BZOJ 1997: [Hnoi2010]Planar( 2sat )

平面图中E ≤ V*2-6..

一个圈上2个点的边可以是在外或者内, 经典的2sat问题..

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#include<cstdio>

#include<cstring>

#include<algorithm>

#include<stack>

 

using namespace std;

 

#define U(x) U[r[x]]

#define V(x) V[r[x]]

#define H(x) H[r[x]]

 

const int maxn = 20009;

 

struct edge {

int to;

edge* next;

} E[1000000], *pt, *head[maxn];

 

void AddEdge(int u, int v) {

pt->to = v; pt->next = head[u]; head[u] = pt++;

}

 

int Low[maxn], Dfn[maxn], Scc[maxn], CK, scc_n;

int U[maxn], V[maxn], H[maxn], P[maxn], _P[maxn], r[maxn], n;

int N, M, T;

stack<int> S;

 

void Init() {

pt = E;

memset(head, 0, sizeof head);

scanf("%d%d", &N, &M);

for(int i = 0; i < M; i++)

scanf("%d%d", U + i, V + i);

for(int i = 0; i < N; i++) {

scanf("%d", _P + i);

P[_P[i]] = i;

}

for(int i = 0; i < N; i++)

H[_P[i]] = _P[(i + 1) % N];

n = scc_n = CK = 0;

memset(Dfn, 0, sizeof Dfn);

memset(Scc, 0, sizeof Scc);

while(!S.empty()) S.pop();

}

 

bool chk(int l, int r, int _l, int _r) {

if(l > r) swap(l, r);

if(_l > _r) swap(_l, _r);

return (l < _l && _l < r && r < _r) || (_l < l && l < _r && _r < r);

}

 

void Tarjan(int x) {

Dfn[x] = Low[x] = ++CK;

S.push(x);

for(edge* e = head[x]; e; e = e->next) if(!Dfn[e->to]) {

Tarjan(e->to);

Low[x] = min(Low[x], Low[e->to]);

} else if(!Scc[e->to])

Low[x] = min(Low[x], Dfn[e->to]);

if(Dfn[x] == Low[x]) {

int t; scc_n++;

do {

t = S.top(); S.pop();

Scc[t] = scc_n;

} while(t != x);

}

}

 

bool Solve() {

if(M > 3 * N - 6) return false;

for(int i = 0; i < M; i++)

if(V[i] != H[U[i]] && U[i] != H[V[i]]) r[n++] = i;

for(int i = 0; i < n; i++)

for(int j = 0; j < i; j++)

if(chk(P[U(i)], P[V(i)], P[U(j)], P[V(j)])) {

AddEdge(i * 2, j * 2 + 1);

AddEdge(i * 2 + 1, j * 2);

AddEdge(j * 2, i * 2 + 1);

AddEdge(j * 2 + 1, i * 2);

}

for(int i = 0; i < 2 * n; i++) {

if(!Dfn[i]) Tarjan(i);

}

for(int i = 0; i < n; i++)

if(Scc[i * 2] == Scc[i * 2 + 1]) return false;

return true;

}

 

int main() {

scanf("%d", &T);

while(T--) {

Init();

puts(Solve() ? "YES" : "NO");

}

return 0;

}

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1997: [Hnoi2010]Planar

Time Limit: 10 Sec  Memory Limit: 64 MB
Submit: 1183  Solved: 458
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Day1