BZOJ 2007 海拔(平面图最小割转对偶图最短路)

首先注意到,把一个点的海拔定为>1的数是毫无意义的。实际上,可以转化为把这些点的海拔要么定为0,要么定为1.

其次,如果一个点周围的点的海拔没有和它相同的,那么这个点的海拔也是可以优化的,即把这个点变为周围海拔一样的显然能使结果变优。

于是问题就变成了,这个图的海拔为0的联通块和起点连在一起,海拔为1的联通块和终点连在一起。

此即为经典的最小割。

由于此图为平面图,我们可以使用平面图最小割转对偶图最短路优化算法。

因为这是有向图,因此构建对偶图的时候注意边的方向即可。

 

# include <cstdio>
# include <cstring>
# include <cstdlib>
# include <iostream>
# include <vector>
# include <queue>
# include <stack>
# include <map>
# include <set>
# include <cmath>
# include <algorithm>
using namespace std;
# define lowbit(x) ((x)&(-x))
# define pi acos(-1.0)
# define eps 1e-7
# define MOD 1024523
# define INF 1e16
# define mem(a,b) memset(a,b,sizeof(a))
# define FOR(i,a,n) for(int i=a; i<=n; ++i)
# define FO(i,a,n) for(int i=a; i<n; ++i)
# define bug puts("H");
# define lch p<<1,l,mid
# define rch p<<1|1,mid+1,r
# define mp make_pair
# define pb push_back
typedef pair<int,int> PII;
typedef vector<int> VI;
# pragma comment(linker, "/STACK:1024000000,1024000000")
typedef long long LL;
int Scan() {
    int x=0,f=1;char ch=getchar();
    while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}
    while(ch>='0'&&ch<='9'){x=x*10+ch-'0';ch=getchar();}
    return x*f;
}
void Out(int a) {
    if(a<0) {putchar('-'); a=-a;}
    if(a>=10) Out(a/10);
    putchar(a%10+'0');
}
const int N=250005;
//Code begin...

struct Edge{int p, next; LL w;}edge[N*40];
struct qnode{
    int v; LL c;
    qnode(int _v=0, LL _c=0):v(_v),c(_c){}
    bool operator<(const qnode&r)const{return c>r.c;}
};
bool vis[N];
int head[N], cnt=1;
LL G1[505][505], G2[505][505], G3[505][505], G4[505][505], dist[N];
priority_queue<qnode>que;

void add_edge(int u, int v, LL w){edge[cnt].p=v; edge[cnt].w=w; edge[cnt].next=head[u]; head[u]=cnt++;}
void Dijkstra(int n, int start){
    mem(vis,false); FOR(i,0,n) dist[i]=INF;
    dist[start]=0; que.push(qnode(start,0));
    qnode tmp;
    while (!que.empty()) {
        tmp=que.top(); que.pop();
        int u=tmp.v;
        if (vis[u]) continue;
        vis[u]=true;
        for (int i=head[u]; i; i=edge[i].next) {
            int v=edge[i].p; LL cost=edge[i].w;
            if (!vis[v]&&dist[v]>dist[u]+cost) dist[v]=dist[u]+cost, que.push(qnode(v,dist[v]));
        }
    }
}
int main ()
{
    int n, s, t, x;
    scanf("%d",&n); s=0; t=n*n+1;
    FOR(i,0,n) FOR(j,1,n) scanf("%lld",&G1[i][j]);
    FOR(i,1,n) FOR(j,0,n) scanf("%lld",&G2[i][j]);
    FOR(i,0,n) FOR(j,1,n) scanf("%lld",&G3[i][j]);
    FOR(i,1,n) FOR(j,0,n) scanf("%lld",&G4[i][j]);
    FOR(i,0,n) FOR(j,1,n) {
        if (i==0) add_edge(s,i*n+j,G1[i][j]), add_edge(i*n+j,s,G3[i][j]);
        else if (i==n) add_edge((i-1)*n+j,t,G1[i][j]), add_edge(t,(i-1)*n+j,G3[i][j]);
        else add_edge((i-1)*n+j,i*n+j,G1[i][j]), add_edge(i*n+j,(i-1)*n+j,G3[i][j]);
    }
    FOR(i,1,n) FOR(j,0,n) {
        if (j==0) add_edge((i-1)*n+j+1,t,G2[i][j]), add_edge(t,(i-1)*n+j+1,G4[i][j]);
        else if (j==n) add_edge(s,(i-1)*n+j,G2[i][j]), add_edge((i-1)*n+j,s,G4[i][j]);
        else add_edge((i-1)*n+j+1,(i-1)*n+j,G2[i][j]), add_edge((i-1)*n+j,(i-1)*n+j+1,G4[i][j]);
    }
    Dijkstra(t,s);
    printf("%lld\n",dist[t]);
    return 0;
}
View Code

 

posted @ 2017-05-05 15:45  free-loop  阅读(142)  评论(0编辑  收藏  举报