edu.princeton.cs.algs4.Arbitrage Maven / Gradle / Ivy
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/******************************************************************************
* Compilation: javac Arbitrage.java
* Execution: java Arbitrage < input.txt
* Dependencies: EdgeWeightedDigraph.java DirectedEdge.java
* BellmanFordSP.java
* Data file: https://algs4.cs.princeton.edu/44sp/rates.txt
*
* Arbitrage detection.
*
* % more rates.txt
* 5
* USD 1 0.741 0.657 1.061 1.005
* EUR 1.349 1 0.888 1.433 1.366
* GBP 1.521 1.126 1 1.614 1.538
* CHF 0.942 0.698 0.619 1 0.953
* CAD 0.995 0.732 0.650 1.049 1
*
* % java Arbitrage < rates.txt
* 1000.00000 USD = 741.00000 EUR
* 741.00000 EUR = 1012.20600 CAD
* 1012.20600 CAD = 1007.14497 USD
*
******************************************************************************/
package edu.princeton.cs.algs4;
/**
* The {@code Arbitrage} class provides a client that finds an arbitrage
* opportunity in a currency exchange table by constructing a
* complete-digraph representation of the exchange table and then finding
* a negative cycle in the digraph.
*
* This implementation uses the Bellman-Ford algorithm to find a
* negative cycle in the complete digraph.
* The running time is proportional to V3 in the
* worst case, where V is the number of currencies.
*
* For additional documentation,
* see Section 4.4 of
* Algorithms, 4th Edition by Robert Sedgewick and Kevin Wayne.
*
* @author Robert Sedgewick
* @author Kevin Wayne
*/
public class Arbitrage {
// this class cannot be instantiated
private Arbitrage() { }
/**
* Reads the currency exchange table from standard input and
* prints an arbitrage opportunity to standard output (if one exists).
*
* @param args the command-line arguments
*/
public static void main(String[] args) {
// V currencies
int V = StdIn.readInt();
String[] name = new String[V];
// create complete network
EdgeWeightedDigraph G = new EdgeWeightedDigraph(V);
for (int v = 0; v < V; v++) {
name[v] = StdIn.readString();
for (int w = 0; w < V; w++) {
double rate = StdIn.readDouble();
DirectedEdge e = new DirectedEdge(v, w, -Math.log(rate));
G.addEdge(e);
}
}
// find negative cycle
BellmanFordSP spt = new BellmanFordSP(G, 0);
if (spt.hasNegativeCycle()) {
double stake = 1000.0;
for (DirectedEdge e : spt.negativeCycle()) {
StdOut.printf("%10.5f %s ", stake, name[e.from()]);
stake *= Math.exp(-e.weight());
StdOut.printf("= %10.5f %s\n", stake, name[e.to()]);
}
}
else {
StdOut.println("No arbitrage opportunity");
}
}
}
/******************************************************************************
* Copyright 2002-2018, Robert Sedgewick and Kevin Wayne.
*
* This file is part of algs4.jar, which accompanies the textbook
*
* Algorithms, 4th edition by Robert Sedgewick and Kevin Wayne,
* Addison-Wesley Professional, 2011, ISBN 0-321-57351-X.
* http://algs4.cs.princeton.edu
*
*
* algs4.jar is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* algs4.jar is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with algs4.jar. If not, see http://www.gnu.org/licenses.
******************************************************************************/