import { typedSchemas } from "../../widgets/registry";
/**
 * Calculates the greatest common divisor (GCD) of two numbers using the Euclidean algorithm.
 * @param a The first number.
 * @param b The second number.
 * @returns The GCD of a and b.
 */
export declare function gcd(a: number, b: number): number;
/**
 * Determines if a fraction results in a terminating decimal.
 * A fraction terminates if and only if the prime factors of its simplified denominator are only 2s and 5s.
 * @param numerator The numerator of the fraction.
 * @param denominator The denominator of the fraction.
 * @returns True if the fraction terminates, false otherwise.
 */
export declare function isTerminatingFraction(numerator: number, denominator: number): boolean;
export declare function encodeDataUri(content: string): string;
export declare function isValidWidgetType(type: string): type is keyof typeof typedSchemas;
/**
 * Attempts to approximate simple multiplicative/divisive expressions that include π or pi
 * by replacing pi with the provided approximation (default 3.14) and evaluating the expression.
 *
 * Supported forms (case-insensitive for "pi"):
 * - "144*pi", "pi*144", "144pi" (implicit multiplication), "pi144" (rare, but treated as pi*144)
 * - Chains with '*' and '/' only, e.g. "3/2*pi", "pi/4", "6*pi/5", "(144) * (pi)"
 * Parentheses are allowed but only for grouping; no addition/subtraction is supported.
 *
 * Returns a normalized decimal string if evaluation succeeds, otherwise null.
 */
export declare function tryApproximatePiProduct(rawExpr: string, piApprox?: number): string | null;
/**
 * Normalizes a string part for use in a derived QTI identifier.
 * Converts to upper snake case and removes invalid characters.
 * @param part The string part to normalize.
 * @returns The normalized string.
 */
export declare function normalizeIdPart(part: string): string;
/**
 * Derives a deterministic, QTI-safe combo identifier from a path of response parts.
 * @param pathParts An array of strings, where each string is a response-value pair (e.g., "RESPONSE_1_A").
 * @returns The fully-formed combo identifier (e.g., "FB__RESPONSE_1_A__RESPONSE_2_CORRECT").
 */
export declare function deriveComboIdentifier(pathParts: string[]): string;
//# sourceMappingURL=helpers.d.ts.map