CF 256C Furlo and Rublo and Game

The brute-force SG function will time out. The positive solution is to process the SG value of less than 10 ^ 6 and calculate the larger value after the root number.

Small Data observations show that sg function values are generated in segments and increase rapidly. Therefore, you can calculate the range of each segment. You only need to create a table.

 

 

 

Nim games:

Nim and: L. bouton gives a theorem in the State (X1, X2 ,..., .... xor Xn = 0. xor is a binary bitwise xor or operation.

 

# Include <iostream> # include <algorithm> using namespace std; typedef long ll; ll x, a [] = {3, 15, 81,672 3, 50625,256 2991875LL }; int sg [] = {0, 1, 2, 0, 3, 1, 2}, n, ans = 0; int main () {cin> n; while (n --) {cin> x; ans ^ = sg [lower_bound (a, a + 6, x)-a];} cout <(ans? "Furlo": "Rublo") <endl; return 0 ;}