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| Time Limit: 1000MS | Memory Limit: 65536K | |
| Total Submissions: 1148 | Accepted: 375 |
Description
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| Figure 1 | Figure 2 | Figure 3a | Figure 3b | Figure 4 |
Your task is to decide if a specified sequence of moves in the board game Twixt ends with a winning move.
In this version of the game, different board sizes may be specified. Pegs are placed on a board at integer coordinates in the range [0, N]. Players Black and White use pegs of their own color. Black always starts and then alternates with White, placing a peg
at one unoccupied position (x,y). Black‘s endzones are where x equals 0 or N, and White‘s endzones are where y equals 0 or N. Neither player may place a peg in the other player‘s endzones. After each play the latest position is connected by a segment to every
position with a peg of the same color that is a chess knight‘s move away (2 away in one coordinate and 1 away in the other), provided that a new segment will touch no segment already added, except at an endpoint. Play stops after a winning move, which is when
a player‘s segments complete a connected path between the player‘s endzones.
For example Figure 1 shows a board with N=4 after the moves (0,2), (2,4), and (4,2). Figure 2 adds the next move (3,2). Figure 3a shows a poor next move of Black to (2,3). Figure 3b shows an alternate move for Black to (2,1) which would win the game.
Figure 4 shows the board with N=7 after Black wins in 11 moves:
(0, 3), (6, 5), (3, 2), (5, 7), (7, 2), (4, 4), (5, 3), (5, 2), (4, 5), (4, 0), (2, 4).
Input
The input contains from 1 to 20 datasets followed by a line containing only two zeroes, "0 0". The first line of each dataset contains the maximum coordinate N and the number of total moves M where 3 < N < 21, 4 < M < 250, and
M is odd. The rest of the dataset contains a total of M coordinate pairs, with one or more pairs per line. All numbers on a line will be separated by a space. M being odd means that Black will always be the last player. All data will be legal. There will never
be a winning move before the last move.
Output
The output contains one line for each data set: "yes" if the last move is a winning move and "no" otherwise.
Sample Input
4 5 0 2 2 4 4 2 3 2 2 3 4 5 0 2 2 4 4 2 3 2 2 1 7 11 0 3 6 5 3 2 5 7 7 2 4 4 5 3 5 2 4 5 4 0 2 4 0 0
Sample Output
no yes yes
Source
Mid-Central USA 2005
黑白棋的游戏，在n*n的棋盘上，黑棋先手，且最后一步是黑棋。当黑棋从x=0连接的到x=n，时黑棋获胜，问最后一步是不是致胜的一步
每个点都可以和它周围的八个点连接，类似象棋中的马，但是在连接两个点的时候，在连线之间不能有其他的连线（包括黑棋自身的连线）。所以在连接一条线的时候，要判断其他的可能会切割这条线的九条线是否存在。
先判断不包含最后一步的黑棋能不能胜利，再判断加上最后一步后能不能获胜，如果开始不能获胜，后来获胜，那么输出yes，否则，输出no
#include <cstdio>
#include <cstring>
#include <queue>
#include <algorithm>
using namespace std ;
int vis[500] ;
int Map[25][25] , c[500][500] ;//ºÚΪ1£¬°×Ϊ-1
queue <int> que ;
void solve1(int i,int j,int n,int temp)
{
if( (i-1) >= 0 && (i+1) < n && (j-1) >= 0 && c[ (i-1)*n+j ][ (i+1)*n+(j-1) ] != 0 )
return ;
if( (i-1) >= 0 && (j-2) >= 0 && (i+1) < n && (j-1) >= 0 && c[ (i-1)*n+(j-2) ][ (i+1)*n+(j-1) ] != 0 )
return ;
if( (j-3) >= 0 && (i+1) < n && (j-1) >= 0 && c[ i*n+(j-3) ][ (i+1)*n+(j-1) ] != 0 )
return ;
if( (j-1) >= 0 && (i+1) < n && (j+1) < n && c[ i*n+(j-1) ][ (i+1)*n+(j+1) ] != 0 )
return ;
if( (j-1) >= 0 && (i+2) < n && c[ i*n+(j-1) ][ (i+2)*n+j ] != 0 )
return ;
if( (j-1) >= 0 && (i+2) < n && (j-2) >= 0 && c[ i*n+(j-1) ][ (i+2)*n+(j-2) ] != 0 )
return ;
if( (i-1) >= 0 && (j-1) >= 0 && (i+1) < n && c[ (i-1)*n+(j-1) ][ (i+1)*n+j ] != 0 )
return ;
if( (i+1) < n && (j-2) >= 0 && c[ (i+1)*n+j ][ i*n+(j-2) ] != 0 )
return ;
if( (j-2) >= 0 && (i+2) < n && (j-1) >= 0 && c[ i*n+(j-2) ][ (i+2)*n+(j-1) ] != 0 )
return ;
c[ i*n+j ][ (i+1)*n+(j-2) ] = c[ (i+1)*n+(j-2) ][ i*n+j ] = temp ;
return ;
}
void solve2(int u,int v,int n,int temp)
{
if( (u-1) >= 0 && (v-1) >= 0 )
{
if( (u+1) < n && c[ (u-1)*n+(v-1) ][ (u+1)*n+v ] != 0 ) return ;
if( (u+1) < n && (v-2) >= 0 && c[ (u-1)*n+(v-1) ][ (u+1)*n+(v-2) ] != 0 ) return ;
if( (v-3) >= 0 && c[ (u-1)*n+(v-1) ][ u*n+(v-3) ] != 0 ) return ;
}
if( (v-1) >= 0 )
{
if( (u-1) >= 0 && (v+1) < n && c[ u*n+(v-1) ][ (u-1)*n+(v+1) ] != 0 ) return ;
if( (u-2) >= 0 && c[ u*n+(v-1) ][ (u-2)*n+v ] != 0 ) return ;
if( (u-2) >= 0 && (v-2) >= 0 && c[ u*n+(v-1) ][ (u-2)*n+(v-2) ] != 0 ) return ;
}
if( (u+1) < n && (v-1) >= 0 && (u-1) >= 0 && c[ (u+1)*n+(v-1) ][ (u-1)*n+v ] != 0 ) return ;
if( (u-1) >= 0 && (v-2) >= 0 && c[ (u-1)*n+v ][ u*n+(v-2) ] != 0 ) return ;
if( (v-2) >= 0 && (u-2) >= 0 && (v-1) >= 0 && c[ u*n+(v-2) ][ (u-2)*n+(v-1) ] != 0 ) return ;
c[ u*n+v ][ (u-1)*n+(v-2) ] = c[ (u-1)*n+(v-2) ][ u*n+v ] = temp ;
return ;
}
void solve3(int u,int v,int n,int temp)
{
if( (u+1) < n )
{
if( (u-1) >= 0 && (v-1) >= 0 && c[ (u+1)*n+v ][ (u-1)*n+(v-1) ] != 0 ) return ;
if( (v-2) >= 0 && c[ (u+1)*n+v ][ u*n+(v-2) ] != 0 ) return ;
if( (u+2) < n && (v-2) >= 0 && c[ (u+1)*n+v ][ (u+2)*n+(v-2) ] != 0 ) return ;
}
if( (u+1) < n && (v-1) >= 0 )
{
if( (v+1) < n && c[ (u+1)*n+(v-1) ][ u*n+(v+1) ] != 0 ) return ;
if( (u+2) < n && (v+1) < n && c[ (u+1)*n+(v-1) ][ (u+2)*n+(v+1) ] != 0 ) return ;
if( (u+3) < n && c[ (u+1)*n+(v-1) ][ (u+3)*n+v ] != 0 ) return ;
}
if( (u+1) < n && (v+1) < n && (v-1) >= 0 && c[ (u+1)*n+(v+1) ][ u*n+(v-1) ] != 0 ) return ;
if( (v-1) >= 0 && (u+2) < n && c[ u*n+(v-1) ][ (u+2)*n+v ] != 0 ) return ;
if( (u+2) < n && (u+1) < n && (v-2) >= 0 && c[ (u+2)*n+v ][ (u+1)*n+(v-2) ] != 0 ) return ;
c[ u*n+v ][ (u+2)*n+(v-1) ] = c[ (u+2)*n+(v-1) ][ u*n+v ] = temp ;
return ;
}
void solve4(int u,int v,int n,int temp)
{
if( (u-1) >= 0 )
{
if( (u-2) >= 0 && (v-2) >= 0 && c[ (u-1)*n+v ][ (u-2)*n+(v-2) ] != 0 ) return ;
if( (v-2) >= 0 && c[ (u-1)*n+v ][ u*n+(v-2) ] != 0 ) return ;
if( (u+1) < n && (v-1) >= 0 && c[ (u-1)*n+v ][ (u+1)*n+(v-1) ] != 0 ) return ;
}
if( (u-1) >= 0 && (v-1) >= 0 )
{
if( (u-3) >= 0 && c[ (u-1)*n+(v-1) ][ (v-3)*n+v ] != 0 ) return ;
if( (u-2) >= 0 && (v+1) < n && c[ (u-1)*n+(v-1) ][ (u-2)*n+(v+1) ] != 0 ) return ;
if( (v+1) < n && c[ (u-1)*n+(v-1) ][ u*n+(v+1) ] != 0 ) return ;
}
if( (u-1) >= 0 && (v+1) < n && (v-1) >= 0 && c[ (u-1)*n+(v+1) ][ u*n+(v-1) ] != 0 ) return ;
if( (v-1) >= 0 && (u-2) >= 0 && c[ u*n+(v-1) ][ (u-2)*n+v ] != 0 ) return ;
if( (u-2) >= 0 && (v-2) >= 0 && c[ (u-2)*n+v ][ (u-1)*n+(v-2) ] != 0 ) return ;
c[ u*n+v ][ (u-2)*n+(v-1) ] = c[ (u-2)*n+(v-1) ][ u*n+v ] = temp ;
return ;
}
int bfs(int u,int n)
{
int v , i , j ;
while( !que.empty() ) que.pop() ;
vis[u] = 1 ;
que.push(u) ;
while( !que.empty() )
{
u = que.front() ;
que.pop() ;
if( u >= (n-1)*n )
return 1 ;
for(i = 0 ; i < n*n ; i++)
{
if( c[u][i] == 1 && vis[i] == 0 )
{
vis[i] = 1 ;
que.push(i) ;
}
}
}
return 0 ;
}
void solve(int temp,int n)
{
int u , v ;
scanf("%d %d", &u, &v) ;
Map[u][v] = temp ;
if( (u+1) < n && (v-2) >= 0 && Map[u][v] == Map[u+1][v-2] )
solve1(u,v,n,temp);
if( (u-1) >= 0 && (v+2) < n && Map[u][v] == Map[u-1][v+2] )
solve1(u-1,v+2,n,temp) ;
if( (u-1) >= 0 && (v-2) >= 0 && Map[u][v] == Map[u-1][v-2] )
solve2(u,v,n,temp) ;
if( (u+1) < n && (v+2) < n && Map[u][v] == Map[u+1][v+2] )
solve2(u+1,v+2,n,temp) ;
if( (u+2) < n && (v-1) >= 0 && Map[u][v] == Map[u+2][v-1] )
solve3(u,v,n,temp) ;
if( (u-2) >= 0 && (v+1) < n && Map[u][v] == Map[u-2][v+1] )
solve3(u-2,v+1,n,temp) ;
if( (u-2) >= 0 && (v-1) >= 0 && Map[u][v] == Map[u-2][v-1] )
solve4(u,v,n,temp) ;
if( (u+2) < n && (v+1) < n && Map[u][v] == Map[u+2][v+1] )
solve4(u+2,v+1,n,temp) ;
}
int main()
{
int n , m , x , y , u , v , temp , i , j ;
while( scanf("%d %d", &n, &m) != EOF )
{
if( m == 0 && n == 0 ) break ;
n++ ;
memset(Map,0,sizeof(vis)) ;
memset(c,0,sizeof(c)) ;
temp = 1 ;
m-- ;
while( m-- )
{
solve(temp,n) ;
temp = -temp ;
}
int k1 = 0 , k2 = 0 ;
memset(vis,0,sizeof(vis)) ;
for(j = 0 ; j < n ; j++)
{
if( Map[0][j] == 1 && vis[j] == 0 )
{
k1 = bfs(j,n) ;
if( k1 == 1 ) break ;
}
}
solve(temp,n) ;
memset(vis,0,sizeof(vis)) ;
for(j = 0 ; j < n ; j++)
{
if( Map[0][j] == 1 && vis[j] == 0 )
{
k2 = bfs(j,n) ;
if( k2 == 1 ) break ;
}
}
if( k1 == 0 && k2 == 1)
printf("yes\n") ;
else
printf("no\n") ;
}
return 0;
}