poj 3678 Katu Puzzle 2-SAT-优快云博客

本文链接：https://blog.youkuaiyun.com/cyendra/article/details/9863131

本文介绍了一种名为KatuPuzzle的图论问题，其中包含节点与边的布尔运算和整数值，旨在确定是否存在一种赋值方式使得所有边的布尔公式成立。通过输入给出的节点数和边数，以及每条边的起始节点、终止节点、整数值和运算符，文章展示了如何判断KatuPuzzle是否可解，并提供了具体的解题步骤和算法实现。

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Katu Puzzle

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 6702		Accepted: 2463

Description

Katu Puzzle is presented as a directed graph G(V, E) with each edge e(a, b) labeled by a boolean operator op (one of AND, OR, XOR) and an integer c (0 ≤ c ≤ 1). One Katu is solvable if one can find each vertex V_i a value X_i (0 ≤ X_i≤ 1) such that for each edge e(a, b) labeled by op and c, the following formula holds:

X_a op X_b = c

The calculating rules are:

AND	0	1
0	0	0
1	0	1

OR	0	1
0	0	1
1	1	1

XOR	0	1
0	0	1
1	1	0

Given a Katu Puzzle, your task is to determine whether it is solvable.

Input

The first line contains two integers N (1 ≤ N ≤ 1000) and M,(0 ≤ M ≤ 1,000,000) indicating the number of vertices and edges.
The following M lines contain three integers a (0 ≤ a < N), b(0 ≤ b < N), c and an operator op each, describing the edges.

Output

Output a line containing "YES" or "NO".

Sample Input

4 4
0 1 1 AND
1 2 1 OR
3 2 0 AND
3 0 0 XOR

Sample Output

YES

Hint

X₀ = 1, X₁ = 1, X₂ = 0, X₃ = 1.

------------

真正理解了2-SAT才能建出图

------------

/** head-file **/

#include <iostream>
#include <fstream>
#include <sstream>
#include <iomanip>
#include <cstdio>
#include <cmath>
#include <cstring>
#include <string>
#include <vector>
#include <queue>
#include <stack>
#include <list>
#include <set>
#include <map>
#include <algorithm>

/** define-for **/

#define REP(i, n) for (int i=0;i<int(n);++i)
#define FOR(i, a, b) for (int i=int(a);i<int(b);++i)
#define DWN(i, b, a) for (int i=int(b-1);i>=int(a);--i)
#define REP_1(i, n) for (int i=1;i<=int(n);++i)
#define FOR_1(i, a, b) for (int i=int(a);i<=int(b);++i)
#define DWN_1(i, b, a) for (int i=int(b);i>=int(a);--i)
#define REP_N(i, n) for (i=0;i<int(n);++i)
#define FOR_N(i, a, b) for (i=int(a);i<int(b);++i)
#define DWN_N(i, b, a) for (i=int(b-1);i>=int(a);--i)
#define REP_1_N(i, n) for (i=1;i<=int(n);++i)
#define FOR_1_N(i, a, b) for (i=int(a);i<=int(b);++i)
#define DWN_1_N(i, b, a) for (i=int(b);i>=int(a);--i)

/** define-useful **/

#define clr(x,a) memset(x,a,sizeof(x))
#define sz(x) int(x.size())
#define see(x) cerr<<#x<<" "<<x<<endl
#define se(x) cerr<<" "<<x
#define pb push_back
#define mp make_pair

/** test **/

#define Display(A, n, m) {                      \
    REP(i, n){                                  \
        REP(j, m) cout << A[i][j] << " ";       \
        cout << endl;                           \
    }                                           \
}

#define Display_1(A, n, m) {                    \
    REP_1(i, n){                                \
        REP_1(j, m) cout << A[i][j] << " ";     \
        cout << endl;                           \
    }                                           \
}

using namespace std;

/** typedef **/

typedef long long LL;

/** Add - On **/

const int direct4[4][2]={ {0,1},{1,0},{0,-1},{-1,0} };
const int direct8[8][2]={ {0,1},{1,0},{0,-1},{-1,0},{1,1},{1,-1},{-1,1},{-1,-1} };
const int direct3[6][3]={ {1,0,0},{0,1,0},{0,0,1},{-1,0,0},{0,-1,0},{0,0,-1} };

const int MOD = 1000000007;
const int INF = 0x3f3f3f3f;
const long long INFF = 1LL << 60;
const double EPS = 1e-9;
const double OO = 1e15;
const double PI = acos(-1.0); //M_PI;

const int maxn=11111;
const int maxm=2111111;
int n,m;
struct EDGENODE{
    int to;
    int next;
};
struct TWO_SAT{
    int head[maxn*2];
    EDGENODE edges[maxm*2];
    int edge;
    int n;
    void init(int n){
        this->n=2*n;
        clr(head,-1);
        edge=0;
    }
    void addedge(int u,int v){
        edges[edge].to=v,edges[edge].next=head[u],head[u]=edge++;
    }
    // x = xval or y = yval
    //!x->y,!y->x
    void add_clause(int x,int xval,int y,int yval){
        x=x*2+xval;
        y=y*2+yval;
        addedge(x^1,y);
        addedge(y^1,x);
    }
    //x=xval
    //!x=x
    void add_con(int x,int xval){
        x=x*2+xval;
        addedge(x^1,x);
    }
    //--
    void add_self(int x,int xval,int y,int yval){
        x=x*2+xval;
        y=y*2+yval;
        addedge(x,y);
    }
    int pre[maxn],lowlink[maxn],sccno[maxn],scc_cnt,dfs_clock;
    stack<int>stk;
    void dfs(int u)
    {
        pre[u]=lowlink[u]=++dfs_clock;
        stk.push(u);
        for (int i=head[u];i!=-1;i=edges[i].next){
            int v=edges[i].to;
            if (!pre[v]){
                dfs(v);
                lowlink[u]=min(lowlink[u],lowlink[v]);
            } else if (!sccno[v]){
                lowlink[u]=min(lowlink[u],pre[v]);
            }
        }
        if (lowlink[u]==pre[u]){
            scc_cnt++;
            int x;
            do{
                x=stk.top();
                stk.pop();
                sccno[x]=scc_cnt;
            }while (x!=u);
        }
    }
    void find_scc(int n)
    {
        dfs_clock=scc_cnt=0;
        clr(sccno,0);
        clr(pre,0);
        while (!stk.empty()) stk.pop();
        REP(i,n) if (!pre[i]) dfs(i);
    }
    bool solve(){
        find_scc(n);
        for (int i=0;i<n;i+=2){
            if (sccno[i]==sccno[i^1]) return false;
        }
        return true;
    }
}TwoSAT;

int main()
{
    int a,b,c;
    char s[4];
    while (~scanf("%d%d",&n,&m))
    {
        TwoSAT.init(n);
        REP(i,m)
        {
            scanf("%d%d%d%s",&a,&b,&c,s);
            /*
            if (!strcmp(s,"AND")){
                if (c==1){
                    TwoSAT.add_self(a,1,a,0);
                    TwoSAT.add_self(b,1,b,0);
                }else if (c==0){
                    TwoSAT.add_self(a,0,b,1);
                    TwoSAT.add_self(b,0,a,1);
                }
            }
            if (!strcmp(s,"OR")){
                if (c==1){
                    TwoSAT.add_self(a,1,b,0);
                    TwoSAT.add_self(b,1,a,0);
                }else if (c==0){
                    TwoSAT.add_self(a,0,a,1);
                    TwoSAT.add_self(b,0,b,1);
                }
            }
            if (!strcmp(s,"XOR")){
                if (c==1){
                    TwoSAT.add_self(a,0,b,1);
                    TwoSAT.add_self(b,0,a,1);
                    TwoSAT.add_self(a,1,b,0);
                    TwoSAT.add_self(b,1,a,0);
                }else if (c==0){
                    TwoSAT.add_self(a,0,b,0);
                    TwoSAT.add_self(b,0,a,0);
                    TwoSAT.add_self(a,1,b,1);
                    TwoSAT.add_self(b,1,a,1);
                }
            }*/
            if (!strcmp(s,"AND")){
                if (c==1){
                    TwoSAT.add_con(a,1);
                    TwoSAT.add_con(b,1);
                }else if (c==0){
                    TwoSAT.add_clause(a,0,b,0);
                }
            }
            if (!strcmp(s,"OR")){
                if (c==1){
                    TwoSAT.add_clause(a,1,b,1);
                }else if (c==0){
                    TwoSAT.add_con(a,0);
                    TwoSAT.add_con(b,0);
                }
            }
            if (!strcmp(s,"XOR")){
                if (c==1){
                    TwoSAT.add_clause(a,1,b,1);
                    TwoSAT.add_clause(a,0,b,0);
                }else if (c==0){
                    TwoSAT.add_clause(a,1,b,0);
                    TwoSAT.add_clause(a,0,b,1);
                }
            }
        }
        if (TwoSAT.solve()) puts("YES");
        else puts("NO");
    }
    return 0;
}