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import type { SeededRandom } from '../../../../lib/SeededRandom'
const GRID_MIN = -15
const GRID_MAX = 15
const MAX_ATTEMPTS = 50
/**
* Equation-first number generation — guarantees integer solutions by construction.
*
* 1. Pick m from frame's slopeRange (per difficulty constraints)
* 2. Pick b from frame's interceptRange (0 at levels 1-2)
* 3. Pick xAnswer from frame's xRange
* 4. Compute yTarget = m * xAnswer + b
* 5. Validate: yTarget in range, everything fits grid bounds
* 6. Retry if invalid (bounded attempts, fallback values)
*/
export function generateNumbers(
frame: SemanticFrame,
difficulty: DifficultyLevel,
rng: SeededRandom
): GeneratedNumbers {
for (let attempt = 0; attempt < MAX_ATTEMPTS; attempt++) {
const result = tryGenerate(frame, difficulty, rng)
if (result) return result
}
// Fallback: simple values guaranteed to work
return fallbackNumbers(frame, difficulty)
}
function tryGenerate(
frame: SemanticFrame,
difficulty: DifficultyLevel,
rng: SeededRandom
): GeneratedNumbers | null {
let m: number
let b: number
if (difficulty === 1) {
// y = b (constant function)
m = 0
b = rng.nextInt(frame.interceptRange.min, frame.interceptRange.max)
if (b === 0) b = 1 // avoid trivial y = 0
} else if (difficulty === 2) {
// y = mx (proportional, no intercept)
m = rng.nextInt(frame.slopeRange.min, frame.slopeRange.max)
b = 0
} else {
// y = mx + b (full linear)
m = rng.nextInt(frame.slopeRange.min, frame.slopeRange.max)
b = rng.nextInt(frame.interceptRange.min, frame.interceptRange.max)
}
const xAnswer = rng.nextInt(frame.xRange.min, frame.xRange.max)
const yTarget = m * xAnswer + b
// Validate y is in frame's range
if (yTarget < frame.yRange.min || yTarget > frame.yRange.max) return null
// Validate key points are within grid bounds (viewport auto-adjusts, but keep reasonable)
if (!fitsGrid(xAnswer, yTarget)) return null
// For level 4 (two points → equation), generate two distinct points on the line
let point1: { x: number; y: number } | undefined
let point2: { x: number; y: number } | undefined
if (difficulty === 4) {
const pts = generateTwoPoints(m, b, frame, rng)
if (!pts) return null
point1 = pts.point1
point2 = pts.point2
}
return { m, b, xAnswer, yTarget, point1, point2 }
}
function generateTwoPoints(
m: number,
b: number,
frame: SemanticFrame,
rng: SeededRandom
): { point1: { x: number; y: number }; point2: { x: number; y: number } } | null {
// Collect all valid integer x values with corresponding y on the line within grid bounds
const validPoints: { x: number; y: number }[] = []
for (
let x = Math.max(GRID_MIN, frame.xRange.min);
x <= Math.min(GRID_MAX, frame.xRange.max);
x++
) {
const y = m * x + b
if (y >= GRID_MIN && y <= GRID_MAX && Number.isInteger(y)) {
validPoints.push({ x, y })
}
}
if (validPoints.length < 2) return null
// Pick two distinct points
const [p1, p2] = rng.pickN(validPoints, 2)
return { point1: p1, point2: p2 }
}
function fitsGrid(xAnswer: number, yTarget: number): boolean {
// xAnswer should be within grid bounds (user needs to find it on the ruler)
if (xAnswer < GRID_MIN || xAnswer > GRID_MAX) return false
// yTarget can exceed default grid view — viewport animation will auto-zoom
// But keep it within a reasonable range for readability
if (yTarget < -500 || yTarget > 500) return false
return true
}
function fallbackNumbers(frame: SemanticFrame, difficulty: DifficultyLevel): GeneratedNumbers {
if (difficulty === 1) {
const b = Math.max(1, frame.interceptRange.min)
return { m: 0, b, xAnswer: 1, yTarget: b }
}
if (difficulty === 2) {
const m = frame.slopeRange.min
return { m, b: 0, xAnswer: 1, yTarget: m }
}
// Level 3+
const m = frame.slopeRange.min
const b = Math.max(frame.interceptRange.min, 1)
const xAnswer = 1
const yTarget = m * xAnswer + b
return {
m,
b,
xAnswer,
yTarget,
...(difficulty === 4 ? { point1: { x: 0, y: b }, point2: { x: 1, y: m + b } } : {}),
}
}
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