BZOJ1001 / LG4001 "ICPC Beijing2006" wolf caught rabbits minimal cut plan shortest turn dual graph

Problem Description

BZOJ1001

LG4001

---

answer

= Minimum cut plan view of the dual FIG shortest

Suppose there are other sides do not intersect a virtual edge between the start and end points.

As shown, a plan view of a number of plane sides is divided into a number of graphics, each graphic is a dual point of FIG.

For each point in the dual graph, between it and adjacent to each side in a plan view with a pattern, the right side edge thereof to separate the original weights of the edges.

Thus the minimum cut is a plan view of the dual shortest FIG.

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\(\mathrm{Code}\)

#include<bits/stdc++.h>
using namespace std;

const int maxn=2*1000*1000+7;
int n,m,S,T;
int Head[maxn],to[maxn*3],Next[maxn*3],tot=1,w[maxn*3];

void addedge(int x,int y,int z){
    to[++tot]=y,Next[tot]=Head[x],Head[x]=tot,w[tot]=z;
}

void add(int x,int y,int z){
    addedge(x,y,z);addedge(y,x,z);
}

void Init(void){
    scanf("%d%d",&n,&m);
}

int id(int x,int y,int type){
    return (x-1)*(m-1)+y+(type-1)*(n-1)*(m-1);
}

void Hori(void){
    for(int i=1,x;i<m;i++){
        scanf("%d",&x);
        add(S,id(1,i,1),x);
    }
    for(int i=2,x;i<n;i++){
        for(int j=1;j<m;j++){
            scanf("%d",&x);
            add(id(i-1,j,2),id(i,j,1),x);
        }
    }
    for(int i=1,x;i<m;i++){
        scanf("%d",&x);
        add(id(n-1,i,2),T,x);
    }
}

void Longi(void){
    for(int i=1,x;i<n;i++){
        scanf("%d",&x);add(T,id(i,1,2),x);
        for(int j=2;j<m;j++){
            scanf("%d",&x);
            add(id(i,j-1,1),id(i,j,2),x);
        }
        scanf("%d",&x);add(id(i,m-1,1),S,x);
    }
}

void Obli(void){
    for(int i=1;i<n;i++){
        for(int j=1,x;j<m;j++){
            scanf("%d",&x);
            add(id(i,j,1),id(i,j,2),x);
        }
    }
}

void Graph_build(void){
    S=(n-1)*(m-1)*2+1,T=S+1;
    Hori();
    Longi();
    Obli();
}

int dis[maxn];
bool vis[maxn];
#define pii(x,y) make_pair(x,y)

void dijkstra(void){
    memset(dis,0x3f,sizeof(dis));
    priority_queue<pair<int,int> >q;
    q.push(pii(0,S));dis[S]=0;
    while(!q.empty()){
        int x=(q.top()).second;q.pop();
        if(vis[x]) continue;vis[x]=1;
        if(x==T) return;
        for(int i=Head[x];i;i=Next[i]){
            int y=to[i];
            if(dis[y]>dis[x]+w[i]){
                dis[y]=dis[x]+w[i];
                q.push(pii(-dis[y],y));
            }
            //if(y==T) return;
        }
    }
}

void One(void){
    int ans=0x3f3f3f3f,x;
    for(int i=1;i<=n;i++) for(int j=1;j<m;j++){
        scanf("%d",&x);ans=min(ans,x);
    }
    for(int i=1;i<n;i++) for(int j=1;j<=m;j++){
        scanf("%d",&x);ans=min(ans,x);
    }
    printf("%d\n",ans);
}

void Work(void){
    if(n==1||m==1){
        One();return;
    }
    Graph_build();
    dijkstra();
    printf("%d\n",dis[T]);
}

int main(){
    Init();
    Work();
    return 0;
}