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2110x 2x 2x 2x 2x 2x 8x 8x 8x 8x 8x 8x 8x 8x 8x 8x 8x 8x 8x 8x 8x 96x 96x 96x 96x 96x 96x 96x 96x 96x 96x 96x 96x 96x 96x 96x 29x 29x 29x 96x 67x 67x 67x 67x 1x 1x 1x 67x 96x 96x 8x 8x 8x 8x 8x 8x 8x 8x 101x 8x 100x 100x 100x 100x 100x 1981x 1981x 100x 100x 100x 100x 1x 1x 100x 99x 99x 99x 99x 100x 8x 8x 8x 2x 2x 2x 2x 1981x 1981x 1981x 1981x 1981x 1981x 1981x 1981x 1981x 5943x 5943x 5943x 5943x 1981x 1981x 1981x 1981x 1981x 1981x 1981x 1981x 1981x 1981x 1981x 1981x 2x 2x 2x 2x 99x 99x 99x 99x 99x 99x 99x 99x 99x 297x 594x 594x 594x 594x 594x 594x 99x 99x 99x 99x 99x 99x 99x 99x 99x 99x 99x 99x 99x 99x 99x 99x 99x 99x 99x 99x 99x 594x 297x 297x 297x 297x 2x 2x 2x 2x 2x 9x 9x 9x 9x 9x 9x 9x 9x 9x 9x 2x 2x 9x 9x 2x 2x 2x 9x 9x 9x 1x 8x 9x 9x 2x 2x 2x 9x 9x 9x 2x 2x 2x 9x 9x 9x 2x 2x 2x 9x 9x 9x 9x 9x 9x 9x | import type {
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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