Data commit

Task/Farey-sequence/Vala/farey-sequence.vala

@@ -0,0 +1,52 @@
+struct Fraction {
+  public uint d;
+  public uint n;
+}
+
+void farey(uint n) {
+  Fraction f1 = {0, 1};
+  Fraction f2 = {1, n};
+  print("0/1 1/%u ", n);
+  while (f2.n > 1) {
+    var k = (n + f1.n) / f2.n;
+    var aux = f1;
+    f1 = f2;
+    f2 = {f2.d * k - aux.d, f2.n * k - aux.n};
+    print("%u/%u ", f2.d, f2.n);
+  }
+  print("\n");
+}
+
+uint fareyLength(uint n, uint[] cache) {
+  if (n >= cache.length) {
+    uint newLen = cache.length;
+    if (newLen == 0)
+      newLen = 16;
+    while (newLen <= n)
+      newLen *= 2;
+    cache.resize((int)newLen);
+  }
+  else if (cache[n] != 0)
+    return cache[n];
+
+  uint length = n * (n + 3) / 2;
+  for (uint p = 2, q = 2; p <= n; p = q) {
+    q = n / (n / p) + 1;
+    length -= fareyLength(n / p, cache) * (q - p);
+  }
+
+  cache[n] = length;
+  return length;
+}
+
+void main() {
+  for (uint n = 1; n < 12; n++)
+  {
+    print("%8u: ", n);
+    farey(n);
+  }
+
+  uint[] cache = new uint[0];
+  for (uint n = 100; n <= 1000; n += 100)
+    print("%8u: %14u items\n", n, fareyLength(n, cache));
+}