pap side 沒有 script encrypted 2-sat when words leading

Get Luffy Out

Time Limit: 2000MS		Memory Limit: 65536K
Total Submissions: 9022		Accepted: 3503

Description

Ratish is a young man who always dreams of being a hero. One day his friend Luffy was caught by Pirate Arlong. Ratish set off at once to Arlong‘s island. When he got there, he found the secret place where his friend was kept, but he could not go straight in. He saw a large door in front of him and two locks in the door. Beside the large door, he found a strange rock, on which there were some odd words. The sentences were encrypted. But that was easy for Ratish, an amateur cryptographer. After decrypting all the sentences, Ratish knew the following facts:

Behind the large door, there is a nesting prison, which consists of M floors. Each floor except the deepest one has a door leading to the next floor, and there are two locks in each of these doors. Ratish can pass through a door if he opens either of the two locks in it. There are 2N different types of locks in all. The same type of locks may appear in different doors, and a door may have two locks of the same type. There is only one key that can unlock one type of lock, so there are 2N keys for all the 2N types of locks. These 2N keys were divided into N pairs, and once one key in a pair is used, the other key will disappear and never show up again.

Later, Ratish found N pairs of keys under the rock and a piece of paper recording exactly what kinds of locks are in the M doors. But Ratish doesn‘t know which floor Luffy is held, so he has to open as many doors as possible. Can you help him to choose N keys to open the maximum number of doors?

Input

There are several test cases. Every test case starts with a line containing two positive integers N (1 <= N <= 2¹⁰) and M (1 <= M <= 2¹¹) separated by a space, the first integer represents the number of types of keys and the second integer represents the number of doors. The 2N keys are numbered 0, 1, 2, ..., 2N - 1. Each of the following N lines contains two different integers, which are the numbers of two keys in a pair. After that, each of the following M lines contains two integers, which are the numbers of two keys corresponding to the two locks in a door. You should note that the doors are given in the same order that Ratish will meet. A test case with N = M = 0 ends the input, and should not be processed.

Output

For each test case, output one line containing an integer, which is the maximum number of doors Ratish can open.

Sample Input

3 6
0 3
1 2
4 5
0 1
0 2
4 1
4 2
3 5
2 2
0 0

Sample Output

4

Source

Beijing 2005 分析：其實這道題的本質就是2-SAT問題，每一個門都是一個限制條件，如果我們要求最多通過的門數，可以按照順序枚舉，每次添加兩對限制條件進去，看看有沒有解就好了.如果想進一步優化可以用二分. 要註意的是可能會存在一個門需要的鑰匙是相同的，這個時候我們就必須選了，也就是不選的點i‘連向選的點i.

#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
#include <cmath>
#include <stack>

using namespace std;

const int maxn = 10010,maxm = 200010;

int n,m,key[maxn],a[maxn],b[maxn],pre[maxn],low[maxn],scc[maxn],dfs_clock,head[maxn],nextt[maxm],to[maxm],tot = 1,top;

stack<int> s;

void add(int x,int y)
{
    to[tot] = y;
    nextt[tot] = head[x];
    head[x] = tot++;
}

void tarjan(int u)
{
    pre[u] = low[u] = ++dfs_clock;
    s.push(u);
    for (int i = head[u];i;i = nextt[i])
    {
        int v = to[i];
        if (!pre[v])
        {
            tarjan(v);
            low[u] = min(low[u],low[v]);
        }
        else
        if (!scc[v])
        low[u] = min(low[u],pre[v]);
    }
    if (low[u] == pre[u])
    {
        top++;
        while (1)
        {
            int t = s.top();
            s.pop();
            scc[t] = top;
            if (t == u)
            break;
        } 
    }
}

bool solve()
{
    for (int i = 0; i < n * 2; i++)
    if (!pre[i])
    tarjan(i);
    for (int i = 0; i < n * 2; i += 2)
    if (scc[i] == scc[i ^ 1])
    return false;
    return true;
}

int main()
{
    while (scanf("%d%d",&n,&m) && (n || m))
    {
        memset(head,0,sizeof(head));
        tot = 1;
        for (int i = 0; i < n; i++)
        {
            int u,v;
            scanf("%d%d",&u,&v);
            key[u] = i * 2;
            key[v] = i * 2 + 1;
        }
        for (int i = 0; i < m; i++)
        scanf("%d%d",&a[i],&b[i]);
        for (int i = 0; i < m; i++)
        {
            if (a[i] == b[i])
            add(key[a[i]] ^ 1,key[a[i]]); //必須選，所以表示不選的點要連向選的點
            else
            {
                add(key[a[i]] ^ 1,key[b[i]]);
                add(key[b[i]] ^ 1,key[a[i]]);
            }
            memset(pre,0,sizeof(pre));
            memset(low,0,sizeof(low));
            memset(scc,0,sizeof(scc));
            top = 0;
            dfs_clock = 0;
            if (!solve())
            {
                printf("%d\n",i);
                break;
            }
            if (i == m - 1)
            printf("%d\n",m);
        }
    }


    return 0;
}

poj2723 Get Luffy Out