Dancing Links x

参考资料：

模板代码抄的网上大神的：博客地址

看了一篇大神的论文：《Dancing Links 在搜索中的应用》

学习的过程前面精确覆盖的时候还好，后面重复覆盖的时候基本懵掉了……当时也没看到大神的博客论文里没模板，我对A*和IDA*一点都不了解。到现在也没怎么看明白，就大概弄明白了点模板怎么用。

第一类问题：精确覆盖

从矩阵中找到一些行，使每一列最多有一个1。

第二类问题：重复覆盖

从矩阵中找到一些行，使每一列至少有一个1。

精确覆盖：

const int maxnode = 100010;
const int MaxM = 1010;
const int MaxN = 1010;
struct DLX
{
int n,m,size;
int U[maxnode],D[maxnode],R[maxnode],L[maxnode],Row[maxnode],Col[maxnode];
int H[MaxN], S[MaxM];
int ansd, ans[MaxN];
void init(int _n,int _m)
{
n = _n;
m = _m;
for(int i = 0;i <= m;i++)
{
S[i] = 0;
U[i] = D[i] = i;
L[i] = i-1;
R[i] = i+1;
}
R[m] = 0; L[0] = m;
size = m;
for(int i = 1;i <= n;i++)
H[i] = -1;
}
void Link(int r,int c)
{
++S[Col[++size]=c];
Row[size] = r;
D[size] = D[c];
U[D[c]] = size;
U[size] = c;
D[c] = size;
if(H[r] < 0)H[r] = L[size] = R[size] = size;
else
{
R[size] = R[H[r]];
L[R[H[r]]] = size;
L[size] = H[r];
R[H[r]] = size;
}
}
void remove(int c)
{
L[R[c]] = L[c]; R[L[c]] = R[c];
for(int i = D[c];i != c;i = D[i])
for(int j = R[i];j != i;j = R[j])
{
U[D[j]] = U[j];
D[U[j]] = D[j];
--S[Col[j]];
}
}
void resume(int c)
{
for(int i = U[c];i != c;i = U[i])
for(int j = L[i];j != i;j = L[j])
++S[Col[U[D[j]]=D[U[j]]=j]];
L[R[c]] = R[L[c]] = c;
}
//d为递归深度
bool Dance(int d)
{
if(R[0] == 0)
{
ansd = d;
return true;
}
int c = R[0];
for(int i = R[0];i != 0;i = R[i])
if(S[i] < S[c])
c = i;
remove(c);
for(int i = D[c];i != c;i = D[i])
{
ans[d] = Row[i];
for(int j = R[i]; j != i;j = R[j])remove(Col[j]);
if(Dance(d+1))return true;
for(int j = L[i]; j != i;j = L[j])resume(Col[j]);
}
resume(c);
return false;
}
};

重复覆盖：

const int maxnode = 3000;
const int MaxM = 55;
const int MaxN = 55;
int K;
struct DLX
{
int n,m,size;
int U[maxnode],D[maxnode],R[maxnode],L[maxnode],Row[maxnode],Col[maxnode];
int H[MaxN],S[MaxN];
int ands,ans[MaxN];
void init(int _n,int _m)
{
n = _n;
m = _m;
for(int i = 0;i <= m;i++)
{
S[i] = 0;
U[i] = D[i] = i;
L[i] = i-1;
R[i] = i+1;
}
R[m] = 0; L[0] = m;
size = m;
for(int i = 1;i <= n;i++)
H[i] = -1;
}
void Link(int r,int c)
{
++S[Col[++size]=c];
Row[size] = r;
D[size] = D[c];
U[D[c]] = size;
U[size] = c;
D[c] = size;
if(H[r] < 0)H[r] = L[size] = R[size] = size;
else
{
R[size] = R[H[r]];
L[R[H[r]]] = size;
L[size] = H[r];
R[H[r]] = size;
}
}
void remove(int c)
{
for(int i = D[c];i != c;i = D[i])
L[R[i]] = L[i], R[L[i]] = R[i];
}
void resume(int c)
{
for(int i = U[c];i != c;i = U[i])
L[R[i]]=R[L[i]]=i;
}
bool v[maxnode];
int f()
{
int ret = 0;
for(int c = R[0];c != 0;c = R[c])v[c] = true;
for(int c = R[0];c != 0;c = R[c])
if(v[c])
{
ret++;
v[c] = false;
for(int i = D[c];i != c;i = D[i])
for(int j = R[i];j != i;j = R[j])
v[Col[j]] = false;
}
return ret;

}
bool Dance(int d)
{
if(d + f() > K)return false;
if(R[0] == 0)return d <= K;
int c = R[0];
for(int i = R[0];i != 0;i = R[i])
if(S[i] < S[c])
c = i;
for(int i = D[c];i != c;i = D[i])
{
remove(i);
for(int j = R[i];j != i;j = R[j])remove(j);
if(Dance(d+1))return true;
for(int j = L[i];j != i;j = L[j])resume(j);
resume(i);
}
return false;
}
};