[POJ 2411] Mondriaan's Dream 状态压缩DP

Posted 2020-10-05

题意

　　给定一个 n * m 的矩形．

　　问有多少种多米诺骨牌覆盖．

　　n, m <= 11 .

 

实现

 1 #include <cstdio>
 2 #include <cstring>
 3 #include <cstdlib>
 4 #include <cctype>
 5 #define F(i, a, b) for (register int i = (a); i <= (b); i++)
 6 #define LL long long
 7 inline int rd(void) {
 8     int f = 1; char c = getchar(); for (; !isdigit(c); c = getchar()) if (c == ‘-‘) f = -1;
 9     int x = 0; for (; isdigit(c); c = getchar()) x = x*10+c-‘0‘; return x*f;
10 }
11 
12 bool Legal(int s, int t, int m) {
13     F(i, 0, m-1)
14         if (!(s >> i & 1)) {
15             if (!(t >> i & 1))
16                 return false;
17             else t ^= 1<<i;
18         }
19     F(i, 0, m-1)
20         if (t >> i & 1) {
21             if (i == m-1 || !(t >> i+1 & 1))
22                 return false;
23             else i++;
24         }
25     return true;
26 }
27 
28 int main(void) {
29     #ifndef ONLINE_JUDGE
30         freopen("poj2411.in", "r", stdin);
31     #endif
32     
33     for (int n = rd(), m = rd(); n != 0 || m != 0; n = rd(), m = rd()) {
34         if ((n&1) && (m&1)) { puts("0"); continue; }
35         
36         static int Go[2048][2048];
37         F(s, 0, (1<<m)-1) {
38             Go[s][0] = 0;
39             F(t, 0, (1<<m)-1)
40                 if (Legal(s, t, m))
41                     Go[s][++Go[s][0]] = t;
42         }
43         
44         static LL f[12][2048];
45         memset(f, 0, sizeof f), f[0][(1<<m)-1] = 1;
46         F(i, 0, n-1) F(s, 0, (1<<m)-1) if (f[i][s] != 0)
47             for (int *t = Go[s]+1; t <= Go[s]+Go[s][0]; t++)
48                 f[i+1][*t] += f[i][s];
49         printf("%lld\n", f[n][(1<<m)-1]);
50     }
51     
52     return 0;
53 }