挑战程序竞赛系列（78）：4.3 2-SAT（2）

挑战程序竞赛系列（78）：4.3 2-SAT（2）

传送门：POJ 3678: Katu Puzzle

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题意：

某组合电路有N个输入，M个与或异或门将其两两相连构成多个输出，问是否存在满足给定输出的输入。

思路：
2-SAT模型都是解题套路，对于每一条边，如 0 1 1 AND：

ANDa b 0 0 00 1 01 0 01 1 1给定c = 1，说明 0-0，0-1，1-0的关系矛盾，据此加边：2 * a， 2 * b 等价于 02 * a + 1 , 2 * b + 1等价于 1scc.add(2 * a, 2 * b + 1);scc.add(2 * b, 2 * a + 1);scc.add(2 * a, 2 * b);scc.add(2 * b + 1, 2 * a + 1);scc.add(2 * a + 1, 2 * b + 1);scc.add(2 * b, 2 * a);给定c = 0，说明 1-1关系矛盾，据此加边：scc.add(2 * a + 1, 2 * b);scc.add(2 * b + 1, 2 * a);异或，或同理。

代码如下：

import java.io.BufferedReader;import java.io.File;import java.io.FileInputStream;import java.io.IOException;import java.io.InputStream;import java.io.InputStreamReader;import java.io.PrintWriter;import java.util.ArrayList;import java.util.Arrays;import java.util.List;import java.util.StringTokenizer;public class Main{    String INPUT = "./data/judge/201709/P3678.txt";    public static void main(String[] args) throws IOException {        new Main().run();    }    class SCC {        static final int MAX_V = 1000 + 8;        List<Integer>[] g  = new List[MAX_V];        List<Integer>[] rg = new List[MAX_V];        List<Integer> po   = new ArrayList<Integer>();        boolean[] used = new boolean[MAX_V];        int[] cmp = new int[MAX_V];        int V;        SCC(int V) {            this.V = V;            po = new ArrayList<Integer>();            Arrays.fill(used, false);            for (int i = 0; i < V; ++i) g[i]  = new ArrayList<Integer>();            for (int i = 0; i < V; ++i) rg[i] = new ArrayList<Integer>();        }        void add(int from, int to) {            g[from].add(to);            rg[to].add(from);        }        void dfs(int v) {            used[v] = true;            for (int u : g[v]) {                if (!used[u]) dfs(u);            }            po.add(v);        }        void rdfs(int v, int k) {            used[v] = true;            cmp[v]  = k;            for (int u : rg[v]) {                if (!used[u]) rdfs(u, k);            }        }        int kosarajuSCC() {            for (int v = 0; v < V; ++v) {                if (!used[v]) dfs(v);            }            Arrays.fill(used, false);            int k = 0;            for (int i = po.size() - 1; i >= 0; --i) {                int v = po.get(i);                if (!used[v]) rdfs(v, k++);            }            return k;        }    }    void read() {        int N = ni();        int M = ni();        SCC scc = new SCC(N * 2);        for (int i = 0; i < M; ++i) {            int a = ni();            int b = ni();            int c = ni();            String op = ns();            if (op.equals("AND")) {                if (c == 0) {                    scc.add(2 * a + 1, 2 * b);                    scc.add(2 * b + 1, 2 * a);                }                else {                    scc.add(2 * a, 2 * b + 1);                    scc.add(2 * b, 2 * a + 1);                    scc.add(2 * a, 2 * b);                    scc.add(2 * b + 1, 2 * a + 1);                    scc.add(2 * a + 1, 2 * b + 1);                    scc.add(2 * b, 2 * a);                }            }            else if (op.equals("OR")) {                if (c == 0) {                    scc.add(2 * a, 2 * b);                    scc.add(2 * b + 1, 2 * a + 1);                    scc.add(2 * a + 1, 2 * b + 1);                    scc.add(2 * b, 2 * a);                    scc.add(2 * a + 1, 2 * b);                    scc.add(2 * b + 1, 2 * a);                }                else {                    scc.add(2 * a, 2 * b + 1);                    scc.add(2 * b, 2 * a + 1);                }            }            else {                if (c == 0) {                    scc.add(2 * a, 2 * b);                    scc.add(2 * b + 1, 2 * a + 1);                    scc.add(2 * a + 1, 2 * b + 1);                    scc.add(2 * b, 2 * a);                }                else {                    scc.add(2 * a, 2 * b + 1);                    scc.add(2 * b, 2 * a + 1);                    scc.add(2 * a + 1, 2 * b);                    scc.add(2 * b + 1, 2 * a);                }            }        }        scc.kosarajuSCC();        for (int i = 0; i < N; ++i) {            if (scc.cmp[2 * i] == scc.cmp[2 * i + 1]) {                out.println("NO");                return;            }        }        out.println("YES");    }    FastScanner in;    PrintWriter out;    void run() throws IOException {        boolean oj;        try {            oj = ! System.getProperty("user.dir").equals("F:\\java_workspace\\leetcode");        } catch (Exception e) {            oj = System.getProperty("ONLINE_JUDGE") != null;        }        InputStream is = oj ? System.in : new FileInputStream(new File(INPUT));        in = new FastScanner(is);        out = new PrintWriter(System.out);        long s = System.currentTimeMillis();        read();        out.flush();        if (!oj){            System.out.println("[" + (System.currentTimeMillis() - s) + "ms]");        }    }    public boolean more(){        return in.hasNext();    }    public int ni(){        return in.nextInt();    }    public long nl(){        return in.nextLong();    }    public double nd(){        return in.nextDouble();    }    public String ns(){        return in.nextString();    }    public char nc(){        return in.nextChar();    }    class FastScanner {        BufferedReader br;        StringTokenizer st;        boolean hasNext;        public FastScanner(InputStream is) throws IOException {            br = new BufferedReader(new InputStreamReader(is));            hasNext = true;        }        public String nextToken() {            while (st == null || !st.hasMoreTokens()) {                try {                    st = new StringTokenizer(br.readLine());                } catch (Exception e) {                    hasNext = false;                    return "##";                }            }            return st.nextToken();        }        String next = null;        public boolean hasNext(){            next = nextToken();            return hasNext;        }        public int nextInt() {            if (next == null){                hasNext();            }            String more = next;            next = null;            return Integer.parseInt(more);        }        public long nextLong() {            if (next == null){                hasNext();            }            String more = next;            next = null;            return Long.parseLong(more);        }        public double nextDouble() {            if (next == null){                hasNext();            }            String more = next;            next = null;            return Double.parseDouble(more);        }        public String nextString(){            if (next == null){                hasNext();            }            String more = next;            next = null;            return more;        }        public char nextChar(){            if (next == null){                hasNext();            }            String more = next;            next = null;            return more.charAt(0);        }    }}