/**
 * Finds the first empty cell in a Sudoku grid.
 * @param grid - The Sudoku grid.
 * @returns The row and column indices of the first empty cell, or an empty array if no empty cells are found.
 */
declare function findFirstEmpty(grid: Array<Array<number>>): [number, number] | [];
/**
 * Finds all empty cells in a Sudoku grid.
 * @param grid - The Sudoku grid.
 * @returns The row and column indices of all empty cells, or an empty array if no empty cells are found.
 */
declare function findAllEmpty(grid: Array<Array<number>>): [number, number][];
/**
 * Checks if placing a number in a cell is valid according to Sudoku rules.
 * @param grid - The Sudoku grid.
 * @param row - The row index.
 * @param col - The column index.
 * @param num - The number to place.
 * @param outputReason - Whether to output the reason for invalid placement.
 * @returns If outputReason is undefined or false, it'll return boolean, else an object with `valid` indicating if the placement is valid and `reason` providing the reason if invalid.
 */
declare function validatePlacement(grid: Array<Array<number>>, row: number, col: number, num: number, outputReason?: boolean): {
    valid: boolean;
    reason?: string;
} | boolean;
/**
 * Validates a Sudoku grid.
 * @param puzzle - The Sudoku grid.
 * @param allowZero - Whether zeros are allowed in the grid, usually applicable to checking if a move is legal.
 * @returns True if valid, false otherwise.
 */
declare function validate(puzzle: Array<Array<number>>, allowZero?: boolean): boolean;
/**
 * Generates a Sudoku puzzle with a specified number of blank cells.
 * @param blank - The number of blank cells.
 * @returns The generated Sudoku grid.
 */
declare function generate(blank?: number): Array<Array<number>>;
/**
 * Solves a Sudoku puzzle.
 * @param puzzle - The Sudoku grid.
 * @returns The solved grid or throws an error if unsolvable.
 */
declare function solve(puzzle: Array<Array<number>>): Array<Array<number>>;

export { findAllEmpty, findFirstEmpty, generate, solve, validate, validatePlacement };