js: n Queens solver

nqueens.js

Queens = function(num) {

	function range(n) {
		return Array.apply(null, new Array(n)).map(function(_, i) { return i; });
	};

	function is_safe(q, qs) {
		if(qs.length == 0) return true;
		return qs.filter(function(x, i) {
			return Math.abs(q - x) != Math.abs(qs.length - (qs.length - (i + 1)));
		}).length == qs.length;
	};

	function permutate(list) {
		if(list.length == 1) return [list];
		var collect = [];

		permutate(list.slice(1)).map(function(p, j, a) {
			range(p.length + 1).map(function(b, i) {
				collect.push(p.slice(0, i).concat([list[0]]).concat(p.slice(i)));
			});
		});

		return collect;
	};

	return {
		solutions: (function(n) {
			var queens = permutate(range(n));

			return queens.filter(function(s) {
				return s.filter(function(q, i, a) { return is_safe(q, a.slice(i + 1)); }).length == s.length;
			});
		})(num),

		show: function(x) {
			var solution = this.solutions[x];
			return "\n" + solution.map(function(s) {
				return range(solution.length).map(function(p, i) {
					return s == i ? ' ' + s + ' ' : ' . ';
				}).join('');
			}).join("\n") + "\n";
		},

		showAll: function() {
			var self = this;
			return range(this.solutions.length).map(function(x) { return self.show(x); }).join("\n");
		}
	};
};