90 lines
2.8 KiB
Java
90 lines
2.8 KiB
Java
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import edu.princeton.cs.introcs.StdIn;
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import edu.princeton.cs.introcs.StdOut;
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/*************************************************************************
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* Compilation: javac Arbitrage.java
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* Execution: java Arbitrage < input.txt
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* Dependencies: EdgeWeightedDigraph.java DirectedEdge.java
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* BellmanFordSP.java
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* Data file: http://algs4.cs.princeton.edu/44sp/rates.txt
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*
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* Arbitrage detection.
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*
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* % more rates.txt
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* 5
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* USD 1 0.741 0.657 1.061 1.005
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* EUR 1.349 1 0.888 1.433 1.366
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* GBP 1.521 1.126 1 1.614 1.538
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* CHF 0.942 0.698 0.619 1 0.953
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* CAD 0.995 0.732 0.650 1.049 1
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*
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* % java Arbitrage < rates.txt
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* 1000.00000 USD = 741.00000 EUR
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* 741.00000 EUR = 1012.20600 CAD
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* 1012.20600 CAD = 1007.14497 USD
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*
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*************************************************************************/
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/**
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* The Arbitrage class provides a client that finds an arbitrage
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* opportunity in a currency exchange table by constructing a
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* complete-digraph representation of the exchange table and then finding
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* a negative cycle in the digraph.
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*
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* This implementation uses the Bellman-Ford algorithm to find a
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* negative cycle in the complete digraph.
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* The running time is proportional to V <sup>3</sup> in the
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* worst case, where V is the number of currencies.
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*
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* For additional documentation,
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* see <a href="http://algs4.cs.princeton.edu/44sp">Section 4.4</a> of
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* Algorithms, 4th Edition by Robert Sedgewick and Kevin Wayne.
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*
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* @author Robert Sedgewick
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* @author Kevin Wayne
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*/
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public class Arbitrage {
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// this class cannot be instantiated
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private Arbitrage() { }
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/**
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* Reads the currency exchange table from standard input and
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* prints an arbitrage opportunity to standard output (if one exists).
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*/
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public static void main(String[] args) {
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// V currencies
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int V = StdIn.readInt();
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String[] name = new String[V];
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// create complete network
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EdgeWeightedDigraph G = new EdgeWeightedDigraph(V);
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for (int v = 0; v < V; v++) {
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name[v] = StdIn.readString();
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for (int w = 0; w < V; w++) {
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double rate = StdIn.readDouble();
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DirectedEdge e = new DirectedEdge(v, w, -Math.log(rate));
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G.addEdge(e);
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}
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}
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// find negative cycle
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BellmanFordSP spt = new BellmanFordSP(G, 0);
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if (spt.hasNegativeCycle()) {
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double stake = 1000.0;
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for (DirectedEdge e : spt.negativeCycle()) {
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StdOut.printf("%10.5f %s ", stake, name[e.from()]);
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stake *= Math.exp(-e.weight());
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StdOut.printf("= %10.5f %s\n", stake, name[e.to()]);
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}
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}
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else {
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StdOut.println("No arbitrage opportunity");
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}
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}
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}
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