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### 11270 - Tiling Dominoes

Posted: **Sun Nov 30, 2008 6:45 am**

by **tryit1**

Did anyone get the recurrence for the general nxm board ? or used the closed form at

http://en.wikipedia.org/wiki/Domino_tiling
Say i didn't know closed form the url , how do i go about solving it ?

### Re: 11270 - Tiling Dominoes

Posted: **Fri Feb 27, 2009 12:49 pm**

by **Jan**

Pre generate the values and store the result in a file. Then store the values in an array. Finally, print the values from the array. That's what I did.

### Re: 11270 - Tiling Dominoes

Posted: **Tue Jun 22, 2010 3:26 pm**

by **mak(cse_DU)**

I pre-calculated all M*N value in a 2D array.

Complexity O(10 * 2^10 * 2^10) .

State F(Row,Mask) .

But my timing 0.044.

Some Input/Output for future reference:

Code: Select all

```
34 2
10 10
8 9
3 3
3 10
4 20
4 25
0 3
9 11
8 12
```

AC output:

Code: Select all

```
9227465
258584046368
108435745
0
571
616891945
114079985111
0
0
82741005829
```

### Re: 11270 - Tiling Dominoes

Posted: **Wed Mar 27, 2013 10:22 pm**

by **mehdiii**

neither n nor m is zero in the judge data.

I have a problem here :

When I produce all

**possible** inputs and I put it in my source code just to print in UVa OJ it gets ACCEPTED.

....

mat[25][4] = 114079985111LL;

mat[26][1] = 1LL;

mat[26][2] = 196418LL;

mat[26][3] = 21489003LL;

....

But when I calculate it in my code instead of writing it in a file, it gets WA.

Is it because of compiler behavior? Or I have a bug in my code?

Code: Select all

```
#include <iostream>
#include <vector>
#include <string>
#include <string.h>
#include <map>
#include <cstdio>
using namespace std;
#define ll long long
map < vector<int>, ll > dp;
int a, b;
ll f(int row, vector <int> v)
{
if(dp.count(v))
return dp[v];
if(v[row] == 0)
return dp[v] = f(row+1, v);
ll &ref = dp[v];
ref = 0;
for(ll j = 0; j < b-1; j ++)
{
if( v[row]&(1<<j) && v[row]&(1<<(j+1)) )
{
v[row] = v[row] ^ (1<<j) ^ (1<<(j+1));
ref += f(row, v);
v[row] = v[row] | (1<<j) | (1<<(j+1));
if(row < a-1)
{
if( v[row+1] & (1<<j) )
{
v[row] = v[row] ^ (1<<j);
v[row+1] = v[row+1] ^ (1<<j);
ref += f(row, v);
}
}
return ref;
}
}
if(row < a-1)
{
for(ll j = 0; j < b; j ++)
{
if(v[row]&(1<<j) && v[row+1]&(1<<j))
{
v[row] = v[row] ^ (1<<j);
v[row+1] = v[row+1] ^ (1<<j);
ref += f(row, v);
return ref;
}
}
}
return ref;
}
ll mat[128][128];
int main()
{
//freopen("a.in", "r", stdin);
//freopen("a.out", "w", stdout);
memset(mat, -1, sizeof mat);
for(int x = 1; x <= 100; x ++)
for(int y = 1; y <= 100; y ++)
//while(cin >> a >> b)
{
if(x*y > 100)
continue;
a = x;
b = y;
dp.clear();
//if(a == 0 || b == 0)
//while(true);
if(a < b)
swap(a, b);
vector <int> v(a, 0);
dp[v] = 1;
for(int i = 0; i < a; i ++)
v[i] = (1<<b)-1;
ll res;
if( a*b % 2 == 1 )
res = 0;
else
res = f(0, v);
mat[a][b] = mat[b][a] = res;
//cout << res << endl;
}
while(cin >> a >> b)
{
if(mat[a][b] == -1 && mat[b][a] == -1)
while(true);
//printf("%lld\n", res);
/*if(mat[a][b] == -1)
cout << mat[b][a] << endl;
else
cout << mat[a][b] << endl;*/
if(a < b)
swap(a, b);
printf("mat[%d][%d] = %lldLL;\n", a, b, mat[a][b]);
}
return 0;
}
```

### Re: 11270 - Tiling Dominoes

Posted: **Thu Mar 28, 2013 9:41 pm**

by **brianfry713**

Your code is producing zeros and doesn't match the sample I/O. See:

https://ideone.com/k5lfQq

### Re: 11270 - Tiling Dominoes

Posted: **Fri Mar 29, 2013 12:20 am**

by **mehdiii**

That's so strange, last night I was testing my program with Visual Studio 2010, and it worked very good, generated correct output as I said in my previous post,

but now, after your reply I tested it with MinGW/G++ and it didn't work, I checked my code again and noticed line 19 :

Make long story short, I think MinGW and VS2010 have different behavior about the above code,

VS2010 first invokes f(row+1, v) and then inserts it to dp,

**in f(row+1, v), dp.count(v) is zero.**
but MinGW first assigns memory for dp[v], then invokes f(row+1, v) and at the end assigns the value to dp[v],

**in f(row+1, v), dp.count(v) is 1.**
I don't know which standard is better

### Re: 11270 - Tiling Dominoes

Posted: **Fri Mar 29, 2013 12:22 am**

by **mehdiii**

By the way, Thank you, I changed it a little bit and got ACCEPTED