Math.random() * candidates.length)]
}
/**
* Generates an explanation for how to solve the sequential problem (addition and/or subtraction)
*/
function generateSequentialExplanation(terms: number[], sum: number, skills: string[]): string {
const explanations: string[] = []
// Check if problem has mixed operations
const hasSubtraction = terms.some((t) => t < 0)
// Create vertical display format for explanation
const verticalDisplay = `${terms.map((term) => ` ${term >= 0 ? '+' : ''}${term}`).join('\n')}\n---\n ${sum}`
const actionWord = hasSubtraction ? 'computing' : 'adding'
explanations.push(
`Calculate this problem by ${actionWord} each number in sequence:\n${verticalDisplay}`
)
// Skill-specific explanations - Addition
if (skills.includes('basic.directAddition')) {
explanations.push('Use direct addition for numbers 1-4.')
}
if (skills.includes('basic.heavenBead')) {
explanations.push('Use the heaven bead when working with 5 or making totals involving 5.')
}
if (skills.includes('basic.simpleCombinations')) {
explanations.push('Use combinations of heaven and earth beads for 6-9.')
}
if (skills.some((skill) => skill.startsWith('fiveComplements.'))) {
const complements = skills.filter((skill) => skill.startsWith('fiveComplements.'))
explanations.push(
`Apply five complements (addition): ${complements.map((s) => s.split('.')[1]).join(', ')}.`
)
}
if (skills.some((skill) => skill.startsWith('tenComplements.'))) {
const complements = skills.filter((skill) => skill.startsWith('tenComplements.'))
explanations.push(
`Apply ten complements (addition): ${complements.map((s) => s.split('.')[1]).join(', ')}.`
)
}
// Skill-specific explanations - Subtraction
if (skills.includes('basic.directSubtraction')) {
explanations.push('Use direct subtraction for numbers 1-4.')
}
if (skills.includes('basic.heavenBeadSubtraction')) {
explanations.push('Remove the heaven bead when subtracting 5.')
}
if (skills.includes('basic.simpleCombinationsSub')) {
explanations.push('Use subtraction combinations for 6-9.')
}
if (skills.some((skill) => skill.startsWith('fiveComplementsSub.'))) {
const complements = skills.filter((skill) => skill.startsWith('fiveComplementsSub.'))
explanations.push(
`Apply five complements (subtraction): ${complements.map((s) => s.split('.')[1]).join(', ')}.`
)
}
if (skills.some((skill) => skill.startsWith('tenComplementsSub.'))) {
const complements = skills.filter((skill) => skill.startsWith('tenComplementsSub.'))
explanations.push(
`Apply ten complements (subtraction/borrowing): ${complements.map((s) => s.split('.')[1]).join(', ')}.`
)
}
// Advanced skill explanations
if (skills.includes('advanced.cascadingCarry')) {
explanations.push(
'This problem involves cascading carry (carry propagates across 2+ place values).'
)
}
if (skills.includes('advanced.cascadingBorrow')) {
explanations.push(
'This problem involves cascading borrow (borrow propagates across 2+ place values).'
)
}
return explanations.join(' ')
}
/**
* Creates a unique signature for a problem to detect duplicates
*/
function getProblemSignature(terms: number[]): string {
return terms.join('-')
}
/**
* Checks if a problem is a duplicate of any existing problems
*/
function isDuplicateProblem(
problem: GeneratedProblem,
existingProblems: GeneratedProblem[]
): boolean {
const signature = getProblemSignature(problem.terms)
return existingProblems.some((existing) => getProblemSignature(existing.terms) === signature)
}
/**
* Generates multiple unique problems for a practice step
*/
export function generateProblems(practiceStep: PracticeStep): GeneratedProblem[] {
const constraints: ProblemConstraints = {
numberRange: practiceStep.numberRange || { min: 1, max: 9 },
maxSum: practiceStep.sumConstraints?.maxSum,
minSum: practiceStep.sumConstraints?.minSum,
maxTerms: practiceStep.maxTerms,
problemCount: practiceStep.problemCount,
}
const problems: GeneratedProblem[] = []
const problemSignatures = new Set<string>()
const maxAttempts = practiceStep.problemCount * 50 // Increased attempts for better uniqueness
let attempts = 0
let consecutiveFailures = 0
while (problems.length < practiceStep.problemCount && attempts < maxAttempts) {
attempts++
const problem = generateSingleProblem(
constraints,
practiceStep.allowedSkills,
practiceStep.targetSkills,
practiceStep.forbiddenSkills,
150 // More attempts per problem for uniqueness
)
if (problem) {
const signature = getProblemSignature(problem.terms)
// Check for duplicates using both the signature set and existing problems
if (!problemSignatures.has(signature) && !isDuplicateProblem(problem, problems)) {
problems.push(problem)
problemSignatures.add(signature)
consecutiveFailures = 0
} else {
consecutiveFailures++
// If we're getting too many duplicates, the constraints might be too restrictive
if (consecutiveFailures > practiceStep.problemCount * 5) {
console.warn('Too many duplicate problems generated. Constraints may be too restrictive.')
break
}
}
} else {
consecutiveFailures++
}
}
// If we couldn't generate enough unique problems, fill with fallback problems
// but ensure even fallbacks are unique
let fallbackIndex = 0
const maxFallbackIterations = practiceStep.problemCount * 10
let fallbackIterations = 0
while (
problems.length < practiceStep.problemCount &&
fallbackIterations < maxFallbackIterations
) {
fallbackIterations++
let fallbackProblem
let fallbackAttempts = 0
do {
fallbackProblem = generateFallbackProblem(constraints, fallbackIndex++)
fallbackAttempts++
} while (fallbackAttempts < 20 && isDuplicateProblem(fallbackProblem, problems))
// Only add if it's unique or we've exhausted attempts
if (!isDuplicateProblem(fallbackProblem, problems)) {
problems.push(fallbackProblem)
problemSignatures.add(getProblemSignature(fallbackProblem.terms))
} else {
// Last resort: modify the last term slightly to create uniqueness
const modifiedProblem = createModifiedUniqueProblem(fallbackProblem, problems, constraints)
if (modifiedProblem) {
problems.push(modifiedProblem)
problemSignatures.add(getProblemSignature(modifiedProblem.terms))
}
}
}
return problems
}
/**
* Generates a simple fallback problem when constraints are too restrictive
*/
function generateFallbackProblem(constraints: ProblemConstraints, index: number): GeneratedProblem {
const { min, max } = constraints.numberRange
const termCount = 3 // Generate 3-term problems as fallback
// Use the seed index to create variation
const seed = index * 7 + 3 // Prime numbers for better distribution
const terms: number[] = []
for (let i = 0; i < termCount; i++) {
// Create pseudo-random but deterministic terms based on index
const term = ((seed + i * 5) % (max - min + 1)) + min
terms.push(Math.max(min, Math.min(max, term)))
}
const sum = terms.reduce((acc, term) => acc + term, 0)
return {
id: `fallback_${index}_${Date.now()}_${Math.random().toString(36).substr(2, 4)}`,
terms,
answer: sum,
skillsUsed: ['basic.directAddition'],
difficulty: 'easy',
explanation: generateSequentialExplanation(terms, sum, ['basic.directAddition']),
}
}
/**
* Creates a modified version of a problem to ensure uniqueness
*/
function createModifiedUniqueProblem(
baseProblem: GeneratedProblem,
existingProblems: GeneratedProblem[],
constraints: ProblemConstraints
): GeneratedProblem | null {
const { min, max } = constraints.numberRange
// Try modifying the last term to create uniqueness
for (let modifier = 1; modifier <= 3; modifier++) {
for (const direction of [1, -1]) {
const newTerms = [...baseProblem.terms]
const lastIndex = newTerms.length - 1
const newLastTerm = newTerms[lastIndex] + modifier * direction
// Check if the new term is within constraints
if (newLastTerm >= min && newLastTerm <= max) {
newTerms[lastIndex] = newLastTerm
const newSum = newTerms.reduce((acc, term) => acc + term, 0)
// Check sum constraints
if (
(!constraints.maxSum || newSum <= constraints.maxSum) &&
(!constraints.minSum || newSum >= constraints.minSum)
) {
const modifiedProblem: GeneratedProblem = {
id: `modified_${Date.now()}_${Math.random().toString(36).substr(2, 4)}`,
terms: newTerms,
answer: newSum,
skillsUsed: baseProblem.skillsUsed,
difficulty: baseProblem.difficulty,
explanation: generateSequentialExplanation(newTerms, newSum, baseProblem.skillsUsed),
}
// Check if this modification creates a unique problem
if (!isDuplicateProblem(modifiedProblem, existingProblems)) {
return modifiedProblem
}
}
}
}
}
return null // Could not create a unique modification
}
/**
* Validates that a practice step configuration can generate problems
*/
export function validatePracticeStepConfiguration(practiceStep: PracticeStep): {
isValid: boolean
warnings: string[]
suggestions: string[]
} {
const warnings: string[] = []
const suggestions: string[] = []
// Check if any allowed skills are enabled
const hasAnyAllowedSkill =
Object.values(practiceStep.allowedSkills.basic).some(Boolean) ||
Object.values(practiceStep.allowedSkills.fiveComplements).some(Boolean) ||
Object.values(practiceStep.allowedSkills.tenComplements).some(Boolean)
if (!hasAnyAllowedSkill) {
warnings.push('No skills are enabled. Problems may be very basic.')
suggestions.push('Enable at least one skill in the "Allowed Skills" section.')
}
// Check number range vs sum constraints
const maxPossibleSum = practiceStep.numberRange?.max
? practiceStep.numberRange.max * practiceStep.maxTerms
: 9 * practiceStep.maxTerms
if (practiceStep.sumConstraints?.maxSum && practiceStep.sumConstraints.maxSum > maxPossibleSum) {
warnings.push('Maximum sum constraint is higher than what the number range allows.')
suggestions.push('Either increase the number range maximum or decrease the sum constraint.')
}
// Check if constraints are too restrictive
if (practiceStep.sumConstraints?.maxSum && practiceStep.sumConstraints.maxSum < 5) {
warnings.push('Very low sum constraint may limit problem variety.')
suggestions.push('Consider increasing the maximum sum to allow more diverse problems.')
}
// Check problem count
if (practiceStep.problemCount > 20) {
warnings.push('High problem count may take a long time to generate and complete.')
suggestions.push('Consider reducing the problem count for better user experience.')
}
return {
isValid: warnings.length === 0,
warnings,
suggestions,
}
}
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