2240. Arbitrage

POJ 刷题系列:2240. Arbitrage

题意:

给出各种货币的相互转换汇率,判断是否存在无限的生钱方式。

思路: 在图模型中找负环即可。此处符合负环的特征如下:在负环上的顶点会不断更新最大值,所以在N轮没有停止更新就说明存在了负环。

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.HashMap;
import java.util.List;
import java.util.Map;
import java.util.StringTokenizer;

public class Main{

    String INPUT = "./data/judge/201712/P2240.txt";

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

    class Edge{
        int from;
        int to;
        double rate;

        Edge(int from, int to, double rate){
            this.from = from;
            this.to   = to;
            this.rate = rate;
        }
    }

    List<Edge> edges;
    boolean bellmanFord(int s, int n) {
        double[] d = new double[n];
        Arrays.fill(d, 0);
        d[s] = 1;
        boolean ok = false;
        for (int i = 0; i < n; ++i) {
            for (Edge e : edges) {
                double nm = d[e.from] * e.rate;
                if (nm > d[e.to]) {
                    d[e.to] = nm;
                    if (i == n - 1) {
                        ok = true;
                    }
                }
            }
        }
        return ok;
    }

    void read() {
        int T = 0;
        while (true) {
            int n = ni();
            if (n == 0) break;
            edges = new ArrayList<Edge>();

            Map<String, Integer> map = new HashMap<String, Integer>();
            for (int i = 0; i < n; ++i) {
                String ns = ns();
                map.put(ns, i);
            }


            int M = ni();
            for (int i = 0; i < M; ++i) {
                String from = ns();
                double rate = nd();
                String to   = ns();
                edges.add(new Edge(map.get(from), map.get(to), rate));
            }

            if (bellmanFord(0, n)){
                out.println("Case " + (++T) + ": Yes");
            }
            else {
                out.println("Case " + (++T) + ": No");
            }
        }
    }

    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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