nQueens.js

import QueenPosition from './QueenPosition';

/**
 * @param {QueenPosition[]} queensPositions
 * @param {number} rowIndex
 * @param {number} columnIndex
 * @return {boolean}
 */
function isSafe(queensPositions, rowIndex, columnIndex) {
  // New position to which the Queen is going to be placed.
  const newQueenPosition = new QueenPosition(rowIndex, columnIndex);

  // Check if new queen position conflicts with any other queens.
  for (let queenIndex = 0; queenIndex < queensPositions.length; queenIndex += 1) {
    const currentQueenPosition = queensPositions[queenIndex];

    if (
      // Check if queen has been already placed.
      currentQueenPosition
      && (
        // Check if there are any queen on the same column.
        newQueenPosition.columnIndex === currentQueenPosition.columnIndex
        // Check if there are any queen on the same row.
        || newQueenPosition.rowIndex === currentQueenPosition.rowIndex
        // Check if there are any queen on the same left diagonal.
        || newQueenPosition.leftDiagonal === currentQueenPosition.leftDiagonal
        // Check if there are any queen on the same right diagonal.
        || newQueenPosition.rightDiagonal === currentQueenPosition.rightDiagonal
      )
    ) {
      // Can't place queen into current position since there are other queens that
      // are threatening it.
      return false;
    }
  }

  // Looks like we're safe.
  return true;
}

/**
 * @param {QueenPosition[][]} solutions
 * @param {QueenPosition[]} previousQueensPositions
 * @param {number} queensCount
 * @param {number} rowIndex
 * @return {boolean}
 */
function nQueensRecursive(solutions, previousQueensPositions, queensCount, rowIndex) {
  // Clone positions array.
  const queensPositions = [...previousQueensPositions].map((queenPosition) => {
    return !queenPosition ? queenPosition : new QueenPosition(
      queenPosition.rowIndex,
      queenPosition.columnIndex,
    );
  });

  if (rowIndex === queensCount) {
    // We've successfully reached the end of the board.
    // Store solution to the list of solutions.
    solutions.push(queensPositions);

    // Solution found.
    return true;
  }

  // Let's try to put queen at row rowIndex into its safe column position.
  for (let columnIndex = 0; columnIndex < queensCount; columnIndex += 1) {
    if (isSafe(queensPositions, rowIndex, columnIndex)) {
      // Place current queen to its current position.
      queensPositions[rowIndex] = new QueenPosition(rowIndex, columnIndex);

      // Try to place all other queens as well.
      nQueensRecursive(solutions, queensPositions, queensCount, rowIndex + 1);

      // BACKTRACKING.
      // Remove the queen from the row to avoid isSafe() returning false.
      queensPositions[rowIndex] = null;
    }
  }

  return false;
}


/**
 * @param {number} queensCount
 * @return {QueenPosition[][]}
 */
export default function nQueens(queensCount) {
  // Init NxN chessboard with zeros.
  // const chessboard = Array(queensCount).fill(null).map(() => Array(queensCount).fill(0));

  // This array will hold positions or coordinates of each of
  // N queens in form of [rowIndex, columnIndex].
  const queensPositions = Array(queensCount).fill(null);

  /** @var {QueenPosition[][]} solutions */
  const solutions = [];

  // Solve problem recursively.
  nQueensRecursive(solutions, queensPositions, queensCount, 0);

  return solutions;
}