# Detecting Arbitrage in Currency Exchange Rates Using Graph Theory and Bellman-Ford Algorithm

How to Identify Arbitrage Opportunities in Currency Markets with Efficient Graph-Based Solutions

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## Problem

Suppose you are given a table of currency exchange rates, represented as a 2D array. Determine whether there is a possible arbitrage: that is, whether there is some sequence of trades you can make, starting with some amount A of any currency, so that you can end up with some amount greater than A of that currency. There are no transaction costs and you can trade fractional quantities.

## Problem Explanation

You are given a 2D array representing currency exchange rates between different currencies. Each element of the array, `rates[i][j]`

, represents the exchange rate from currency `i`

to currency `j`

. The goal is to determine if there is an arbitrage opportunity, meaning if you can start with an amount of currency, perform a series of trades, and end up with more of that currency than you started with.

## Approach

This problem can be solved using **graph theory**, specifically **Bellman-Ford algorithm**. Here’s how it works: