## 2013年9月18日 星期三

### UVA 11198 - Dancing Digits

Keyword: BFS, prime number, map(hash)

Algorithm:

Using BFS, list all states after dancing for one time.
If not done, dance the second, and the third... time.
Before dancing, make sure it can be done by dancing.
If numbers are all positive or negative and the list is not sorted, it'll never be sorted because no dance can happen.
Be careful when moving the digits. :)

Code:
```#include<cstdio>
#include<map>
#include<queue>
#include<cctype>
#include<cmath>
#include<cstdlib>
#define t true
#define f false
using namespace std;
const int power10[ 8 ] = { 10000000, 1000000, 100000, 10000, 1000, 100, 10, 1 };
const bool prime[] = { f, f, t, t, f, t, f, t, f, f, f, t, f, t, f, f };
inline int getdig( int num, int dig ) { return num / power10[ dig ] % 10; }
int cov( int *n )
{
if( n == NULL )
return -1;
int back = 0;
for( int i = 0; i < 8; ++i )
back += abs( n[ i ] ) * power10[ i ];
return back;
}
int* cov( int n, int *array )
{
for( int i = 0; i < 8; ++i )
array[ i ] = getdig( n, i );
return array;
}
bool cant( int *n, bool greater )
{
for( int i = 1; i < 8; ++i )
if( n[ i ] > 0 != greater )
return false;
return true;
}
int* insert( bool *sign, int *array, int from, int to )
{
int ins = array[ from ], tmp = 0;
for( int i = 0; i < 8; ++i )
if( array[ i ] != ins )
array[ tmp++ ] = array[ i ];
for( int i = 7; i > to; --i )
array[ i ] = array[ i-1 ];
array[ to ] = ins;
if( to && prime[ array[ to ] + array[ to-1 ] ] )
if( sign[ array[ to ] ] ^ sign[ array[ to-1 ] ] )
return array;
if( to < 7 && prime[ array[ to ] + array[ to+1 ] ] )
if( sign[ array[ to ] ] ^ sign[ array[ to+1 ] ] )
return array;
return NULL;
}

int main()
{
int dig[ 9 ] = { 0 }, T = 0;

while( scanf( "%d", dig ) && *dig )
{
int status, cp[ 9 ] = { 0 };
bool sign[ 9 ] = { false };
queue<int> perm;
map<int,int> visited;
for( int i = 1; i < 8; ++i )
scanf( "%d", dig+i );
for( int i = 0; i < 8; ++i )
sign[ dig[ i ] ] = dig[ i ] > 0;
status = cov( dig );
perm.push( status );
visited[ status ] = 1;

if( cant( dig, *dig > 0 ) && status != 12345678 )
printf( "Case %d: -1\n", ++T );
else
{
while( !perm.empty() && perm.front() != 12345678 )
{
for( int i = 0; i < 8; ++i )
for( int j = 0; j < 8; ++j )
if( i != j )
{
int tmp = cov( insert( sign, cov( perm.front(), cp ), i, j ) );
if( tmp == -1 )
continue;
if( visited[ tmp ] == 0 )
{
visited[ tmp ] = visited[ perm.front() ]+1;
perm.push( tmp );
}
if( tmp == 12345678 )
goto ans;
}
perm.pop();
}
ans:
printf( "Case %d: %d\n", ++T, visited[ 12345678 ]-1 );
}
}
return 0;
}```