2-sat(石头、剪刀、布)hdu4115

Eliminate the Conflict

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)

Total Submission(s): 1732    Accepted Submission(s): 751

Problem Description

Conflicts are everywhere in the world, from the young to the elderly, from families to countries. Conflicts cause quarrels, fights or even wars. How wonderful the world will be if all conflicts can be eliminated.

Edward contributes his lifetime to invent a 'Conflict Resolution Terminal' and he has finally succeeded. This magic item has the ability to eliminate all the conflicts. It works like this:

If any two people have conflict, they should simply put their hands into the 'Conflict Resolution Terminal' (which is simply a plastic tube). Then they play 'Rock, Paper and Scissors' in it. After they have decided what they will play, the tube should be opened
and no one will have the chance to change. Finally, the winner have the right to rule and the loser should obey it. Conflict Eliminated!

But the game is not that fair, because people may be following some patterns when they play, and if the pattern is founded by others, the others will win definitely.

Alice and Bob always have conflicts with each other so they use the 'Conflict Resolution Terminal' a lot. Sadly for Bob, Alice found his pattern and can predict how Bob plays precisely. She is very kind that doesn't want to take advantage of that. So she tells
Bob about it and they come up with a new way of eliminate the conflict:

They will play the 'Rock, Paper and Scissors' for N round. Bob will set up some restricts on Alice.

But the restrict can only be in the form of "you must play the same (or different) on the ith and jth rounds". If Alice loses in any round or break any of the rules she loses, otherwise she wins.

Will Alice have a chance to win?

 

Input

The first line contains an integer T(1 <= T <= 50), indicating the number of test cases.

Each test case contains several lines.

The first line contains two integers N,M(1 <= N <= 10000, 1 <= M <= 10000), representing how many round they will play and how many restricts are there for Alice.

The next line contains N integers B₁,B₂, ...,B_N, where B_i represents what item Bob will play in the i^th round. 1 represents Rock, 2 represents Paper, 3 represents Scissors.

The following M lines each contains three integers A,B,K(1 <= A,B <= N,K = 0 or 1) represent a restrict for Alice. If K equals 0, Alice must play the same on A^th and B^th round. If K equals 1, she must play different items on Ath and Bthround.

 

Output

For each test case in the input, print one line: "Case #X: Y", where X is the test case number (starting with 1) and Y is "yes" or "no" represents whether Alice has a chance to win.

Sample Input

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

 

Sample Output

Case #1: no
Case #2: yes

Hint

'Rock, Paper and Scissors' is a game which played by two person. They should play Rock, Paper or Scissors by their hands at the same time.
Rock defeats scissors, scissors defeats paper and paper defeats rock. If two people play the same item, the game is tied..

题意：两个人玩石头剪刀布，进行n轮比赛，首先给出B的这n轮的手势，然后m行对A的限制，每行a，b，c当c==0的时候代表A第a轮和第b轮的手势相同，c==1表示第a轮和第b轮的手势不同，如果A在任何一轮中输掉或者违反规定的话，A就是输的，问A有没有赢的可能；
分析：开始看的时候每轮A都是有3个选择，但是其实只有两个合法的选择，即平局和胜利的手势，所以应该是用2-sat判矛盾，主要是建图，当c==0时说明ab两轮的手势相同就是合法的，不同就是矛盾，对于矛盾建边，c==1的时候同理；

#include"stdio.h"
#include"string.h"
#include"stdlib.h"
#include"queue"
#include"algorithm"
#include"string.h"
#include"string"
#include"stack"
#include"map"
#define inf 0x3f3f3f3f
#define M 20009
using namespace std;
struct node
{
    int u,v,next;
}edge[M*20];
stack<int>q;
int t,head[M],low[M],dfn[M],belong[M],num,index,use[M];
void init()
{
    t=0;
    memset(head,-1,sizeof(head));
}
void add(int u,int v)
{
    edge[t].u=u;
    edge[t].v=v;
    edge[t].next=head[u];
    head[u]=t++;
}
void tarjan(int u)
{
    low[u]=dfn[u]=++index;
    q.push(u);
    use[u]=1;
    for(int i=head[u];i!=-1;i=edge[i].next)
    {
        int v=edge[i].v;
        if(!dfn[v])
        {
            tarjan(v);
            low[u]=min(low[u],low[v]);
        }
        else if(use[v])
            low[u]=min(low[u],dfn[v]);
    }
    if(low[u]==dfn[u])
    {
        num++;
        int vv;
        do
        {
            vv=q.top();
            q.pop();
            use[vv]=0;
            belong[vv]=num;
        }while(vv!=u);
    }
}
int psq(int n)
{
    int i;
    num=index=n;
    memset(use,0,sizeof(use));
    memset(dfn,0,sizeof(dfn));
    for(i=1;i<=2*n;i++)
        if(!dfn[i])
        tarjan(i);
    for(i=1;i<=n;i++)
        if(belong[i]==belong[i+n])
        return 0;
    return 1;
}
int a[M],b[M];
int main()
{
    int T,m,n,i,u,v,w,kk=1;
    scanf("%d",&T);
    while(T--)
    {
        scanf("%d%d",&n,&m);
        init();
        for(i=1;i<=n;i++)
        {
            scanf("%d",&b[i]);
            a[i]=((b[i]+1)%3==0)?3:(b[i]+1)%3;
            a[i+n]=b[i];
        }
        for(i=1;i<=m;i++)
        {
            scanf("%d%d%d",&u,&v,&w);
            if(w==0)
            {
                if(a[u]!=a[v])
                {
                    add(u,v+n);
                    add(v,u+n);
                }
                if(a[u]!=a[v+n])
                {
                    add(u,v);
                    add(v+n,u+n);
                }
                if(a[u+n]!=a[v])
                {
                    add(u+n,v+n);
                    add(v,u);
                }
                if(a[u+n]!=a[v+n])
                {
                    add(u+n,v);
                    add(v+n,u);
                }
            }
            else
            {
                if(a[u]==a[v])
                {
                    add(u,v+n);
                    add(v,u+n);
                }
                if(a[u]==a[v+n])
                {
                    add(u,v);
                    add(v+n,u+n);
                }
                if(a[u+n]==a[v])
                {
                    add(u+n,v+n);
                    add(v,u);
                }
                if(a[u+n]==a[v+n])
                {
                    add(u+n,v);
                    add(v+n,u);
                }
            }
        }
        printf("Case #%d: ",kk++);
        if(psq(n))
            printf("yes\n");
        else
            printf("no\n");
    }
}