[javascript]n-queens in evolutional way

nqueens.js

// queens: column numbers of queen in each row : 0-7
var isValid = function (queens) {
    return queens.every(function (cur, index) {
        for (var i = index + 1; i < queens.length; i++) {
            if (cur === queens[i]) return false;  // as same column
            if (cur + index === queens[i] + i) return false; // as 07=16=25=...
            if (cur - index === queens[i] - i) return false; // as 00=11=22=...
        }
        return true;
    })
};


//[S1] iterating solution
var nQueens1 = function (n) {
    var init = function (n) {
        return Array.apply(null, Array(n)).map(function () {return 0;});
    };
    var next = function (queens) {
        for (var i = 0; i < queens.length; i++) {
            if (queens[i] + 1 !== queens.length) {
                queens[i] += 1;
                return true;
            } else {
                queens[i] = 0; //carry up
            }
        }
        return queens[queens.length - 1] !== 0; // false when overflow
    };

    // main
    var queens = init(n);
    var c = 0;
    do {
        if (isValid(queens)) {
            //console.log(queens);
            c++;
        }
    } while (next(queens));
    return c;
};
console.log("[S1]", nQueens1(8)); // 92


//[S2] backtracking solution
var nQueens2 = function (n) {
    var c = 0;
    var queens = [];
    (function solve() {
        if (queens.length === n) {
            if (isValid(queens)) {
                //console.log(queens);
                c++;
            }
            return;
        }

        for (var i = 0; i < n; i++) {
            queens.push(i);
            solve();
            queens.pop();
        }
    })();
    return c;
};
console.log("[S2]", nQueens2(8)); // 92


//[S3] backtracking solution2: high perfoemance
var nQueens3 = function (n) {
    var c = 0;
    var queens = [];
    (function solve() {
        if (queens.length === n) {
            //console.log(queens);
            c++;
            return;
        }

        for (var i = 0; i < n; i++) {
            queens.push(i);
            if (isValid(queens)) solve();
            queens.pop();
        }
    })();
    return c;
};
console.log("[S3]", nQueens3(8)); // 92


//[S4] immutable list solution
var nQueens4 = function (n) {
    var c = 0;
    (function solve(queens) {
        if (queens.length === n) {
            //console.log(queens);
            c++;
            return;
        }
        
        for (var i = 0; i < n; i++) {
            var nextqueens = queens.concat([i]);
            if (isValid(nextqueens)) solve(nextqueens);
        }
    })([]);
    return c;
};
console.log("[S4]", nQueens4(8)); // 92


//[S5] functional way: everything immutable
var nQueens5 = function (n) {
    // list helpers
    var range = function (n) {
        return Array.apply(null, Array(n)).map(function (e, i) {return i;});
    };
    
    return (function solve(queens) {
        if (queens.length === n) {
            //console.log(queens);
            return 1;
        }

        return range(n).map(function (i) {
            return queens.concat([i]);
        }).filter(isValid).map(solve).reduce(function (total, c) {
            return total + c;
        }, 0);
    })([]);
};
console.log("[S5]", nQueens5(8)); // 92