29 n-queens puzzle - the backtracking solution

queens.js

// the backtracking (one kind of recursion) code paradigm: 
// - build a helper function with extra arguments to pass on choices and other useful information during recursive calls
// - in the helper function, the base case is for handling the result after series of choices
// - in the helper function, the recursive case is usually in the 'choose-explore-unchoose' pattern

function queen(size) {
  var result = queenHelper(size, [], [])
  return result
}

function queenHelper(size, chosen, solutions) {
  if (chosen.length == size) {
    solutions.push(chosen.slice())
  } else {
    for (var i = 0; i < size; i++) {
      if (safe(i, chosen)) {
        chosen.push(i)
        queenHelper(size, chosen, solutions)
        chosen.pop()
      }
    }
    return solutions
  }
}

function safe(x, positions) {
  return !included(x, positions) && !diagonal(x, positions)
}

function included(x, arr) {
  return arr.some(i => i == x)
}

function diagonal(x, arr) {
  return arr.some((t, i) => x - arr.length == t - i || x + arr.length == t + i)
}

var result = queen(8)
console.log(result.length) // 92