# Light OJ: 1401 – No More Tic-tac-toe / UVa 11534 – Say Goodbye to Tic-Tac-Toe

http://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&category=24&page=show_problem&problem=2529

http://www.lightoj.com/volume_showproblem.php?problem=1401

Solutiono Idea: Straight Forward Grundy theory. Think a gap as a nim pile.

```
#include &lt;bits/stdc++.h&gt;
//#include &lt;ext/pb_ds/assoc_container.hpp&gt;
//#include &lt;ext/pb_ds/tree_policy.hpp&gt;

#define pii              pair &lt;int,int&gt;
#define pll              pair &lt;long long,long long&gt;
#define sc               scanf
#define pf               printf
#define Pi               2*acos(0.0)
#define ms(a,b)          memset(a, b, sizeof(a))
#define pb(a)            push_back(a)
#define MP               make_pair
#define db               double
#define ll               long long
#define EPS              10E-10
#define ff               first
#define ss               second
#define sqr(x)           (x)*(x)
#define D(x)             cerr&lt;&lt;#x &quot; = &quot;&lt;&lt;(x)&lt;&lt;endl
#define VI               vector &lt;int&gt;
#define DBG              pf(&quot;Hi\n&quot;)
#define MOD              1000000007
#define CIN              ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0)
#define SZ(a)            (int)a.size()
#define sf(a)            scanf(&quot;%d&quot;,&amp;a)
#define sfl(a)           scanf(&quot;%lld&quot;,&amp;a)
#define sff(a,b)         scanf(&quot;%d %d&quot;,&amp;a,&amp;b)
#define sffl(a,b)        scanf(&quot;%lld %lld&quot;,&amp;a,&amp;b)
#define sfff(a,b,c)      scanf(&quot;%d %d %d&quot;,&amp;a,&amp;b,&amp;c)
#define sfffl(a,b,c)     scanf(&quot;%lld %lld %lld&quot;,&amp;a,&amp;b,&amp;c)
#define stlloop(v)       for(__typeof(v.begin()) it=v.begin();it!=v.end();it++)
#define loop(i,n)        for(int i=0;i&lt;n;i++)
#define loop1(i,n)       for(int i=1;i&lt;=n;i++)
#define REP(i,a,b)       for(int i=a;i&lt;b;i++)
#define RREP(i,a,b)      for(int i=a;i&gt;=b;i--)
#define TEST_CASE(t)     for(int z=1;z&lt;=t;z++)
#define PRINT_CASE       printf(&quot;Case %d: &quot;,z)
#define LINE_PRINT_CASE  printf(&quot;Case %d:\n&quot;,z)
#define CASE_PRINT       cout&lt;&lt;&quot;Case &quot;&lt;&lt;z&lt;&lt;&quot;: &quot;
#define all(a)           a.begin(),a.end()
#define intlim           2147483648
#define infinity         (1&lt;&lt;28)
#define ull              unsigned long long
#define gcd(a, b)        __gcd(a, b)
#define lcm(a, b)        ((a)*((b)/gcd(a,b)))

using namespace std;

//using namespace __gnu_pbds;
//typedef tree&lt;int, null_type, less&lt;int&gt;, rb_tree_tag, tree_order_statistics_node_update&gt; ordered_set;

/*----------------------Graph Moves----------------*/
//const int fx[]={+1,-1,+0,+0};
//const int fy[]={+0,+0,+1,-1};
//const int fx[]={+0,+0,+1,-1,-1,+1,-1,+1};   // Kings Move
//const int fy[]={-1,+1,+0,+0,+1,+1,-1,-1};  // Kings Move
//const int fx[]={-2, -2, -1, -1,  1,  1,  2,  2};  // Knights Move
//const int fy[]={-1,  1, -2,  2, -2,  2, -1,  1}; // Knights Move
/*------------------------------------------------*/

//int Set(int N,int pos){return N=N | (1&lt;&lt;pos);}
//int reset(int N,int pos){return N= N &amp; ~(1&lt;&lt;pos);}
//bool check(int N,int pos){return (bool)(N &amp; (1&lt;&lt;pos));}
/*------------------------------------------------*/

char str[201];

int dp[102][3][3];

int grundy(int len, int lft, int rgt)
{
if(len&lt;=0) return 0;
if(len==1 &amp;&amp; lft==rgt &amp;&amp; lft!=2) return 1;
if(len==1 &amp;&amp; lft!=rgt &amp;&amp; lft!=2 &amp;&amp; rgt!=2 ) return 0;
int &amp;ret=dp[len][lft][rgt];
if(ret!=-1) return ret;
set&lt;int&gt;st;
for(int i=1; i&lt;=len; i++)
{
int a=0,b=0;
if(i==1)
{
if(lft!=0)
{a=grundy(i-1,lft,0)^grundy(len-i,0,rgt);st.insert(a);}
if(lft!=1)
{b=grundy(i-1,lft,1)^grundy(len-i,1,rgt);st.insert(b);}
}
else if(i==len)
{
if(rgt!=0)
{a=grundy(i-1,lft,0)^grundy(len-i,0,rgt);st.insert(a);}
if(rgt!=1)
{b=grundy(i-1,lft,1)^grundy(len-i,1,rgt);st.insert(b);}
}
else
{
a=grundy(i-1,lft,0)^grundy(len-i,0,rgt);
b=grundy(i-1,lft,1)^grundy(len-i,1,rgt);
st.insert(a);
st.insert(b);
}
}

int x=0;
while(st.find(x)!=st.end()) x++;
return ret=x;
}

int main()
{

//    freopen(&quot;in.txt&quot;,&quot;r&quot;,stdin);
//	  freopen(&quot;out.txt&quot;,&quot;w&quot;,stdout);

int t;
sf(t);
ms(dp,-1);
TEST_CASE(t)
{
scanf(&quot; %s&quot;,str);
int ans=0;
int len=strlen(str);
int last=-1;
for(int i=0; i&lt;len; i++)
{
if(str[i]!='.')
{
if(str[i]=='O')
{
ans^=grundy(i-last-1,2,0);
}
else
{
ans^=grundy(i-last-1,2,1);
}
last=i;
break;
}
}

for(int i=last+1; i&lt;len; i++)
{
if(str[i]!='.')
{
if(str[i]=='O')
{
ans^=grundy(i-last-1,str[last]=='X',0);
}
else
{
ans^=grundy(i-last-1,str[last]=='X',1);
}
last=i;
}
}
if(last==-1)
ans^=grundy(len-last-1,2,2);
else
ans^=grundy(len-last-1,str[last]=='X',2);

//        PRINT_CASE;

int cnt=0;
for(int i=0; i&lt;len; i++) cnt+=(str[i]!='.');
if(cnt%2==0)
{

if(ans)
printf(&quot;Possible.\n&quot;);
else
printf(&quot;Impossible.\n&quot;);
}
else
{
if(ans==0)
printf(&quot;Possible.\n&quot;);
else
printf(&quot;Impossible.\n&quot;);
}
}

return 0;
}

```