added brent cycle finding algorithm

Author: fredbr

math/brent.cpp

@@ -0,0 +1,41 @@
+#include <tuple>
+
+using namespace std;
+
+template<typename T>
+tuple<int, int> brent(T const& v) {
+    int power = 1;
+    int lam = 1;
+    auto tortoise = v, hare = next(v);
+
+    while (tortoise != hare) {
+        if (power == lam) {
+            tortoise = hare;
+            power *= 2;
+            lam = 0;
+        }
+        hare = next(hare);
+        lam++;
+    }
+
+    int it = 0;
+    tortoise = hare = v;
+    for (int i = 0; i < lam; i++) {
+        hare = next(hare);
+    }
+    // now hare has walked lambda distance
+
+    int mu = 0;
+    tortoise = v;
+    while (tortoise != hare) {
+        tortoise = next(tortoise);
+        hare = next(hare);
+        mu++;
+    }
+    // hare has walked lambda+mu and 
+    // tortoise has walked mu
+    // they meet at start of cycle
+
+    // lenght outside of cycle and cycle lenght
+    return {mu, lam};
+}