teamnote history merge

2024fall/source/Math/PolladRho.cpp

@@ -0,0 +1,32 @@
+void fact(ll n, vl& ret)
+{
+    if(n == 1) return;
+    if(n%2 == 0)
+    {
+        ret.pb(2);
+        fact(n/2, ret);
+        return;
+    }
+    if(is_p(n))
+    {
+        ret.pb(n);
+        return;
+    }
+    
+    ll a, b, c, g = n;
+    auto f = [&c, &n](ll x)->ll{return (c+(lll)x*x)%n;};
+    do
+    {
+        if(g == n) a=b=rand()%(n-2)+2, c=rand()%20+1;
+        a=f(a); b=f(f(b));
+        g = gcd(a-b, n);
+    }while(g == 1);
+    fact(g, ret); fact(n/g, ret);
+}
+vl po_rho(ll n)
+{
+    vl ret;
+    fact(n, ret);
+    sort(all(ret));
+    return ret;
+}