list_monad_send_money.js

// Inspired by http://blog.plover.com/prog/monad-search-2.html

//     S E N D
// +   M O R E
// -----------
//   M O N E Y

function toNumber(digits) {
    var r = 0;
    for (var i = 0; i < digits.length; i++) {
        r += digits[i] * Math.pow(10, digits.length - i - 1);
    }
    return r;
}

function chooseADigit(digits, each) {
    for (var i = 0; i < digits.length; i++) {
        var digit = digits[i];
        var remain = digits.slice(0, i).concat(digits.slice(i + 1));
        each(remain, digit);
    }
}

function chooseFilter(choice, filter, digits, each) {
    choice(digits, function got(digits, digit) {
        if (filter(digit)) {
            each(digits, digit);
        }
    });
}

function notZero(digit) {
    return digit !== 0;
}

function chooseWaterfall(choices, digits, each) {
    if (!choices.length) {
        each(digits, []);
        return;
    }

    firstChoice(digits, [], 0);

    function firstChoice(digits, r, i) {
        choices[i](digits, function got(digits, digit) {
            var s = r.concat([digit]);
            nextChoice(digits, s, 1);
        });
    }

    function nextChoice(digits, r, i) {
        if (i >= choices.length) {
            each(digits, r);
            return;
        }

        choices[i](r, digits, function got(digits, digit) {
            var s = r.concat([digit]);
            nextChoice(digits, s, i + 1);
        });
    }
}

function chooseSeries(choices, digits, each) {
    nextChoice(digits, [], 0);

    function nextChoice(digits, r, i) {
        if (i >= choices.length) {
            each(digits, r);
            return;
        }

        choices[i](digits, function got(digits, digit) {
            var s = r.concat([digit]);
            nextChoice(digits, s, i + 1);
        });
    }
}


var start = process.hrtime();

function chooseThree(digits, next) {
    return chooseSeries([
        chooseADigit,
        chooseADigit,
        chooseADigit
    ], digits, next);
}

function chooseTwo(digits, next) {
    return chooseSeries([
        chooseADigit,
        chooseADigit
    ], digits, next);
}

function chooseInitial(digits, next) {
    chooseFilter(chooseADigit, notZero, digits, next);
}

function chooseTwoInitials(digits, next) {
    chooseSeries([
        chooseInitial,
        chooseInitial
    ], digits, next);
}

function chooseDEY(digits, next) {
    chooseFilter(chooseThree, checkSum, digits, next);
}

function chooseNR(groups, digits, next) {
    chooseFilter(chooseTwo, checkSecondSum, digits, next);
    function checkSecondSum(nr) {
        return checkSum(groups[0], nr);
    }
}

function chooseO(groups, digits, next) {
    chooseFilter(chooseADigit, checkThirdSum, digits, next);
    function checkThirdSum(o) {
        return checkSum(groups[0], groups[1], o);
    }
}

function chooseSM(groups, digits, next) {
    chooseFilter(chooseTwoInitials, function checkFourthSum(sm) {
        return checkSum(groups[0], groups[1], groups[2], sm);
    }, digits, next);
}

function checkSum(dey, nr, o, sm) {
    var d = dey[0];
    var e = dey[1];
    var y = dey[2];
    if ((d + e) % 10 != y) return false;

    if (nr === undefined) return true;
    var rem1 = Math.floor((d + e) / 10);

    var n = nr[0];
    var r = nr[1];
    if ((n + r + rem1) % 10 != e) return false;

    if (o === undefined) return true;
    var rem2 = Math.floor((n + r + rem1) / 10);

    if ((e + o + rem2) % 10 != n) return false;


    if (sm === undefined) return true;
    var rem3 = Math.floor((e + o + rem2) / 10);

    var s = sm[0];
    var m = sm[1];

    if ((s + m + rem3) % 10 !== o) return false;

    var rem4 = Math.floor((s + m + rem3) / 10);
    return rem4 === m;
}

chooseWaterfall([
    chooseDEY,
    chooseNR,
    chooseO,
    chooseSM
], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], function process(digits, groups) {
    var dey = groups[0];
    var d = dey[0];
    var e = dey[1];
    var y = dey[2];

    var nr = groups[1];
    var n = nr[0];
    var r = nr[1];

    var o = groups[2];

    var sm = groups[3];
    var s = sm[0];
    var m = sm[1];

    var send = toNumber([s, e, n, d]);
    var more = toNumber([m, o, r, e]);
    var money = toNumber([m, o, n, e, y]);

    console.log('%s + %s = %s', send, more, money);
});
var end = process.hrtime();

var d = [
    end[0] - start[0],
    end[1] - start[1]
];
if (d[1] < 0) {
    d[0]--;
    d1 += 1e9;
}
console.log('took %sms', d[0] * 1e3 + d[1] / 1e6);