Data commit

Task/Zumkeller-numbers/D/zumkeller-numbers.d

@@ -0,0 +1,91 @@
+import std.algorithm;
+import std.stdio;
+
+int[] getDivisors(int n) {
+    auto divs = [1, n];
+    for (int i = 2; i * i <= n; i++) {
+        if (n % i == 0) {
+            divs ~= i;
+
+            int j = n / i;
+            if (i != j) {
+                divs ~= j;
+            }
+        }
+    }
+    return divs;
+}
+
+bool isPartSum(int[] divs, int sum) {
+    if (sum == 0) {
+        return true;
+    }
+    auto le = divs.length;
+    if (le == 0) {
+        return false;
+    }
+    auto last = divs[$ - 1];
+    int[] newDivs;
+    for (int i = 0; i < le - 1; i++) {
+        newDivs ~= divs[i];
+    }
+    if (last > sum) {
+        return isPartSum(newDivs, sum);
+    } else {
+        return isPartSum(newDivs, sum) || isPartSum(newDivs, sum - last);
+    }
+}
+
+bool isZumkeller(int n) {
+    auto divs = getDivisors(n);
+    auto sum = divs.sum();
+    // if sum is odd can't be split into two partitions with equal sums
+    if (sum % 2 == 1) {
+        return false;
+    }
+    // if n is odd use 'abundant odd number' optimization
+    if (n % 2 == 1) {
+        auto abundance = sum - 2 * n;
+        return abundance > 0 && abundance % 2 == 0;
+    }
+    // if n and sum are both even check if there's a partition which totals sum / 2
+    return isPartSum(divs, sum / 2);
+}
+
+void main() {
+    writeln("The first 220 Zumkeller numbers are:");
+    int i = 2;
+    for (int count = 0; count < 220; i++) {
+        if (isZumkeller(i)) {
+            writef("%3d ", i);
+            count++;
+            if (count % 20 == 0) {
+                writeln;
+            }
+        }
+    }
+
+    writeln("\nThe first 40 odd Zumkeller numbers are:");
+    i = 3;
+    for (int count = 0; count < 40; i += 2) {
+        if (isZumkeller(i)) {
+            writef("%5d ", i);
+            count++;
+            if (count % 10 == 0) {
+                writeln;
+            }
+        }
+    }
+
+    writeln("\nThe first 40 odd Zumkeller numbers which don't end in 5 are:");
+    i = 3;
+    for (int count = 0; count < 40; i += 2) {
+        if (i % 10 != 5 && isZumkeller(i)) {
+            writef("%7d ", i);
+            count++;
+            if (count % 8 == 0) {
+                writeln;
+            }
+        }
+    }
+}