Game theory AcWing 894. Split -Nim game

Original link

AcWing 894. Split -Nim game

Algorithm tags

Math knowledge Game theory SG function

Ideas

Code

#include<bits/stdc++.h>
#define int long long
#define abs fabs
#define rep(i, a, b) for(int i=a;i<b;++i)
#define Rep(i, a, b) for(int i=a;i>=b;--i)
using namespace std;
const int N = 105, M = 10005;
int f[M];
int n;
inline int read(){
   int s=0,w=1;
   char ch=getchar();
   while(ch<'0'||ch>'9'){if(ch=='-')w=-1;ch=getchar();}
   while(ch>='0'&&ch<='9') s=s*10+ch-'0',ch=getchar();
   return s*w;
}
void put(int x) {
    if(x<0) putchar('-'),x=-x;
    if(x>=10) put(x/10);
    putchar(x%10^48);
}
int sg(int x){
    if(f[x]!=-1){
        return f[x]; 
    }else{
        unordered_set<int> S;
        //  Quantity requirements for the first pile 
        rep(i, 0, x){
        	//  Quantity requirements of the second pile 
            rep(j, 0, i+1){
                S.insert(sg(i)^sg(j));
            }
        }
        // mex  function 
        for(int i=0;;++i){
            if(!S.count(i)){
                return f[x]=i;
            }
        }
    }
}
signed main(){
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);
    memset(f, -1, sizeof f);
    n=read();
    int ans=0;
    while(n--){
        int x=read();
        ans^=sg(x);
    }
    if(ans){
        puts("Yes");
    }else{
        puts("No");
    }
}

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