HDU5731 Solid Dominoes Tilings 状压dp+状压容斥
题意：给定n,m的矩阵，就是求稳定的骨牌完美覆盖,也就是相邻的两行或者两列都至少有一个骨牌
分析：第一步：
如果是单单求骨牌完美覆盖，请先去学基础的插头dp(其实也是基础的状压dp)骨牌覆盖
hihocoder有全套课程：骨牌覆盖（一, 二，三），状态压缩（二）
学好了以后，首先打一个预处理没有限制的表，由于赛后补题，我就没自己打，直接从网上粘的表
我的表来自：http://blog.csdn.net/u012015746/article/details/51971977
第二步：
这就是容斥的过程了，我们可以枚举每种列分割状态，计算出每种列分割状态下行合法的方案数
然后用总数，减去一个列分割数为1的，加上列分割数为2.........这就是容斥的过程了
细节处理：每种列状态下如何求合法的行状态呢，每种状态在用一下递推一下就好了（枚举依据是前j行无行分割，后i-j行有行分割）
其实是枚举的第一个行分割线出现的位置，上面不能有，下面就可以随意了
详情请参考上面的链接
复杂度：O（T*(n^2)*(2^m))，大概是这个复杂度
#include <cstdio> #include <algorithm> using namespace std; typedef long long LL; const LL mod = 1e9+7; LL RES[20][20]; void init(); LL dp[17]; LL solve(int n,int m){ int pos[20],tot=(1<<(m-1)); LL ret=0; for(int cur=0;cur<tot;++cur){ int cnt=1;pos[cnt]=0; for(int i=0;i<m-1;++i)if(cur&(1<<i))pos[++cnt]=i+1; pos[++cnt]=m; for(int i=cnt;i>1;--i)pos[i]-=pos[i-1]; for(int i=1;i<=n;++i){ for(int j=0;j<i;++j){ LL tmp=1; for(int k=2;k<=cnt;++k) tmp=tmp*RES[i-j][pos[k]]%mod; if(!j)dp[i]=tmp; else dp[i]=(dp[i]-tmp*dp[j]%mod+mod)%mod; } } if(cnt&1)ret=(ret-dp[n]+mod)%mod; else ret=(ret+dp[n])%mod; } return ret; } int main(){ init(); int n,m; while(~scanf("%d%d",&n,&m)){ printf("%I64d\n",solve(n,m)); } return 0; } void init() { RES[1][1] = 0; RES[1][2] = 1; RES[1][3] = 0; RES[1][4] = 1; RES[1][5] = 0; RES[1][6] = 1; RES[1][7] = 0; RES[1][8] = 1; RES[1][9] = 0; RES[1][10] = 1; RES[1][11] = 0; RES[1][12] = 1; RES[1][13] = 0; RES[1][14] = 1; RES[1][15] = 0; RES[1][16] = 1; RES[2][1] = 1; RES[2][2] = 2; RES[2][3] = 3; RES[2][4] = 5; RES[2][5] = 8; RES[2][6] = 13; RES[2][7] = 21; RES[2][8] = 34; RES[2][9] = 55; RES[2][10] = 89; RES[2][11] = 144; RES[2][12] = 233; RES[2][13] = 377; RES[2][14] = 610; RES[2][15] = 987; RES[2][16] = 1597; RES[3][1] = 0; RES[3][2] = 3; RES[3][3] = 0; RES[3][4] = 11; RES[3][5] = 0; RES[3][6] = 41; RES[3][7] = 0; RES[3][8] = 153; RES[3][9] = 0; RES[3][10] = 571; RES[3][11] = 0; RES[3][12] = 2131; RES[3][13] = 0; RES[3][14] = 7953; RES[3][15] = 0; RES[3][16] = 29681; RES[4][1] = 1; RES[4][2] = 5; RES[4][3] = 11; RES[4][4] = 36; RES[4][5] = 95; RES[4][6] = 281; RES[4][7] = 781; RES[4][8] = 2245; RES[4][9] = 6336; RES[4][10] = 18061; RES[4][11] = 51205; RES[4][12] = 145601; RES[4][13] = 413351; RES[4][14] = 1174500; RES[4][15] = 3335651; RES[4][16] = 9475901; RES[5][1] = 0; RES[5][2] = 8; RES[5][3] = 0; RES[5][4] = 95; RES[5][5] = 0; RES[5][6] = 1183; RES[5][7] = 0; RES[5][8] = 14824; RES[5][9] = 0; RES[5][10] = 185921; RES[5][11] = 0; RES[5][12] = 2332097; RES[5][13] = 0; RES[5][14] = 29253160; RES[5][15] = 0; RES[5][16] = 366944287; RES[6][1] = 1; RES[6][2] = 13; RES[6][3] = 41; RES[6][4] = 281; RES[6][5] = 1183; RES[6][6] = 6728; RES[6][7] = 31529; RES[6][8] = 167089; RES[6][9] = 817991; RES[6][10] = 4213133; RES[6][11] = 21001799; RES[6][12] = 106912793; RES[6][13] = 536948224; RES[6][14] = 720246619; RES[6][15] = 704300462; RES[6][16] = 289288426; RES[7][1] = 0; RES[7][2] = 21; RES[7][3] = 0; RES[7][4] = 781; RES[7][5] = 0; RES[7][6] = 31529; RES[7][7] = 0; RES[7][8] = 1292697; RES[7][9] = 0; RES[7][10] = 53175517; RES[7][11] = 0; RES[7][12] = 188978103; RES[7][13] = 0; RES[7][14] = 124166811; RES[7][15] = 0; RES[7][16] = 708175999; RES[8][1] = 1; RES[8][2] = 34; RES[8][3] = 153; RES[8][4] = 2245; RES[8][5] = 14824; RES[8][6] = 167089; RES[8][7] = 1292697; RES[8][8] = 12988816; RES[8][9] = 108435745; RES[8][10] = 31151234; RES[8][11] = 940739768; RES[8][12] = 741005255; RES[8][13] = 164248716; RES[8][14] = 498190405; RES[8][15] = 200052235; RES[8][16] = 282756494; RES[9][1] = 0; RES[9][2] = 55; RES[9][3] = 0; RES[9][4] = 6336; RES[9][5] = 0; RES[9][6] = 817991; RES[9][7] = 0; RES[9][8] = 108435745; RES[9][9] = 0; RES[9][10] = 479521663; RES[9][11] = 0; RES[9][12] = 528655152; RES[9][13] = 0; RES[9][14] = 764896039; RES[9][15] = 0; RES[9][16] = 416579196; RES[10][1] = 1; RES[10][2] = 89; RES[10][3] = 571; RES[10][4] = 18061; RES[10][5] = 185921; RES[10][6] = 4213133; RES[10][7] = 53175517; RES[10][8] = 31151234; RES[10][9] = 479521663; RES[10][10] = 584044562; RES[10][11] = 472546535; RES[10][12] = 732130620; RES[10][13] = 186229290; RES[10][14] = 274787842; RES[10][15] = 732073997; RES[10][16] = 320338127; RES[11][1] = 0; RES[11][2] = 144; RES[11][3] = 0; RES[11][4] = 51205; RES[11][5] = 0; RES[11][6] = 21001799; RES[11][7] = 0; RES[11][8] = 940739768; RES[11][9] = 0; RES[11][10] = 472546535; RES[11][11] = 0; RES[11][12] = 177126748; RES[11][13] = 0; RES[11][14] = 513673802; RES[11][15] = 0; RES[11][16] = 881924366; RES[12][1] = 1; RES[12][2] = 233; RES[12][3] = 2131; RES[12][4] = 145601; RES[12][5] = 2332097; RES[12][6] = 106912793; RES[12][7] = 188978103; RES[12][8] = 741005255; RES[12][9] = 528655152; RES[12][10] = 732130620; RES[12][11] = 177126748; RES[12][12] = 150536661; RES[12][13] = 389322891; RES[12][14] = 371114062; RES[12][15] = 65334618; RES[12][16] = 119004311; RES[13][1] = 0; RES[13][2] = 377; RES[13][3] = 0; RES[13][4] = 413351; RES[13][5] = 0; RES[13][6] = 536948224; RES[13][7] = 0; RES[13][8] = 164248716; RES[13][9] = 0; RES[13][10] = 186229290; RES[13][11] = 0; RES[13][12] = 389322891; RES[13][13] = 0; RES[13][14] = 351258337; RES[13][15] = 0; RES[13][16] = 144590622; RES[14][1] = 1; RES[14][2] = 610; RES[14][3] = 7953; RES[14][4] = 1174500; RES[14][5] = 29253160; RES[14][6] = 720246619; RES[14][7] = 124166811; RES[14][8] = 498190405; RES[14][9] = 764896039; RES[14][10] = 274787842; RES[14][11] = 513673802; RES[14][12] = 371114062; RES[14][13] = 351258337; RES[14][14] = 722065660; RES[14][15] = 236847118; RES[14][16] = 451896972; RES[15][1] = 0; RES[15][2] = 987; RES[15][3] = 0; RES[15][4] = 3335651; RES[15][5] = 0; RES[15][6] = 704300462; RES[15][7] = 0; RES[15][8] = 200052235; RES[15][9] = 0; RES[15][10] = 732073997; RES[15][11] = 0; RES[15][12] = 65334618; RES[15][13] = 0; RES[15][14] = 236847118; RES[15][15] = 0; RES[15][16] = 974417347; RES[16][1] = 1; RES[16][2] = 1597; RES[16][3] = 29681; RES[16][4] = 9475901; RES[16][5] = 366944287; RES[16][6] = 289288426; RES[16][7] = 708175999; RES[16][8] = 282756494; RES[16][9] = 416579196; RES[16][10] = 320338127; RES[16][11] = 881924366; RES[16][12] = 119004311; RES[16][13] = 144590622; RES[16][14] = 451896972; RES[16][15] = 974417347; RES[16][16] = 378503901; }
