Poj 3678 Katu puzzle

Katu puzzletime limit: 1000 msmemory limit: 65536 kbthis problem will be judged on PKU. Original ID: 3678
64-bit integer Io format: % LLD Java class name: Main

Katu puzzle is presented as a Directed GraphG(V,E) With each edgeE(A,B) Labeled by a boolean operatorOP(One of and, Or, XOR) and an integerC(0 ≤C≤ 1). One Katu is solvable if one can find each vertexVIA ValueXI(0 ≤XI≤ 1) such that for each edgeE(A,B) LabeledOPAndC, The following formula holds:

 XA OP XB=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 integersN(1 ≤N≤ 1000) andM, (0 ≤M≤ 1,000,000) indicating the number of vertices and edges. The followingMLines contain three IntegersA(0 ≤A<N),B(0 ≤B<N),CAnd an operatorOPEach, describing the edges.

Output

Output A line containing "yes" or "no ".

Sample Input

4 40 1 1 AND1 2 1 OR3 2 0 AND3 0 0 XOR

Sample output

YES

Sourcepoj founder monthly contest-2008.07.27 problem solving: 2sat

  1 #include <iostream>  2 #include <cstdio>  3 #include <cstring>  4 #include <cmath>  5 #include <algorithm>  6 #include <climits>  7 #include <vector>  8 #include <queue>  9 #include <cstdlib> 10 #include <string> 11 #include <set> 12 #include <stack> 13 #define LL long long 14 #define pii pair<int,int> 15 #define INF 0x3f3f3f3f 16 using namespace std; 17 const int maxn = 2010; 18 struct arc{ 19     int to,next; 20     arc(int x = 0,int y = -1){ 21         to = x; 22         next = y; 23     } 24 }; 25 arc e[4000010]; 26 int head[maxn],dfn[maxn],low[maxn],belong[maxn]; 27 int tot,cnt,scc,n,m; 28 bool instack[maxn]; 29 stack<int>stk; 30 void add(int u,int v){ 31     e[tot] = arc(v,head[u]); 32     head[u] = tot++; 33 } 34 void init(){ 35     for(int i = 0; i < maxn; i++){ 36         belong[i] = 0; 37         low[i] = dfn[i] = 0; 38         head[i] = -1; 39         instack[i] = false; 40     } 41     while(!stk.empty()) stk.pop(); 42     tot = cnt = scc = 0; 43 } 44 void tarjan(int u){ 45     dfn[u] = low[u] = ++cnt; 46     instack[u] = true; 47     stk.push(u); 48     for(int i = head[u]; ~i; i = e[i].next){ 49         if(!dfn[e[i].to]){ 50             tarjan(e[i].to); 51             if(low[e[i].to] < low[u]) low[u] = low[e[i].to]; 52         }else if(instack[e[i].to] && dfn[e[i].to] < low[u]) 53             low[u] = dfn[e[i].to]; 54     } 55     if(dfn[u] == low[u]){ 56         scc++; 57         int v; 58         do{ 59             v = stk.top(); 60             stk.pop(); 61             instack[v] = false; 62             belong[v] = scc; 63         }while(v != u); 64     } 65 } 66 bool solve(){ 67     for(int i = 0; i < (n<<1); i++) 68         if(!dfn[i]) tarjan(i); 69     for(int i = 0; i < n; i++) 70         if(belong[i] == belong[i+n]) return false; 71     return true; 72 } 73 int main() { 74     char op[5]; 75     int u,v,c; 76     while(~scanf("%d %d",&n,&m)){ 77         init(); 78         while(m--){ 79             scanf("%d %d %d %s",&u,&v,&c,op); 80             if(op[0] == ‘A‘){ 81                 if(c){ 82                     add(u+n,v+n); 83                     add(v+n,u+n); 84                     add(u,u+n); 85                     add(v,v+n); 86                 }else{ 87                     add(u+n,v); 88                     add(v+n,u); 89                 } 90             }else if(op[0] == ‘O‘){ 91                 if(c){ 92                     add(u,v+n); 93                     add(v,u+n); 94                 }else{ 95                     add(u,v); 96                     add(v,u); 97                     add(u+n,u); 98                     add(v+n,v); 99                 }100             }else if(op[0] == ‘X‘){101                 if(c){102                     add(u,v+n);103                     add(v,u+n);104                     add(u+n,v);105                     add(v+n,u);106                 }else{107                     add(u,v);108                     add(v,u);109                     add(u+n,v+n);110                     add(v+n,u+n);111                 }112             }113         }114         printf("%s\n",solve()?"YES":"NO");115     }116     return 0;117 }

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Poj 3678 Katu puzzle