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Task/Digital-root-Multiplicative-digital-root/D/digital-root-multiplicative-digital-root-1.d

@@ -0,0 +1,27 @@
+import std.stdio, std.algorithm, std.typecons, std.range, std.conv;
+
+/// Multiplicative digital root.
+auto mdRoot(in int n) pure /*nothrow*/ {
+    auto mdr = [n];
+    while (mdr.back > 9)
+        mdr ~= reduce!q{a * b}(1, mdr.back.text.map!(d => d - '0'));
+        //mdr ~= mdr.back.text.map!(d => d - '0').mul;
+        //mdr ~= mdr.back.reverseDigits.mul;
+    return tuple(mdr.length - 1, mdr.back);
+}
+
+void main() {
+    "Number: (MP, MDR)\n======  =========".writeln;
+    foreach (immutable n; [123321, 7739, 893, 899998])
+        writefln("%6d: (%s, %s)", n, n.mdRoot[]);
+
+    auto table = (int[]).init.repeat.enumerate!int.take(10).assocArray;
+    auto n = 0;
+    while (table.byValue.map!walkLength.reduce!min < 5) {
+        table[n.mdRoot[1]] ~= n;
+        n++;
+    }
+    "\nMP: [n0..n4]\n==  ========".writeln;
+    foreach (const mp; table.byKey.array.sort())
+        writefln("%2d: %s", mp, table[mp].take(5));
+}

Task/Digital-root-Multiplicative-digital-root/D/digital-root-multiplicative-digital-root-2.d

@@ -0,0 +1,34 @@
+import std.stdio, std.algorithm, std.typecons, std.range;
+
+uint digitsProduct(uint n) pure nothrow @nogc {
+    typeof(return) result = !!n;
+    while (n) {
+        result *= n % 10;
+        n /= 10;
+    }
+    return result;
+}
+
+/// Multiplicative digital root.
+Tuple!(size_t, uint) mdRoot(uint m) pure nothrow {
+    auto mdr = m
+               .recurrence!((a, n) => a[n - 1].digitsProduct)
+               .until!q{ a <= 9 }(OpenRight.no).array;
+    return tuple(mdr.length - 1, mdr.back);
+}
+
+void main() {
+    "Number: (MP, MDR)\n======  =========".writeln;
+    foreach (immutable n; [123321, 7739, 893, 899998])
+        writefln("%6d: (%s, %s)", n, n.mdRoot[]);
+
+    auto table = (int[]).init.repeat.enumerate!int.take(10).assocArray;
+    auto n = 0;
+    while (table.byValue.map!walkLength.reduce!min < 5) {
+        table[n.mdRoot[1]] ~= n;
+        n++;
+    }
+    "\nMP: [n0..n4]\n==  ========".writeln;
+    foreach (const mp; table.byKey.array.sort())
+        writefln("%2d: %s", mp, table[mp].take(5));
+}

Task/Digital-root-Multiplicative-digital-root/D/digital-root-multiplicative-digital-root-3.d

@@ -0,0 +1,36 @@
+import std.stdio, std.algorithm, std.range;
+
+/// Multiplicative digital root.
+uint[2] mdRoot(in uint n) pure nothrow @nogc {
+    uint mdr = n;
+    uint count = 0;
+
+    while (mdr > 9) {
+        uint m = mdr;
+        uint digitsMul = !!m;
+        while (m) {
+            digitsMul *= m % 10;
+            m /= 10;
+        }
+        mdr = digitsMul;
+        count++;
+    }
+
+    return [count, mdr];
+}
+
+void main() {
+    "Number: [MP, MDR]\n======  =========".writeln;
+    foreach (immutable n; [123321, 7739, 893, 899998])
+        writefln("%6d: %s", n, n.mdRoot);
+
+    auto table = (int[]).init.repeat.enumerate!int.take(10).assocArray;
+    auto n = 0;
+    while (table.byValue.map!walkLength.reduce!min < 5) {
+        table[n.mdRoot[1]] ~= n;
+        n++;
+    }
+    "\nMP: [n0..n4]\n==  ========".writeln;
+    foreach (const mp; table.byKey.array.sort())
+        writefln("%2d: %s", mp, table[mp].take(5));
+}