hdu 5795

Posted 2020-08-16 见字如面

A Simple Nim

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/65536 K (Java/Others)
Total Submission(s): 948    Accepted Submission(s): 559

Problem Description

Two players take turns picking candies from n heaps,the player who picks the last one will win the game.On each turn they can pick any number of candies which come from the same heap(picking no candy is not allowed).To make the game more interesting,players can separate one heap into three smaller heaps(no empty heaps)instead of the picking operation.Please find out which player will win the game if each of them never make mistakes.

 

 

Input

Intput contains multiple test cases. The first line is an integer 1≤T≤100, the number of test cases. Each case begins with an integer n, indicating the number of the heaps, the next line contains N integers s[0],s[1],....,s[n?1], representing heaps with s[0],s[1],...,s[n?1] objects respectively.(1≤n≤106,1≤s[i]≤109)

 

 

Output

For each test case,output a line whick contains either"First player wins."or"Second player wins".

 

 

Sample Input

2 2 4 4 3 1 2 4

 

 

Sample Output

Second player wins. First player wins.

 

 

Author

UESTC

 

 

Source

2016 Multi-University Training Contest 6

 最近学长讲博弈论  给我们讲了些题目 包括这道题 

主要是求sg函数，打表1-40就可以看出规律，(带码学别人的）

x%8==7 sg（）=x+1；

x%8==0 sg（）=x-1；

其他  sg（）=x

 1 #include<iostream>
 2 #include<cstdio>
 3 #include<cmath>
 4 #include<cstring>
 5 using namespace std;
 6 int visited[100];
 7 int sg[100];
 8 int main(){
 9     /*int i,j,k;
10     for(i=1;i<40;i++){
11         memset(visited,0,sizeof(visited));
12         for(j=0;j<i;j++)visited[sg[j]]=1;
13         for(j=1;j<i;j++){
14             for(k=1;k+j<i;k++){
15                 visited[sg[j]^sg[k]^sg[i-k-j]]=1;
16             }
17         }
18         for(j=0;j<40;j++){
19             if(visited[j]==0){
20                 break;
21             }
22         }
23         sg[i]=j;
24     }
25     for(i=1;i<40;i++){
26         cout<<i<<" "<<sg[i]<<endl;
27     }*/
28     int t;
29     scanf("%d",&t);
30     int n,i,x;
31     int ans;
32     while(t--){
33         scanf("%d",&n);
34         ans=0;
35         for(i=0;i<n;i++){
36             scanf("%d",&x);
37             if(x%8==0){
38                 x=x-1;
39                 ans=ans^x;
40             }
41             else if(x%8==7){
42                 x=x+1;
43                 ans=ans^x;
44             }
45             else
46                 ans=ans^x;
47 
48         }
49         cout<<ans<<endl;
50     }
51 }