CDE

Task/Average-loop-length/D/average-loop-length.d

@@ -0,0 +1,44 @@
+import std.stdio, std.random, std.math, std.algorithm, std.range;
+
+real analytical(in int n) /*pure nothrow*/ {
+    real total = 0.0;
+    foreach (immutable k; 1 .. n + 1) {
+        immutable x = reduce!q{a * b}(1.0L, iota(n - k + 1, n + 1))
+                      * k ^^ 2;
+        total += x / ((cast(real)n) ^^ (k + 1));
+    }
+    return total;
+}
+
+size_t loopLength(size_t maxN)(in int size, ref Xorshift rng) {
+    __gshared bool[maxN + 1] seen;
+    seen[0 .. size + 1] = false;
+    int current = 1;
+    size_t steps = 0;
+    while (!seen[current]) {
+        seen[current] = true;
+        current = uniform(1, size + 1, rng);
+        steps++;
+    }
+    return steps;
+}
+
+void main() {
+    enum maxN  = 40;
+    enum nTrials = 300_000;
+    auto rng = Xorshift(unpredictableSeed);
+    writeln(" n    average    analytical     (error)");
+    writeln("===  =========  ============  ==========");
+
+    foreach (immutable n; 1 .. maxN + 1) {
+        long total = 0;
+        foreach (immutable _; 0 .. nTrials)
+            total += loopLength!maxN(n, rng);
+        immutable average = total / cast(real)nTrials;
+        immutable an = analytical(n);
+        immutable percentError = abs(an - average) / an * 100;
+        immutable errorS = format("%2.4f", percentError);
+        writefln("%3d  %9.5f  %12.5f  (%7s%%)",
+                 n, average, an, errorS);
+    }
+}