11270 - Tiling Dominoes

All about problems in Volume 112. If there is a thread about your problem, please use it. If not, create one with its number in the subject.

Moderator: Board moderators

tryit1
Experienced poster
Posts: 119
Joined: Sun Aug 24, 2008 9:09 pm

11270 - Tiling Dominoes

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 ?

Jan
Guru
Posts: 1334
Joined: Wed Jun 22, 2005 10:58 pm
Contact:

Re: 11270 - Tiling Dominoes

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.
Ami ekhono shopno dekhi...
HomePage

mak(cse_DU)
Learning poster
Posts: 72
Joined: Tue May 30, 2006 5:57 pm

Re: 11270 - Tiling Dominoes

I pre-calculated all M*N value in a 2D array.
Complexity O(10 * 2^10 * 2^10) .
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
Mak
Help me PLZ!!

mehdiii
New poster
Posts: 9
Joined: Fri Nov 02, 2012 1:35 pm

Re: 11270 - Tiling Dominoes

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 = 114079985111LL;
mat = 1LL;
mat = 196418LL;
mat = 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;

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;
}

brianfry713
Guru
Posts: 5947
Joined: Thu Sep 01, 2011 9:09 am
Location: San Jose, CA, USA

Re: 11270 - Tiling Dominoes

Your code is producing zeros and doesn't match the sample I/O. See:https://ideone.com/k5lfQq
Check input and AC output for thousands of problems on uDebug!

mehdiii
New poster
Posts: 9
Joined: Fri Nov 02, 2012 1:35 pm

Re: 11270 - Tiling Dominoes

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 :

Code: Select all

return dp[v] = f(row+1, v);
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 mehdiii
New poster
Posts: 9
Joined: Fri Nov 02, 2012 1:35 pm

Re: 11270 - Tiling Dominoes

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