Proper divisors: Difference between revisions

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@@ Line 2,328: / Line 2,328: @@
 <lang JavaScript>(() => {
+    'use strict';
     // properDivisors :: Int -> [Int]
-    let properDivisors = n => {
+    const properDivisors = n => {
-            let rRoot = Math.sqrt(n),
+        // The integer divisors of n, excluding n itself.
+        const
-                intRoot = Math.floor(rRoot),
-                blnPerfectSquare = rRoot === intRoot,
+            rRoot = Math.sqrt(n),
+            intRoot = Math.floor(rRoot),
+            blnPerfectSquare = rRoot === intRoot,
+            lows = enumFromTo(1)(intRoot)
+            .filter(x => 0 === (n % x));
+        // For perfect squares, we can drop
+        // the head of the 'highs' list
+        return lows.concat(lows
+                .map(x => n / x)
+                .reverse()
+                .slice(blnPerfectSquare | 0)
+            )
+            .slice(0, -1); // except n itself
+    };
-                lows = range(1, intRoot)
-                .filter(x => (n % x) === 0);
+    // ------------------------TESTS-----------------------
-            // for perfect squares, we can drop
-            // the head of the 'highs' list
+    // main :: IO ()
+    const main = () =>
-            return lows.concat(lows
-                    .map(x => n / x)
+        console.log([
-                    .reverse()
+            fTable('Proper divisors of [1..10]:')(str)(
-                    .slice(blnPerfectSquare | 0)
+                JSON.stringify
+            )(properDivisors)(
+                enumFromTo(1)(10)
+            ),
+            '',
+            'Example of maximum divisor count in the range [1..20000]:',
+            '    ' + maximumBy(comparing(snd))(
+                enumFromTo(1)(20000).map(
+                    n => [n, properDivisors(n).length]
                 )
-                .slice(0, -1); // except n itself
+            ).join(' has ') + ' proper divisors.'
-        },
+        ].join('\n'));
-        // range :: Int -> Int -> [Int]
+    // -----------------GENERIC FUNCTIONS------------------
-        range = (m, n) => Array.from({
-            length: (n - m) + 1
+    // comparing :: (a -> b) -> (a -> a -> Ordering)
+    const comparing = f =>
+        x => y => {
+            const
+                a = f(x),
+                b = f(y);
+            return a < b ? -1 : (a > b ? 1 : 0);
+        };
+    // enumFromTo :: Int -> Int -> [Int]
+    const enumFromTo = m => n =>
+        Array.from({
+            length: 1 + n - m
         }, (_, i) => m + i);
+    // fTable :: String -> (a -> String) -> (b -> String)
+    //                      -> (a -> b) -> [a] -> String
+    const fTable = s => xShow => fxShow => f => xs => {
+        // Heading -> x display function ->
+        //           fx display function ->
+        //    f -> values -> tabular string
+        const
+            ys = xs.map(xShow),
+            w = Math.max(...ys.map(x => x.length));
+        return s + '\n' + zipWith(
+            a => b => a.padStart(w, ' ') + ' -> ' + b
+        )(ys)(
+            xs.map(x => fxShow(f(x)))
+        ).join('\n');
+    };
+    // maximumBy :: (a -> a -> Ordering) -> [a] -> a
+    const maximumBy = f => xs =>
+< xs.length ? (
+            xs.slice(1)
+            .reduce((a, x) => 0 < f(x)(a) ? x : a, xs[0])
+        ) : undefined;
+    // snd :: (a, b) -> b
-    return {
+    const snd = tpl => tpl[1];
-        properDivisorsOf1to10: range(1, 10)
-            .reduce((a, x) => (
-                a[x.toString()] = properDivisors(x),
-                a
-            ), {}),
+    // str :: a -> String
-        intMaxDivisorsUnder20k: range(1, 20000)
-            .reduce((a, x) => {
+    const str = x => x.toString();
-                let intDivisors = properDivisors(x)
-                    .length;
-                return intDivisors >= a.divisors ? {
+    // until :: (a -> Bool) -> (a -> a) -> a -> a
-                    max: x,
+    const until = p => f => x => {
-                    divisors: intDivisors
+        let v = x;
-                } : a;
+        while (!p(v)) v = f(v);
+        return v;
+    };
-            }, {
+    // zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]
-                max: 0,
+    const zipWith = f => xs => ys => {
-                divisors: 0
+        const
-            })
+            lng = Math.min(xs.length, xs.length),
+            as = xs.slice(0, lng),
+            bs = ys.slice(0, lng);
+        return Array.from({
+            length: lng
+        }, (_, i) => f(as[i])(
+            bs[i]
+        ));
     };
+    // MAIN ---
+    return main();
 })();</lang>
 {{Out}}
+<pre>Proper divisors of [1..10]:
-<lang JavaScript>{
+-> []
-  "properDivisorsOf1to10":{
+-> [1]
-    "1":[], "2":[1], "3":[1], "4":[1, 2], "5":[1],
+-> [1]
-    "6":[1, 2, 3], "7":[1], "8":[1, 2, 4], "9":[1, 3], "10":[1, 2, 5]
-  },
+-> [1,2]
+-> [1]
-  "intMaxDivisorsUnder20k":{"max":18480, "divisors":79}
+-> [1,2,3]
-}</lang>
+-> [1]
+-> [1,2,4]
+-> [1,3]
+-> [1,2,5]
+Example of maximum divisor count in the range [1..20000]:
+has 79 proper divisors.</pre>
 =={{header|jq}}==