bzoj2595[Wc2008]游览计划

http://www.lydsy.com/JudgeOnline/problem.php?id=2595

斯坦纳树。

斯坦纳树是在求一个图中的包含某些特定点的最小生成树，注意其他点不一定要包含。

这道题可以算是斯坦纳树的入门题了。

题解请戳

#include<cstdio>
#include<cstdlib>
#include<iostream>
#include<fstream>
#include<algorithm>
#include<cstring>
#include<string>
#include<cmath>
#include<queue>
#include<stack>
#include<map>
#include<utility>
#include<set>
#include<bitset>
#include<vector>
#include<functional>
#include<deque>
#include<cctype>
#include<climits>
#include<complex>
//#include<bits/stdc++.h>适用于CF,UOJ，但不适用于poj
 
using namespace std;

typedef long long LL;
typedef double DB;
typedef pair<int,int> PII;
typedef complex<DB> CP;

#define mmst(a,v) memset(a,v,sizeof(a))
#define mmcy(a,b) memcpy(a,b,sizeof(a))
#define fill(a,l,r,v) fill(a+l,a+r+1,v)
#define re(i,a,b)  for(i=(a);i<=(b);i++)
#define red(i,a,b) for(i=(a);i>=(b);i--)
#define ire(i,x) for(typedef(x.begin()) i=x.begin();i!=x.end();i++)
#define fi first
#define se second
#define m_p(a,b) make_pair(a,b)
#define p_b(a) push_back(a)
#define SF scanf
#define PF printf
#define two(k) (1<<(k))

template<class T>inline T sqr(T x){return x*x;}
template<class T>inline void upmin(T &t,T tmp){if(t>tmp)t=tmp;}
template<class T>inline void upmax(T &t,T tmp){if(t<tmp)t=tmp;}

const DB EPS=1e-9;
inline int sgn(DB x){if(abs(x)<EPS)return 0;return(x>0)?1:-1;}
const DB Pi=acos(-1.0);

inline int gint()
  {
        int res=0;bool neg=0;char z;
        for(z=getchar();z!=EOF && z!='-' && !isdigit(z);z=getchar());
        if(z==EOF)return 0;
        if(z=='-'){neg=1;z=getchar();}
        for(;z!=EOF && isdigit(z);res=res*10+z-'0',z=getchar());
        return (neg)?-res:res; 
    }
inline LL gll()
  {
      LL res=0;bool neg=0;char z;
        for(z=getchar();z!=EOF && z!='-' && !isdigit(z);z=getchar());
        if(z==EOF)return 0;
        if(z=='-'){neg=1;z=getchar();}
        for(;z!=EOF && isdigit(z);res=res*10+z-'0',z=getchar());
        return (neg)?-res:res; 
    }

const int maxN=10;
const int maxK=10;
const int INF=0xf0f0f0f;
const int dx[]={1,-1,0,0};
const int dy[]={0,0,1,-1};

int N,M,K;
int a[maxN+10][maxN+10];
int id[maxN+10][maxN+10];

int F[maxN+10][maxN+10][two(maxK)+100];
struct Tpre
  {
      int x,y,s;
      inline Tpre(int _x=0,int _y=0,int _s=0){x=_x;y=_y;s=_s;}
  }pre[maxN+10][maxN+10][two(maxK)+100];

inline int update(int x,int y,int state,int px,int py,int pstate,int v)
  {
      if(v<F[x][y][state]) return F[x][y][state]=v,pre[x][y][state]=Tpre(px,py,pstate),1;
      return 0;
  }

queue<PII>Q;
int vis[maxN+10][maxN+10];

inline void SPFA(int state)
  {
      while(!Q.empty())
        {
            int i,x=Q.front().fi,y=Q.front().se;Q.pop();
            vis[x][y]=0;
            re(i,0,3)
              {
                  int _x=x+dx[i],_y=y+dy[i];
                  if(_x<1 || _x>N || _y<1 || _y>M)continue;
                  if(update(_x,_y,state,x,y,state,F[x][y][state]+a[_x][_y]) && !vis[_x][_y])vis[_x][_y]=1,Q.push(PII(_x,_y));
              }
        }
  }

inline void DFS(int i,int j,int state)
  {
      if(i==0 && j==0 && state==0)return;
      vis[i][j]=1;
      int x=pre[i][j][state].x,y=pre[i][j][state].y,s=pre[i][j][state].s;
      DFS(x,y,s);
      if(i==x && j==y)DFS(x,y,state-s);
  }

inline void output()
  {
      int i,j;
        re(i,1,N)
          {
              re(j,1,M)
                    if(a[i][j]==0)
                      putchar('x');
                    else
                    if(vis[i][j])
                      putchar('o');
                    else
                      putchar('_');
                putchar('
');
            }
    }

int main()
  {
      freopen("bzoj2595.in","r",stdin);
      freopen("bzoj2595.out","w",stdout);
      int i,j;
      N=gint();M=gint();
      mmst(F,0xf);
      re(i,1,N)re(j,1,M)
          {
              a[i][j]=gint();
                if(a[i][j]==0)id[i][j]=++K,F[i][j][two(K-1)]=0;
            }
        int state,maxstate=two(K)-1;
        re(state,1,maxstate)
          {
              re(i,1,N)re(j,1,M)
                {
                  for(int s=state&(state-1);s;s=(s-1)&state)
                    update(i,j,state,i,j,s,F[i][j][s]+F[i][j][state-s]-a[i][j]);
                        if(F[i][j][state]!=INF)Q.push(PII(i,j)),vis[i][j]=1;
                }
              SPFA(state);
          }
        re(i,1,N)re(j,1,M)if(a[i][j]==0)
          {
              cout<<F[i][j][maxstate]<<endl;
              DFS(i,j,maxstate);
              output();
              return 0;
            }
        return 0;
    }