export type DifficultyName = 'easy' | 'medium' | 'hard' | 'very-hard' | 'insane' | 'inhuman';
export type Difficulty = DifficultyName | number;

const DIGITS = '123456789';
const ROWS = 'ABCDEFGHI';
const COLS = DIGITS;
let SQUARES: string[] = [];
let UNITS: string[][] = [];
let SQUARE_UNITS_MAP: Record<string, string[][]> = {};
let SQUARE_PEERS_MAP: Record<string, string[]> = {};

const MIN_GIVENS = 17;
const NR_SQUARES = 81;

const DIFFICULTY: Record<DifficultyName, number> = {
  easy: 62,
  medium: 53,
  hard: 44,
  'very-hard': 35,
  insane: 26,
  inhuman: 17,
};

const BLANK_CHAR = '.';
const BLANK_BOARD = BLANK_CHAR.repeat(NR_SQUARES);

function initialize() {
  SQUARES = cross(ROWS, COLS);
  UNITS = getAllUnits(ROWS, COLS);
  SQUARE_UNITS_MAP = getSquareUnitsMap(SQUARES, UNITS);
  SQUARE_PEERS_MAP = getSquarePeersMap(SQUARES, SQUARE_UNITS_MAP);
}

function cross(a: string, b: string) {
  const res: string[] = [];
  for (const ai of a) {
    for (const bi of b) {
      res.push(ai + bi);
    }
  }
  return res;
}

function inStr(v: string, seq: string) {
  return seq.indexOf(v) !== -1;
}

function shuffle<T>(seq: T[]): T[] {
  const arr = [...seq];
  for (let i = arr.length - 1; i > 0; i--) {
    const j = Math.floor(Math.random() * (i + 1));
    [arr[i], arr[j]] = [arr[j], arr[i]];
  }
  return arr;
}

function randRange(max: number, min = 0) {
  return Math.floor(Math.random() * (max - min)) + min;
}

function stripDups<T>(seq: T[]): T[] {
  return Array.from(new Set(seq));
}

function forceRange(nr: number, max: number, min = 0) {
  return Math.min(Math.max(nr || 0, min), max);
}

function getAllUnits(rows: string, cols: string) {
  const units: string[][] = [];
  for (const r of rows) units.push(cross(r, cols));
  for (const c of cols) units.push(cross(rows, c));
  const row_blocks = ['ABC', 'DEF', 'GHI'];
  const col_blocks = ['123', '456', '789'];
  for (const rb of row_blocks) {
    for (const cb of col_blocks) {
      units.push(cross(rb, cb));
    }
  }
  return units;
}

function getSquareUnitsMap(squares: string[], units: string[][]) {
  const map: Record<string, string[][]> = {};
  for (const s of squares) {
    const list: string[][] = [];
    for (const u of units) {
      if (u.includes(s)) list.push(u);
    }
    map[s] = list;
  }
  return map;
}

function getSquarePeersMap(squares: string[], units_map: Record<string, string[][]>) {
  const map: Record<string, string[]> = {};
  for (const s of squares) {
    const peers: string[] = [];
    for (const unit of units_map[s]) {
      for (const sq of unit) {
        if (sq !== s && !peers.includes(sq)) peers.push(sq);
      }
    }
    map[s] = peers;
  }
  return map;
}

function getSquareValsMap(board: string) {
  const map: Record<string, string> = {};
  if (board.length !== SQUARES.length) throw 'Board length mismatch';
  for (let i = 0; i < SQUARES.length; i++) {
    map[SQUARES[i]] = board[i];
  }
  return map;
}

function validateBoard(board: string): true | string {
  if (!board) return 'Empty board';
  if (board.length !== NR_SQUARES) return 'Invalid board size';
  for (let i = 0; i < board.length; i++) {
    const c = board[i];
    if (!inStr(c, DIGITS) && c !== BLANK_CHAR) {
      return `Invalid char at ${i}: ${c}`;
    }
  }
  return true;
}

function getCandidatesMap(board: string): Record<string, string> | false {
  const report = validateBoard(board);
  if (report !== true) throw report;

  const map: Record<string, string> = {};
  const squares_values = getSquareValsMap(board);

  for (const s of SQUARES) map[s] = DIGITS;

  for (const s in squares_values) {
    const val = squares_values[s];
    if (inStr(val, DIGITS)) {
      const new_candidates = assign(map, s, val);
      if (!new_candidates) return false;
    }
  }
  return map;
}

function assign(candidates: Record<string, string>, square: string, val: string) {
  const others = candidates[square].replace(val, '');
  for (const v of others) {
    const next = eliminate(candidates, square, v);
    if (!next) return false;
  }
  return candidates;
}

function eliminate(candidates: Record<string, string>, square: string, val: string) {
  if (!inStr(val, candidates[square])) return candidates;

  candidates[square] = candidates[square].replace(val, '');
  const n = candidates[square].length;

  if (n === 1) {
    const target_val = candidates[square];
    for (const peer of SQUARE_PEERS_MAP[square]) {
      const next = eliminate(candidates, peer, target_val);
      if (!next) return false;
    }
  } else if (n === 0) return false;

  for (const unit of SQUARE_UNITS_MAP[square]) {
    const places: string[] = [];
    for (const sq of unit) {
      if (inStr(val, candidates[sq])) places.push(sq);
    }
    if (places.length === 0) return false;
    else if (places.length === 1) {
      const next = assign(candidates, places[0], val);
      if (!next) return false;
    }
  }
  return candidates;
}

function search(candidates: Record<string, string>, reverse: boolean): any {
  if (!candidates) return false;
  reverse = reverse || false;

  let max_nr_candidates = 0;
  for (const s of SQUARES) {
    const n = candidates[s].length;
    if (n > max_nr_candidates) {
      max_nr_candidates = n;
    }
  }
  if (max_nr_candidates === 1) return candidates;

  let min_nr_candidates = 10;
  let min_square = '';
  for (const s of SQUARES) {
    const n = candidates[s].length;
    if (n < min_nr_candidates && n > 1) {
      min_nr_candidates = n;
      min_square = s;
    }
  }

  const min_candidates = candidates[min_square];
  if (!reverse) {
    for (const v of min_candidates) {
      const copy = JSON.parse(JSON.stringify(candidates));
      const next = search(assign(copy, min_square, v), reverse);
      if (next) return next;
    }
  } else {
    for (let i = min_candidates.length - 1; i >= 0; --i) {
      const v = min_candidates[i];
      const copy = JSON.parse(JSON.stringify(candidates));
      const next = search(assign(copy, min_square, v), reverse);
      if (next) return next;
    }
  }
  return false;
}

export class SudokuGenerator {
  static generate(difficulty: Difficulty, unique?: boolean): string {
    let numericDifficulty: number;
    if (typeof difficulty === 'string' || typeof difficulty === 'undefined') {
      numericDifficulty = DIFFICULTY[difficulty as DifficultyName] || DIFFICULTY.easy;
    } else {
      numericDifficulty = difficulty;
    }

    numericDifficulty = forceRange(numericDifficulty, NR_SQUARES + 1, MIN_GIVENS);
    unique = unique ?? true;

    const blank_board = BLANK_BOARD;
    let candidates = getCandidatesMap(blank_board);

    if (!candidates) return SudokuGenerator.generate(numericDifficulty);

    const shuffled_squares = shuffle(SQUARES);

    for (const square of shuffled_squares) {
      const rand_candidate_idx = randRange(candidates[square].length);
      const rand_candidate = candidates[square][rand_candidate_idx];
      if (!assign(candidates, square, rand_candidate)) break;

      const single_candidates: string[] = [];
      for (const s of SQUARES) {
        if (candidates[s].length === 1) single_candidates.push(candidates[s]);
      }

      if (
        single_candidates.length >= numericDifficulty &&
        stripDups(single_candidates).length >= 8
      ) {
        let board = '';
        let givens_idxs: number[] = [];

        for (let i = 0; i < SQUARES.length; i++) {
          const s = SQUARES[i];
          if (candidates[s].length === 1) {
            board += candidates[s];
            givens_idxs.push(i);
          } else {
            board += BLANK_CHAR;
          }
        }

        if (givens_idxs.length > numericDifficulty) {
          givens_idxs = shuffle(givens_idxs);
          for (let i = 0; i < givens_idxs.length - numericDifficulty; ++i) {
            const target = givens_idxs[i];
            board =
              board.substring(0, target) +
              BLANK_CHAR +
              board.substring(target + 1);
          }
        }

        if (SudokuGenerator.solve(board)) return board;
      }
    }

    return SudokuGenerator.generate(numericDifficulty);
  }

  static solve(board: string, reverse?: boolean): string | false {
    const report = validateBoard(board);
    if (report !== true) throw report;

    let nr_givens = 0;
    for (const ch of board) {
      if (ch !== BLANK_CHAR && inStr(ch, DIGITS)) nr_givens++;
    }
    if (nr_givens < MIN_GIVENS) throw 'Too few givens';

    reverse = reverse || false;
    const candidates = getCandidatesMap(board);
    if (!candidates) return false;
    
    const result = search(candidates, reverse);

    if (result) {
      let solution = '';
      for (const s of SQUARES) solution += result[s];
      return solution;
    }
    return false;
  }
}

initialize();