Treblecross UVA - 10561

版权声明：如有错误，请指出，不胜感激。 https://blog.csdn.net/qq_36424540/article/details/82918186

每个X把区域分成了禁区，也就是说谁先进入必死，因为他下一个，别人就一定会赢，也就是必胜态的位置。

也就是我们如果先手，一定要给对手留下一个必败态，这样对方才会输。所以就是枚举一下位置，判断一下NIM和就好了。

#include<bits/stdc++.h>
using namespace std;
typedef long long LL;
typedef unsigned long long ULL;

#define rep(i,a,b) for(int i=a;i<b;++i)
#define per(i,a,b) for(int i=b-1;i>=a;--i)

const int N=210;

char s[N];
int limit[N];

vector<int> vec;

int sg[N];
bool mex[N];

void get_sg()
{
    sg[0]=0;
    sg[1]=sg[2]=sg[3]=1;
    for(int i=4; i<N; i++) {
        memset(mex,0,sizeof(mex));
        for(int j=i-3; j>=0; --j) {
            int t=max(0,i-(j+5));
            mex[sg[t]^sg[j]]=1;
        }
        for(int j=0;; j++) {
            if(!mex[j]) {
                sg[i]=j;
                break;
            }
        }
    }
    //rep(i,0,50)printf("i:%d %d\n",i,sg[i]);
}

int st[N],ed[N];

int main()
{
	//freopen("123.txt","w",stdout);
    //double t1=clock();
    get_sg();
    //double t2=clock();
    //printf("%.2f\n",(t2-t1)/CLOCKS_PER_SEC);
    int T;
    scanf("%d",&T);
    rep(kase,0,T) {
        scanf("%s",s);
        int len=strlen(s);

        vec.clear();
        fill(st,st+len+1,-1);
        fill(ed,ed+len+1,-1);
        fill(limit,limit+len+1,0);

        rep(i,0,len) {
            if(s[i]=='X') {
                rep(j,0,3) {
                    if(i-j>=0)limit[i-j]=1;
                    if(i+j<len) limit[i+j]=1;
                }
            }
        }

        rep(i,0,len) {
            if(!limit[i]||s[i]=='X')continue;
            if(i+2<len&&s[i+1]=='X'&&s[i+2]=='X'||i-2>=0&&s[i-1]=='X'&&s[i-2]=='X'||i-1>=0&&i+1<len&&s[i-1]=='X'&&s[i+1]=='X')
                vec.push_back(i);
        }
        //rep(i,0,vec.size())printf("i:%d %d\n",i,vec[i]);

        rep(i,0,len) {
            if(limit[i])continue;
            if(i-1>=0&&st[i-1]!=-1)st[i]=st[i-1];
            else st[i]=i;
        }

        per(i,0,len) {
            if(limit[i])continue;
            if(i+1<len&&ed[i+1]!=-1)ed[i]=ed[i+1];
            else ed[i]=i;
        }

        //rep(i,0,len)printf("i:%d st:%d ed:%d\n",i,st[i],ed[i]);

        int sum=0;
        rep(i,0,len) {
            if(limit[i]||s[i]=='X')continue;
            sum=sum^sg[(ed[i]-st[i]+1)];
            i=ed[i];
        }

        //printf("sum:%d\n",sum);

        int sz=vec.size();
        if(sz&&sum==0) {
            printf("WINNING\n");
            rep(i,0,sz)printf("%d%c",vec[i]+1,i==sz-1?'\n':' ');
            continue;
        }


        int t;
        if(sum&&!sz) {
            rep(i,0,len) {
                if(limit[i]||s[i]=='X')continue;
                t=sum^sg[(ed[i]-st[i]+1)];
                int l=max(0,i-st[i]+1-3),r=max(0,ed[i]-i+1-3);
                //printf("i:%d l:%d r:%d t:%d\n",i,l,r,t);
                int tmp=t^sg[l]^sg[r];
                //	printf("tmp:%d\n",tmp);
                if(tmp==0)vec.push_back(i);
            }
        }

        sort(vec.begin(),vec.end());
        sz=vec.size();
        if(sz) {
            printf("WINNING\n");
            rep(i,0,sz)printf("%d%c",vec[i]+1,i==sz-1?'\n':' ');
        } else {
            printf("LOSING\n\n");
        }
    }
    return 0;
}