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<Edge> edges = new ArrayList<Edge>();        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 <K> void inc(Map<K, Integer> mem, K k) {            if (!mem.containsKey(k)) mem.put(k, 0);            mem.put(k, mem.get(k) + 1);        }    }}