POJ 刷题系列：1860. Currency Exchange

POJ 刷题系列：1860. Currency Exchange

传送门：1860. Currency Exchange

题意：

N种货币，任意货币之间可以相互转换，转换需要手续费commission，假设货币A当前金额为money，转换公式如下：（money - commission） * rate，现给出任意货币之间的转换手续和转换率，问从S点出发，是否存在一条路径使得回到S时，能够增值。

思路：
实际上，该问题和判断负环类似，只要在S的路径上存在一条环，使得经过该环上的结点出现增值，那么就能产生无限的现金。自然地，定义dp[i]：表示从源点S出发到结点i的现金流。如果不存在这样的环，必然最多经过N-1次就停止更新，否则就会无限更新下去。

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.Map;
import java.util.StringTokenizer;

public class Main{

    String INPUT = "./data/judge/201712/P1860.txt";

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

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

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

        @Override
        public String toString() {
            return from + " " + to;
        }
    }

    void read() {
        int N = ni();
        int M = ni();
        int S = ni();
        double money = nd();

        List edges = new ArrayList();

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

        double[] dp = new double[N];
        dp[S - 1] = money;

        boolean valid = false;
        for (int i = 0; i < N; ++i) {
            for (Edge e : edges) {
                double preMoney = dp[e.from];
                if (preMoney - e.commission >= 0) {
                    double nxtMoney = (preMoney - e.commission) * e.rate;
                    if (nxtMoney > dp[e.to]) {
                        dp[e.to] = nxtMoney;
                        if (i == N - 1) {
                            valid = true;
                        }
                    }
                }
            }
        }


        out.println(valid ? "YES" : "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  void inc(Map mem, K k) {
            if (!mem.containsKey(k)) mem.put(k, 0);
            mem.put(k, mem.get(k) + 1);
        }
    }
}