poj2723

poj2723

题意

m道门，每道门两把锁，有n对钥匙，对应2*n把锁，已知一对钥匙内取出一把另一把就会消失，求按顺序最多可开多少门 。

分析

任意一道门都是一个子句，两把锁A和B是OR的关系。即 A OR B = 1 <=> !A->B AND !B->A

二分最大可以开门的数量，判断可行性。

code

#include<cstdio>
#include<cstring>
#include<iostream>
#include<algorithm>
#include<vector>
using namespace std;
typedef long long ll;

const int INF = 1e9;
const int MAXN = 3e3 + 5;
int vis[MAXN], flag[MAXN];
vector<int> G[MAXN], rG[MAXN];
vector<int> vs;
int n, m;
void addedge(int x, int y)
{
    G[x].push_back(y);
    rG[y].push_back(x);
}

void dfs(int u)
{
    vis[u] = 1;
    for(int i = 0; i < G[u].size(); i++)
    {
        int v = G[u][i];
        if(!vis[v]) dfs(v);
    }
    vs.push_back(u);
}

void rdfs(int u, int k)
{
    vis[u] = 1; flag[u] = k;
    for(int i = 0; i < rG[u].size(); i++)
    {
        int v = rG[u][i];
        if(!vis[v]) rdfs(v, k);
    }
}

int scc()
{
    vs.clear();
    memset(vis, 0, sizeof vis);
    for(int i = 0; i < n; i++)
        if(!vis[i]) dfs(i);
    memset(vis, 0, sizeof vis);
    int k = 0;
    for(int i = vs.size() - 1; i >= 0; i--)
        if(!vis[vs[i]]) rdfs(vs[i], k++);
    return k;
}

int deny[MAXN], a[MAXN], b[MAXN];
bool judge()
{
    int N = n;
    n = 2 * n;
    scc();
    n /= 2;
    for(int i = 0; i < 2 * n; i++)
        if(flag[i] == flag[deny[i]]) return false;
    return true;
}
int solve()
{
    int l = 0, r = m, mid;
    while(l < r)
    {
        mid = (l + r) / 2;
        memset(G, 0, sizeof G);
        memset(rG, 0, sizeof rG);
        for(int i = 0; i <= mid; i++)
        {
            addedge(deny[a[i]], b[i]);
            addedge(deny[b[i]], a[i]);
        }
        if(judge()) l = mid + 1;
        else r = mid;
    }
    return l;
}
int main()
{
    while(~scanf("%d%d", &n, &m) && (n + m))
    {
        for(int i = 0; i < n; i++)
        {
            int x, y;
            scanf("%d%d", &x, &y);
            deny[x] = y; deny[y] = x;
        }
        for(int i = 0; i < m; i++)
            scanf("%d%d", &a[i], &b[i]);
        printf("%d\n", solve());
    }
    return 0;
}