September 2017 Update

Task/Narcissistic-decimal-number/JavaScript/narcissistic-decimal-number-4.js

@@ -0,0 +1,107 @@
+(() => {
+    'use strict';
+
+    // DAFFODILS --------------------------------------------------------------
+
+    // narcissiOfLength :: Int -> [Int]
+    const narcissiOfLength = n =>
+        n > 0 ? filter(curry(isDaffodil)(n), digitPowerSums(n)) : [0];
+
+    // Do the decimal digits of N, each raised to the power E, sum to N itself ?
+
+// isDaffodil :: Int -> Int -> Bool
+const isDaffodil = (e, n) => {
+    const
+        powerSum = (n, xs) => xs.reduce((a, x) => a + Math.pow(x, n), 0),
+        digitList = n => (n > 0) ? (
+            cons((n % 10), digitList(Math.floor(n / 10)))
+        ) : [],
+        ds = digitList(n);
+    return e === ds.length && n === powerSum(e, ds);
+};
+
+    // The subset of integers of n digits that actually need daffodil checking:
+
+    // (Flattened leaves of a tree of unique digit combinations, in which
+    // order is not significant. Digit sequence doesn't affect power summing)
+
+    // digitPowerSums :: Int -> [Int]
+    const digitPowerSums = nDigits => {
+        const
+            digitPowers = map(x => [x, pow(x, nDigits)], enumFromTo(0, 9)),
+            treeGrowth = (n, parentPairs) => (n > 0) ? (
+                treeGrowth(n - 1,
+                    isNull(parentPairs) ? (
+                        digitPowers
+                    ) : concatMap(([parentDigit, parentSum]) =>
+                        map(([leafDigit, leafSum]) => //
+                            [leafDigit, parentSum + leafSum],
+                            take(parentDigit + 1, digitPowers)
+                        ),
+                        parentPairs
+                    ))
+            ) : parentPairs;
+        return map(snd, treeGrowth(nDigits, []));
+    };
+
+    // GENERIC FUNCTIONS ------------------------------------------------------
+
+    // enumFromTo :: Int -> Int -> Maybe Int -> [Int]
+    const enumFromTo = (m, n, step) => {
+        const d = (step || 1) * (n >= m ? 1 : -1);
+        return Array.from({
+            length: Math.floor((n - m) / d) + 1
+        }, (_, i) => m + (i * d));
+    };
+    // concatMap :: (a -> [b]) -> [a] -> [b]
+    const concatMap = (f, xs) => [].concat.apply([], xs.map(f));
+
+    // cons :: a -> [a] -> [a]
+    const cons = (x, xs) => [x].concat(xs);
+
+    // 2 or more arguments
+    // curry :: Function -> Function
+    const curry = (f, ...args) => {
+        const go = xs => xs.length >= f.length ? (f.apply(null, xs)) :
+            function () {
+                return go(xs.concat([].slice.apply(arguments)));
+            };
+        return go([].slice.call(args, 1));
+    };
+
+    // filter :: (a -> Bool) -> [a] -> [a]
+    const filter = (f, xs) => xs.filter(f);
+
+    // map :: (a -> b) -> [a] -> [b]
+    const map = curry((f, xs) => xs.map(f));
+
+    // isNull :: [a] -> Bool
+    const isNull = xs => (xs instanceof Array) ? xs.length < 1 : undefined;
+
+    // length :: [a] -> Int
+    const length = xs => xs.length;
+
+    // pow :: Int -> Int -> Int
+    const pow = Math.pow
+
+    // take :: Int -> [a] -> [a]
+    const take = (n, xs) => xs.slice(0, n);
+
+    // show ::
+    // (a -> String) f,  Num n =>
+    // a -> maybe f -> maybe n -> String
+    const show = JSON.stringify;
+
+    // snd :: (a, b) -> b
+    const snd = tpl => Array.isArray(tpl) ? tpl[1] : undefined;
+
+
+    // TEST -------------------------------------------------------------------
+
+    // return length(concatMap(digitPowerSums, enumFromTo(0, 7)));
+
+    return show(
+        //digitPowerSums(3)
+        concatMap(narcissiOfLength, enumFromTo(0, 7))
+    );
+})();