POJ 2749

二分+2SAT的题

写错了HIGH和LOW与MID的变换，TLE了好几次。。

按HATE和LIKE关系先加边，再用距离的限制加边。

dist(i,S1)+dist(S1,j)>limit  Xi->~Xj  Xj->Xi

dist(i,S2)+dist(S2,j)>limit  ~Xi->Xj  ~Xj->Xi

dist(i,S1)+dist(S1,S2)+dist(S2,j)>limit Xi->Xj  ~Xj->~Xi

dist(i,S2)+dist(S2,S1)+dist(S1,j)>limit ~Xi->~Xj  Xj->Xi

用离散数学的知识就能推出来，以上借别人的一用。

  1 #include <iostream>
  2 #include <cstdio>
  3 #include <cstring>
  4 #include <algorithm>
  5 #include <cmath>
  6
  7 using namespace std;
  8
  9 const int inf=8500000;
 10 const int MAXN=1050;
 11 const int MAXM=20000000;
 12 int s1_s2,dis1[MAXN],dis2[MAXN],head[MAXN],dfn[MAXN],low[MAXN],belong[MAXN];
 13 int st[MAXN],stop,indx,tot,pat;
 14 bool stack[MAXN]; int leng;
 15 int n,hn,ln;
 16 struct d{
 17     int x,y;
 18 }point[MAXN],s1,s2;
 19 struct h{
 20     int u,v;
 21 }hate[MAXN*2];
 22 struct l{
 23     int u,v;
 24 }like[MAXN*2];
 25
 26 struct ei{
 27     int u,v;
 28     int next;
 29 }edge[MAXM];
 30
 31 void addedge(int u,int v){
 32     edge[tot].u=u;
 33     edge[tot].v=v;
 34     edge[tot].next=head[u];
 35     head[u]=tot++;
 36 }
 37
 38 void tarjan(int u){
 39     int v;
 40     dfn[u]=low[u]=++indx;
 41     st[stop++]=u;
 42     stack[u]=true;
 43     for(int e=head[u];e!=-1;e=edge[e].next){
 44         v=edge[e].v;
 45         if(dfn[v]==0){
 46             tarjan(v);
 47             low[u]=min(low[u],low[v]);
 48         }
 49         else if(stack[v]){
 50             low[u]=min(low[u],dfn[v]);
 51         }
 52     }
 53     if(dfn[u]==low[u]){
 54         pat++;
 55         do{
 56             v=st[--stop];
 57             stack[v]=false;
 58             belong[v]=pat;
 59         }while(u!=v);
 60     }
 61 }
 62
 63 bool slove(){
 64     int u,v;
 65
 66     memset(head,-1,sizeof(head));
 67     memset(dfn,0,sizeof(dfn));
 68     memset(low,0,sizeof(low));
 69     memset(belong,0,sizeof(belong));
 70     stop=0; indx=0; tot=0; pat=0;
 71     memset(stack,false,sizeof(stack));
 72
 73
 74     for(int i=0;i<hn;i++){
 75         u=hate[i].u;
 76         v=hate[i].v;
 77         addedge(u*2,v*2+1);
 78         addedge(v*2,u*2+1);
 79         addedge(2*u+1,2*v);
 80         addedge(2*v+1,2*u);
 81     }
 82     for(int i=0;i<ln;i++){
 83         u=like[i].u;
 84         v=like[i].v;
 85         addedge(u*2,v*2);
 86         addedge(v*2,u*2);
 87         addedge(2*u+1,2*v+1);
 88         addedge(2*v+1,2*u+1);
 89     }
 90     for(int i=0;i<n;i++){
 91         for(int j=i+1;j<n;j++){
 92             if(dis1[i]+dis1[j]>leng){
 93                 addedge(i*2,j*2+1);
 94                 addedge(j*2,i*2+1);
 95             }
 96             if(dis2[i]+dis2[j]>leng){
 97                 addedge(i*2+1,j*2);
 98                 addedge(j*2+1,i*2);
 99             }
100             if(dis1[i]+s1_s2+dis2[j]>leng){
101                 addedge(i*2,j*2);
102                 addedge(j*2+1,i*2+1);
103             }
104             if(dis2[i]+s1_s2+dis1[j]>leng){
105                 addedge(j*2,i*2);
106                 addedge(i*2+1,j*2+1);
107             }
108         }
109     }
110     for(int i=0;i<2*n;i++){
111         if(dfn[i]==0)
112         tarjan(i);
113     }
114     bool flag=true;
115     for(int i=0;i<n;i++){
116         if(belong[2*i]==belong[2*i+1]){
117             flag=false;
118             break;
119         }
120     }
121     return flag;
122 }
123
124 int main(){
125     int u,v; int tmp;
126     while(scanf("%d%d%d",&n,&hn,&ln)!=EOF){
127         scanf("%d%d%d%d",&s1.x,&s1.y,&s2.x,&s2.y);
128         for(int i=0;i<n;i++){
129         scanf("%d%d",&point[i].x,&point[i].y);
130         }
131         for(int i=0;i<hn;i++){
132             scanf("%d%d",&u,&v);
133             u--; v--;
134             hate[i].u=u; hate[i].v=v;
135         }
136         for(int i=0;i<ln;i++){
137             scanf("%d%d",&u,&v);
138             u--; v--;
139             like[i].u=u; like[i].v=v;
140         }
141         for(int i=0;i<n;i++){
142             tmp=abs(point[i].x-s1.x)+abs(point[i].y-s1.y);
143             dis1[i]=tmp;
144             tmp=abs(point[i].x-s2.x)+abs(point[i].y-s2.y);
145             dis2[i]=tmp;
146         }
147         s1_s2=abs(s1.x-s2.x)+abs(s1.y-s2.y);
148         int lown=1,high=inf,ans=-1;
149         while(lown<=high){
150             int mid=(lown+high)/2;
151             leng=mid;
152             if(slove()){
153                 ans=mid;
154                 high=mid-1;
155             }
156             else lown=mid+1;
157         }
158         printf("%d\n",ans);
159     }
160     return 0;
161 }

POJ 2749