/**
 * Random practice-problem generator.
 *
 * Problems are built BACKWARD from a chosen integer answer: pick the solution
 * first, then assemble an equation around it. This guarantees the problem is
 * solvable, the answer is clean, and difficulty is exactly the templates and
 * coefficient ranges we draw from. Every problem returns its solution(s) so a
 * practice loop can check the learner and serve the next one.
 *
 * The engine stays pure: randomness is an injected `Rng` (a `() => number` in
 * [0, 1)), never ambient `Math.random`. Callers pass `Math.random` (or a seeded
 * PRNG in tests).
 *
 * Single-variable topics go through `generateProblem`; two-variable systems
 * (two equations) go through `generateSystem`.
 */
import { type Equation } from "./expr.js";
import { Rational } from "./rational.js";
export type Difficulty = "easy" | "medium" | "hard";
export type ProblemTopic = "linear-one-step" | "linear-two-step" | "linear-both-sides" | "distribution" | "fractions" | "power" | "inequality" | "quadratic";
export interface ProblemSpec {
    readonly topic: ProblemTopic;
    readonly difficulty: Difficulty;
}
export interface GeneratedProblem {
    readonly equation: Equation;
    /** Value(s) of the variable that solve it — two for a distinct-root
     *  quadratic; for an inequality, a witness point inside the solution set. */
    readonly solutions: readonly Rational[];
    readonly topic: ProblemTopic;
    readonly difficulty: Difficulty;
}
export interface SystemProblem {
    readonly equations: readonly [Equation, Equation];
    readonly x: Rational;
    readonly y: Rational;
    readonly difficulty: Difficulty;
}
/** Uniform random in [0, 1) — inject `Math.random` or a seeded PRNG. */
export type Rng = () => number;
/** Topics with display labels, for building a picker. */
export declare const PROBLEM_TOPICS: readonly {
    readonly id: ProblemTopic;
    readonly label: string;
}[];
export declare const DIFFICULTIES: readonly Difficulty[];
/**
 * Generate a random single-variable problem. The equation is guaranteed
 * well-formed and solvable, with `solutions` its exact answer(s) (a witness
 * point for inequalities). `rng` supplies randomness — `Math.random` in the
 * app, a seeded PRNG in tests.
 */
export declare function generateProblem(spec: ProblemSpec, rng: Rng): GeneratedProblem;
/**
 * Generate a random 2×2 linear system with a unique integer solution (x, y).
 * The coefficient matrix is non-singular by construction, so it solves by
 * substitution or elimination.
 */
export declare function generateSystem(difficulty: Difficulty, rng: Rng): SystemProblem;
//# sourceMappingURL=generate.d.ts.map