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POJ 刷题系列:3436. ACM Computer Factory

题意:

一个工厂,有n台机器,每台机器均有输入条件和输出结果,比如3个零件,机器1,输入0 0 1,表示输入机器1之前必须拥有零件3,输出 1 1 1,则表示通过该机器,能够制造出零件2。每台机器每小时也有它的最大产量w,问n台机器最多能制造多少台。

思路: 最大流,不要把机器当结点了,而是机器的每个输入和输出当结点,因为输出的结点可以进一步当作另外一台机器的输入。所以每台机器拆分成两个结点,i 和 i + n,并且建立边容量为w[i], 其次只有输入的零件均为0的结点才能与源点相连,只有输出零件全为1的结点连接汇点。其余关系边,只要一台机器的输入和前一台机器的输出不矛盾,就可以构造边。

代码如下:

package com.daimens.algorithm.january;

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.ArrayDeque;
import java.util.Arrays;
import java.util.Map;
import java.util.Queue;
import java.util.StringTokenizer;

public class SolutionDay09_P3436 {

    String INPUT = "./data/judge/201801/P3436.txt";

    public static void main(String[] args) throws IOException {
        new SolutionDay09_P3436().run();
    }

    static final int INF = 0x3f3f3f3f;

    int[][] G;
    int[] level;
    int V;


    void bfs(int s, int t) {
        level = new int[V];
        Arrays.fill(level, -1);
        Queue<Integer> q = new ArrayDeque<Integer>();
        q.offer(s);
        level[s] = 0;
        while (!q.isEmpty()) {
            int now = q.poll();
            for (int i = 0; i < V; ++i) {
                if (G[now][i] > 0 && level[i] < 0) {
                    level[i] = level[now] + 1;
                    q.offer(i);
                }
            }
        }
    }

    int dfs(int s, int t, int f, boolean vis[]) {
        if (s == t) return f;
        vis[s] = true;
        for (int i = 0; i < V; ++i) {
            if (!vis[i] && G[s][i] > 0 && level[s] + 1 == level[i]) {
                int d = dfs(i, t, Math.min(G[s][i], f), vis);
                if (d > 0) {
                    G[s][i] -= d;
                    G[i][s] += d;
                    return d;
                }
            }
        }
        return 0;
    }


    int dinic(int s, int t) {
        int flow = 0;
        for(;;) {
            bfs(s, t);
            if (level[t] < 0) break;
            int f = 0;
            while ((f = dfs(s, t, INF, new boolean[V])) > 0) flow += f;
        }
        return flow;
    }

    void read() {
        while(more()) {
            int p = ni();
            int n = ni();
            int[] w = new int[n];
            int[][] input  = new int[n][p];
            int[][] output = new int[n][p];
            for (int i = 0; i < n; ++i) {
                w[i] = ni();
                for (int j = 0; j < p; ++j) {
                    input[i][j] = ni();
                }
                for (int j = 0; j < p; ++j) {
                    output[i][j] = ni();
                }
            }
            // build G
            V = 2 * n + 2;
            G = new int[2 * n + 2][2 * n + 2];
            for (int i = 1; i <= n; ++i) {
                G[i][i + n] = w[i - 1];
            }
            for (int i = 1; i <= n; ++i) {
                for (int j = 1; j <= n; ++j) {
                    boolean ok = true;
                    for (int k = 0; k < p; ++k) {
                        if (input[j - 1][k] == 0 && output[i - 1][k] == 1 || input[j - 1][k] == 1 && output[i - 1][k] == 0) {
                            ok = false;
                        }
                    }
                    if (ok) {
                        G[i + n][j] = Math.min(w[i - 1], w[j - 1]);
                    }
                }
            }
            for (int i = 1; i <= n; ++i) {
                boolean ok = true;
                for (int k = 0; k < p; ++k) {
                    if (input[i - 1][k] == 1) ok = false;
                }
                if (ok) G[0][i] = INF;
                ok = true;
                for (int k = 0; k < p; ++k) {
                    if (output[i - 1][k] == 0) ok = false;
                }
                if (ok) G[i + n][2 * n + 1] = INF;
            }

            int[][] G2 = arrayCopy(G);
            int flow = dinic(0, 2 * n + 1);
            int tot = 0;
            int[][] ans = new int[n * n][3];
            for (int i = 0; i < n; ++i) {
                for (int j = 0; j < n; ++j) {
                    if (G2[i + 1 + n][j + 1] > G[i + 1 + n][j + 1]) {
                        ans[tot][0] = i + 1;
                        ans[tot][1] = j + 1;
                        ans[tot][2] = G2[i + 1 + n][j + 1] - G[i + 1 + n][j + 1];
                        tot ++;
                    }
                }
            }
            out.println(flow + " " + tot);
            for (int i = 0; i < tot; ++i) {
                out.println(ans[i][0] + " " + ans[i][1] + " " + ans[i][2]);
            }
        }
    }

    int[][] arrayCopy(int[][] G){
        int n = G.length;
        int m = G[0].length;
        int[][] aux = new int[n][m];
        for (int i = 0; i < n; ++i) 
            for (int j = 0; j < m; ++j)
                aux[i][j] = G[i][j];
        return aux;
    }

    FastScanner in;
    PrintWriter out;

    void run() throws IOException {
        boolean oj;
        try {
            oj = ! System.getProperty("user.dir").equals("F:\\oxygen_workspace\\Algorithm");
        } 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);
        }
    }

    static class D{

        public static void pp(int[][] board, int row, int col) {
            StringBuilder sb = new StringBuilder();
            for (int i = 0; i < row; ++i) {
                for (int j = 0; j < col; ++j) {
                    sb.append(board[i][j] + (j + 1 == col ? "\n" : " "));
                }
            }
            System.out.println(sb.toString());
        }

        public static void pp(char[][] board, int row, int col) {
            StringBuilder sb = new StringBuilder();
            for (int i = 0; i < row; ++i) {
                for (int j = 0; j < col; ++j) {
                    sb.append(board[i][j] + (j + 1 == col ? "\n" : " "));
                }
            }
            System.out.println(sb.toString());
        }
    }

    static class ArrayUtils {

        public static void fill(int[][] f, int value) {
            for (int i = 0; i < f.length; ++i) {
                Arrays.fill(f[i], value);
            }
        }

        public static void fill(int[][][] f, int value) {
            for (int i = 0; i < f.length; ++i) {
                fill(f[i], value);
            }
        }

        public static void fill(int[][][][] f, int value) {
            for (int i = 0; i < f.length; ++i) {
                fill(f[i], value);
            }
        }
    }

    static class Num{
        public static <K> void inc(Map<K, Integer> mem, K k) {
            if (!mem.containsKey(k)) mem.put(k, 0);
            mem.put(k, mem.get(k) + 1);
        }
    }
}

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