Dancing links 基础题

全部都是数独类的题目

POJ 3074

</pre><pre name="code" class="cpp">//      whn6325689
//		Mr.Phoebe
//		http://blog.csdn.net/u013007900
#include <algorithm>
#include <iostream>
#include <iomanip>
#include <cstring>
#include <climits>
#include <complex>
#include <fstream>
#include <cassert>
#include <cstdio>
#include <bitset>
#include <vector>
#include <deque>
#include <queue>
#include <stack>
#include <ctime>
#include <set>
#include <map>
#include <cmath>
#include <functional>
#include <numeric>
#pragma comment(linker, "/STACK:1024000000,1024000000")


using namespace std;

typedef long long ll;
typedef long double ld;
typedef pair<ll, ll> pll;
typedef complex<ld> point;
typedef pair<int, int> pii;
typedef pair<pii, int> piii;
typedef vector<int> vi;

#define CLR(x,y) memset(x,y,sizeof(x))
#define mp(x,y) make_pair(x,y)
#define pb(x) push_back(x)
#define lowbit(x) (x&(-x))
#define MID(x,y) (x+((y-x)>>1))
#define eps 1e-9
#define PI acos(-1.0)
#define INF 0x3f3f3f3f
#define LLINF 1LL<<62

template<class T>
inline bool read(T &n)
{
    T x = 0, tmp = 1; char c = getchar();
    while((c < '0' || c > '9') && c != '-' && c != EOF) c = getchar();
    if(c == EOF) return false;
    if(c == '-') c = getchar(), tmp = -1;
    while(c >= '0' && c <= '9') x *= 10, x += (c - '0'),c = getchar();
    n = x*tmp;
    return true;
}
template <class T>
inline void write(T n)
{
    if(n < 0)
    {
        putchar('-');
        n = -n;
    }
    int len = 0,data[20];
    while(n)
    {
        data[len++] = n%10;
        n /= 10;
    }
    if(!len) data[len++] = 0;
    while(len--) putchar(data[len]+48);
}
//-----------------------------------

const int M=1024*110;
const int N=1024;
char str[111];

struct DLX
{
	int l[M], r[M], d[M], u[M], col[M], row[M], h[N], control[N];
	int dcnt;
	void init(int cols)
	{
		memset(control,0,sizeof(control));
		memset(h,-1,sizeof(h));
		for(int i=0;i<=cols;i++)
		{
			u[i]=d[i]=i;
			l[i]=i-1;
			r[i]=i+1;
		}
		r[cols]=0;l[0]=cols;
		dcnt = cols;
	}

	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];
	            control[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])
	            control[col[u[d[j]]=d[u[j]]=j]]++;
        r[l[c]]=l[r[c]]=c;
	}

	bool dance(int deep)
	{
	    if(r[0]==0)
	    {
	        puts(str);
	        return true;
	    }

	    int tempc=r[0];
	    for(int i=r[0];i!=0;i=r[i])
			if(control[i]<control[tempc])
	        	tempc=i;
	    remove(tempc);
	    for(int i=d[tempc];i!=tempc;i=d[i])
	    {
	        str[row[i]/9]=row[i]%9+'1';
	        for(int j=r[i];j!=i;j=r[j]) remove(col[j]);
	        if(dance(deep+1)) return true;
	        for(int j=l[i];j!=i;j=l[j]) resume(col[j]);
	    }
	    resume(tempc);
	    return false;
	}

	inline void link(int x, int y)
	{
		++control[col[++dcnt]=y];
		row[dcnt]=x;
		d[dcnt]=d[y];
		u[d[y]]=dcnt;
		u[dcnt]=y;
		d[y]= dcnt;
		if(h[x]<0)
			h[x]=l[dcnt]=r[dcnt]=dcnt;
		else
		{
			r[dcnt]=r[h[x]];
			l[r[h[x]]]=dcnt;
			l[dcnt]=h[x];
			r[h[x]]=dcnt;
		}
	}
}dlx;


int main()
{
//	freopen("data.txt","r",stdin);
    while(~scanf("%s", str) && strcmp(str, "end")!=0)
    {
        dlx.init(4*9*9);
        for(int i=0;i<9;i++)
			for(int j=0;j<9;j++)
	            for(int k=1;k<=9;k++)
					if(str[i*9+j]=='.' || str[i*9+j]=='0'+k)
		            {
		                int rr=i*9*9+j*9+k-1;
		                dlx.link(rr, 81*0+i*9+k);
		                dlx.link(rr, 81*1+j*9+k);
		                dlx.link(rr, 81*2+(i/3+j/3*3)*9+k);
		                dlx.link(rr, 81*3+i*9+j+1);
		            }
        dlx.dance(0);
    }
}

POJ 3076

这个模板需要从第0行开始

否则无法进行递归

//      whn6325689
//		Mr.Phoebe
//		http://blog.csdn.net/u013007900
#include <algorithm>
#include <iostream>
#include <iomanip>
#include <cstring>
#include <climits>
#include <complex>
#include <fstream>
#include <cassert>
#include <cstdio>
#include <bitset>
#include <vector>
#include <deque>
#include <queue>
#include <stack>
#include <ctime>
#include <set>
#include <map>
#include <cmath>
#include <functional>
#include <numeric>
#pragma comment(linker, "/STACK:1024000000,1024000000")


using namespace std;

typedef long long ll;
typedef long double ld;
typedef pair<ll, ll> pll;
typedef complex<ld> point;
typedef pair<int, int> pii;
typedef pair<pii, int> piii;
typedef vector<int> vi;

#define CLR(x,y) memset(x,y,sizeof(x))
#define mp(x,y) make_pair(x,y)
#define pb(x) push_back(x)
#define lowbit(x) (x&(-x))
#define MID(x,y) (x+((y-x)>>1))
#define eps 1e-9
#define PI acos(-1.0)
#define INF 0x3f3f3f3f
#define LLINF 1LL<<62

template<class T>
inline bool read(T &n)
{
    T x = 0, tmp = 1; char c = getchar();
    while((c < '0' || c > '9') && c != '-' && c != EOF) c = getchar();
    if(c == EOF) return false;
    if(c == '-') c = getchar(), tmp = -1;
    while(c >= '0' && c <= '9') x *= 10, x += (c - '0'),c = getchar();
    n = x*tmp;
    return true;
}
template <class T>
inline void write(T n)
{
    if(n < 0)
    {
        putchar('-');
        n = -n;
    }
    int len = 0,data[20];
    while(n)
    {
        data[len++] = n%10;
        n /= 10;
    }
    if(!len) data[len++] = 0;
    while(len--) putchar(data[len]+48);
}
//-----------------------------------


const int M=4096*5;

int l[M], r[M], d[M], u[M], col[M], row[M], h[4100], control[1030];
int dcnt = 0;
char str[16][17];

inline void addnode(int &x)
{
    ++x;
    r[x]=l[x]=u[x]=d[x]=x;
}

inline void insert_row(int rowx, int x)
{
    r[l[rowx]]=x;
    l[x]=l[rowx];
    r[x]=rowx;
    l[rowx]=x;
}

inline void insert_col(int colx, int x)
{
    d[u[colx]]=x;
    u[x]=u[colx];
    d[x]=colx;
    u[colx]=x;
}

void dlx_init(int cols)
{
    memset(h, -1, sizeof(h));
    memset(control, 0, sizeof(control));
    dcnt=-1;
    addnode(dcnt);

    for(int i=1;i<=cols;++i)
    {
        addnode(dcnt);
        insert_row(0, dcnt);
    }
}

inline 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];
            control[col[j]]--;
        }
}

inline void resume(int c)
{
    for(int i=u[c];i!=c;i=u[i])
        for(int j=l[i];j!=i;j=l[j])
        {
            u[d[j]]=j;
            d[u[j]]=j;
            control[col[j]]++;
        }
        l[r[c]]=c;
        r[l[c]]=c;
}

bool DLX(int deep)
{
    if(r[0]==0)
    {
        for(int i=0;i<16;i++)
            puts(str[i]);
        return true;
    }

    int min=M, tempc;
    for(int i=r[0];i!=0;i=r[i]) if(control[i]<min)
    {
        min=control[i];
        tempc=i;
    }
    remove(tempc);
    for(int i=d[tempc];i!=tempc;i=d[i])
    {
        str[row[i]/256][row[i]/16%16]=row[i]%16+'A';
        for(int j=r[i];j!=i;j=r[j]) remove(col[j]);
        if(DLX(deep+1)) return true;
        for(int j=l[i];j!=i;j=l[j]) resume(col[j]);
    }
    resume(tempc);
    return false;
}

inline void insert_node(int x, int y)
{
    control[y]++;
    addnode(dcnt);
    row[dcnt]=x;
    col[dcnt]=y;
    insert_col(y, dcnt);
    if(h[x]==-1)
        h[x]=dcnt;
    else
        insert_row(h[x], dcnt);
}

int main()
{
#ifdef ACM
    freopen("in.txt", "r", stdin);
#endif

    while(~scanf("%s", str[0]))
    {
        for(int i=1;i<16;i++) scanf("%s", str[i]);

        dlx_init(4*16*16);
        for(int i=1;i<=16;i++) for(int j=1;j<=16;j++)
        {
            for(int k=1;k<=16;k++) if(str[i-1][j-1]=='-' || str[i-1][j-1]=='A'+(k-1))
            {
                int rr=(i-1)*256+(j-1)*16+(k-1);
                insert_node(rr, 16*16*0+(i-1)*16+k);
                insert_node(rr, 16*16*1+(j-1)*16+k);
                insert_node(rr, 16*16*2+(i-1)/4+(j-1)/4*4+(k-1)*16+1);
                insert_node(rr, 16*16*3+(i-1)*16+j);
            }
        }

        DLX(0);
        puts("");
    }
}

HDU 4069

这个模板行必须从1开始，因为没有初始化第0行

//      whn6325689
//		Mr.Phoebe
//		http://blog.csdn.net/u013007900
#include <algorithm>
#include <iostream>
#include <iomanip>
#include <cstring>
#include <climits>
#include <complex>
#include <fstream>
#include <cassert>
#include <cstdio>
#include <bitset>
#include <vector>
#include <deque>
#include <queue>
#include <stack>
#include <ctime>
#include <set>
#include <map>
#include <cmath>
#include <functional>
#include <numeric>
#pragma comment(linker, "/STACK:1024000000,1024000000")


using namespace std;

typedef long long ll;
typedef long double ld;
typedef pair<ll, ll> pll;
typedef complex<ld> point;
typedef pair<int, int> pii;
typedef pair<pii, int> piii;
typedef vector<int> vi;

#define CLR(x,y) memset(x,y,sizeof(x))
#define mp(x,y) make_pair(x,y)
#define pb(x) push_back(x)
#define lowbit(x) (x&(-x))
#define MID(x,y) (x+((y-x)>>1))
#define eps 1e-9
#define PI acos(-1.0)
#define INF 0x3f3f3f3f
#define LLINF 1LL<<62

template<class T>
inline bool read(T &n)
{
    T x = 0, tmp = 1; char c = getchar();
    while((c < '0' || c > '9') && c != '-' && c != EOF) c = getchar();
    if(c == EOF) return false;
    if(c == '-') c = getchar(), tmp = -1;
    while(c >= '0' && c <= '9') x *= 10, x += (c - '0'),c = getchar();
    n = x*tmp;
    return true;
}
template <class T>
inline void write(T n)
{
    if(n < 0)
    {
        putchar('-');
        n = -n;
    }
    int len = 0,data[20];
    while(n)
    {
        data[len++] = n%10;
        n /= 10;
    }
    if(!len) data[len++] = 0;
    while(len--) putchar(data[len]+48);
}
//-----------------------------------
const int N = 9; //3*3Êý¶À
const int MaxN = N*N*N + 10;
const int MaxM = N*N*4 + 10;
const int maxnode = MaxN*4 + MaxM + 10;
char g[MaxN];
int cnt;
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;
	}
	void Dance(int d)
	{
		if(cnt > 1)return;
		if(R[0] == 0)
		{
			for(int i = 0;i < d;i++)g[(ans[i]-1)/9] = (ans[i]-1)%9 + '1';
			cnt++;
			return;
		}
		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]);
			Dance(d+1);
			if(cnt > 1)return;
			for(int j = L[i];j != i;j = L[j])resume(Col[j]);
		}
		resume(c);
	}
};

int id[20][20];
int a[20][20];
void bfs(int sx,int sy,int d)
{
	queue<pair<int,int> >q;
	q.push(make_pair(sx,sy));
	id[sx][sy] = d;
	while(!q.empty())
	{
		pair<int,int> tmp = q.front();
		int x = tmp.first;
		int y = tmp.second;
		q.pop();
		if(x > 0 && ((a[x][y]%32)/16) == 0)
			if(id[x-1][y] == -1)
			{
				id[x-1][y] = d;
				q.push(make_pair(x-1,y));
			}
		if(x < N-1 && ((a[x][y]%128)/64) == 0)
			if(id[x+1][y] == -1)
			{
				id[x+1][y] = d;
				q.push(make_pair(x+1,y));
			}
		if(y > 0 && ((a[x][y])/128) == 0)
			if(id[x][y-1] == -1)
			{
				id[x][y-1] = d;
				q.push(make_pair(x,y-1));
			}
		if(y < N-1 && ((a[x][y]%64)/32) == 0)
			if(id[x][y+1] == -1)
			{
				id[x][y+1] = d;
				q.push(make_pair(x,y+1));
			}
	}
}
DLX dlx;

int main()
{
    //freopen("in.txt","r",stdin);
    //freopen("out.txt","w",stdout);
	int T;
	scanf("%d",&T);
	int iCase = 0;
	while(T--)
	{
		iCase++;
		for(int i = 0;i < N;i++)
			for(int j = 0;j < N;j++)
				scanf("%d",&a[i][j]);
		memset(id,-1,sizeof(id));
		int index = 0;
		for(int i = 0;i < N;i++)
			for(int j = 0;j < N;j++)
				if(id[i][j] == -1)
					bfs(i,j,++index);
		dlx.init(N*N*N,N*N*4);
		for(int i = 0;i < N;i++)
			for(int j = 0;j < N;j++)
				for(int k = 1;k <= N;k++)
				{
					if(a[i][j]%16 != 0 && a[i][j]%16 != k)continue;
					int r = (i*N+j)*N + k;
					int c1 = i*N+j+1;
					int c2 = N*N+i*N+k;
					int c3 = N*N*2+j*N+k;
					int c4 = N*N*3+(id[i][j]-1)*N+k;
					dlx.Link(r,c1);
					dlx.Link(r,c2);
					dlx.Link(r,c3);
					dlx.Link(r,c4);
				}
		cnt = 0;
		dlx.Dance(0);
		printf("Case %d:\n",iCase);
		if(cnt == 0)printf("No solution\n");
		else if(cnt > 1)printf("Multiple Solutions\n");
		else
		{
			for(int i = 0;i < N*N;i++)
			{
				printf("%c",g[i]);
				if(i % N == N - 1)
					printf("\n");
			}
		}
	}
    return 0;
}