Hdu1847 good luck in CET-4 everybody! , Bashi game, understanding SG Functions

Hdu1847 good luck in CET-4 everybody!

Question:

There are n cards in total, and both parties take turns to capture cards. The number of cards each time can only be 2 power times (I .e., 16 ...), After the card is captured, the result of the victory is also displayed: the winner of the card is the final one. Give N. Can I ask if I win first or later?

PS: of course, this question can be launched directly n % 3 = 0 to defeat, otherwise it will win. // Bashi game

The following introduces another method.

SG value: the SG value of a vertex is the smallest integer greater than or equal to zero that is not equal to the SG value of its successor vertex. // Same as the Mex () function

Simply put, it is the distance from the current status to the nearest point of failure.

SG (x) = Mex {SG (s )}
S is a set of SG function values in the subsequent State of X. Mex (s) indicates the minimum non-negative integer that is not in S.
SG (x) = 0 if and only if X is defeated.

Let's enumerate the SG values with a card number of 0 to 10:
Num: 0 1 2 3 4 5 6 7 8 9 10
SG value: 0 1 2 0 1 2 0 1 2 0 1

# Include <cstdio> # include <cstring> # include <algorithm> using namespace STD; const int maxn = 1000 + 10; int arr [11], SG [maxn]; void pre () {// calculate all the cards that may be taken within 1000 at a time! Arr [0] = 1; for (INT I = 1; I <= 10; ++ I) Arr [I] = arr [I-1] * 2 ;} int Mex (int x) {// This is an algorithm function for solving the SG value of this point (using a memory search) if (SG [x]! =-1) return SG [X]; bool vis [maxn]; memset (VIS, false, sizeof vis); For (INT I = 0; I <10; ++ I) {int temp = x-Arr [I]; If (temp <0) break; SG [temp] = Mex (temp ); vis [SG [temp] = true;} For (INT I = 0; ++ I) {If (! Vis [I]) {SG [x] = I; break;} return SG [X];} int main () {int N; Pre (); while (scanf ("% d", & N )! = EOF) {memset (SG,-1, sizeof SG); If (MEX (N) printf ("Kiki \ n "); else printf ("Cici \ n");} return 0 ;}

Hdu1847 good luck in CET-4 everybody! , Bashi game, understanding SG Functions