BZOJ 1997 HNOI 2010 Planar 2-SAT

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题目大意：给出一个无向图，保证这个图有哈密顿回路，求这个图是不是平面图。

思路：平面图的判定条件之一：如果边数大于点数*3+6那么这个图一定不是平面图。这算是一个强剪枝吧。

我们把图中哈密顿回路的这个环上的边去掉，就变成了判定边能否不想交的2-SAT问题，POJ好像有一个原题来着。建图方法我就不说了，相信大家看到2-SAT就知道怎么写了。

CODE：

#include <cstdio>#include <cstring>#include <iostream>#include <algorithm>#define MAX 10010using namespace std; struct Edge{    int x,y;         Edge(int _,int __):x(_),y(__) {}    Edge() {}    void Read() {        scanf("%d%d",&x,&y);    }}edge[MAX],stack[MAX];int top; int cases,points,edges;int C[MAX]; inline bool Judge(const Edge &a,const Edge &b){    return b.x > a.x && b.x < a.y && b.y > a.y;} namespace II_SAT{    int head[MAX],total;    int next[819200],aim[819200];         int dfn[MAX],low[MAX],_clock;    int stack[MAX],top;    bool in_stack[MAX];    int changed[MAX],scc;         void Initialize() {        total = _clock = scc = top = 0;        memset(head,0,sizeof(head));        memset(dfn,0,sizeof(dfn));        memset(in_stack,false,sizeof(in_stack));    }    void Add(int x,int y) {        next[++total] = head[x];        aim[total] = y;        head[x] = total;    }    void Tarjan(int x) {        dfn[x] = low[x] = ++_clock;        stack[++top] = x;        in_stack[x] = true;        for(int i = head[x]; i; i = next[i]) {            if(!dfn[aim[i]])                Tarjan(aim[i]),low[x] = min(low[x],low[aim[i]]);            else if(in_stack[aim[i]])                low[x] = min(low[x],dfn[aim[i]]);        }        if(dfn[x] == low[x]) {            ++scc;            int temp;            do {                temp = stack[top--];                in_stack[temp] = false;                changed[temp] = scc;            }while(temp != x);        }    }} int main(){    for(cin >> cases; cases--;) {        scanf("%d%d",&points,&edges);        for(int i = 1; i <= edges; ++i)            edge[i].Read();        for(int x,i = 1; i <= points; ++i) {            scanf("%d",&x);            C[x] = i;        }        if(edges > 3 * points + 6) {            puts("NO");            continue;        }        top = 0;        for(int i = 1; i <= edges; ++i) {            int s = C[edge[i].x],t = C[edge[i].y];            if(s > t)    swap(s,t);            if(!((s + 1 == t) || (s == 1 && t == points)))                stack[++top] = Edge(s,t);        }        II_SAT::Initialize();        for(int i = 1; i <= top; ++i)            for(int j = i + 1; j <= top; ++j)                if(Judge(stack[i],stack[j]) || Judge(stack[j],stack[i])) {                    II_SAT::Add(i << 1,j << 1|1);                    II_SAT::Add(j << 1|1,i << 1);                    II_SAT::Add(j << 1,i << 1|1);                    II_SAT::Add(i << 1|1,j << 1);                }        for(int i = 2; i <= (top << 1|1); ++i)            if(!II_SAT::dfn[i])                II_SAT::Tarjan(i);        bool flag = true;        for(int i = 1; i <= top; ++i)            if(II_SAT::changed[i << 1] == II_SAT::changed[i << 1|1]) {                flag = false;                break;            }        puts(&"NO\0YES"[flag * 3]);    }    return 0;}

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