28 n-queens puzzle - a declarative solution

queens.js

function queen(n) {
  // a array of numerical sequence from 0 to n - 1
  var sequence = enumerateInterval(0, n - 1)
  // returns the sub-solution for n-queen's problem while placing k(k < n) queens on the first k rows of the board
  function queenRow(k) {
    if (k == 0) {
      return [[]]
    } else {
      var restQueens = queenRow(k - 1)
      // just place the nth queen on any place of the new row to generate a bunch of new solutions
      var solutions = combine(restQueens, sequence)
      // and filter solutions that is safe
      return filter((positions) => safe(positions), solutions)
    }
  }
  return queenRow(n)
}

// a1 is an array of array, a2 is an array
// this function will append every element in a2 into every element(array) in a1 and flatten the result
// ex. combine([[0, 1], [2, 3]], [4, 5]) will return [ [ 0, 1, 4 ], [ 0, 1, 5 ], [ 2, 3, 4 ], [ 2, 3, 5 ] ]
function combine(a1, a2) {
  return flatMap((x) => {
    return map((y) => {
      if (typeof x == 'object') {
        var t = x.slice()
        t.push(y)
        return t
      } else {
        return [x, y]
      }
    }, a2)
  }, a1)
}

// test if the positions of queens is not attacking each other
// because of recursion, we can assume that all but the last queen is safe.
// therefore we only check the last queen against other queens
function safe(positions) {
  var pos = positions.slice()
  var i = pos.pop()
  return _safe(i, pos)
}

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)
}

function enumerateInterval(low, high) {
  var result = []
  for (var i = low; i <= high; i++) {
    result.push(i)
  }
  return result
}

function flatMap(proc, list) {
  return flatten(map(proc, list))
}

function flatten(arr) {
  return arr.reduce((a, b) => {
    return a.concat(b)
  }, [])
}

function map(proc, list) {
  return list.map(proc)
}

function filter(proc, list) {
  return list.filter(proc)
}

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