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StormTest

stormtest

Things happened as Pencroft had predicted

What you will be building, see the and for more info. live demo GitHub repo Introduction The demand for Web3.0 solutions is at an all-time high, but there isn't enough material available to usher in the army of developers required to fill the job openings. To assist other web developers, I've created this tutorial to help you understand how to build a decentralized eCommerce platform that transacts Ethers. You will be able to do the following by the end of this tutorial: Build an eCommerce app. Integrate Web3.0 Payment solution. Incorporate Customer Chat functionality. Interact with a Database using Firebase v9. Code and Deploy a Solidity Smart Contract. Hookup Smart Contract with React App. Lot’s more. This is tutorial is PART-ONE of a two-part series, we will begin with developing the solidity smart contract. So If you are pumped for this build, then let’s get coding… Prerequisites For PART-ONE of this tutorial, you will need the following items to build along with me; installed on your machine. NodeJs installed. Yarn package manager installed. Truffle installed. Ganache installed. Git CLI And an agile determination to learn. Installing App Dependencies To save you the pain of installing one dependency after another, I’ve prepared you a . Clone and install the dependencies with the instructions below. And… don’t forget to star the project. starter kit on my git repo On your terminal, navigate to the location of your project and run the code below: # Make sure you have the above prerequisites installed already!
git clone https://github.com/Daltonic/truffle-starter-kit.git freshers
cd frehsers # Navigate to the new folder.
yarn install # Installs all the dependencies. I recommend you use for the tutorial, it has everything you will need for coding. vs code If you’ve done that, you’re awesome, let’s proceed to the next step… Coding the Smart Contract Open the project in VS code and head on to the contracts directory, you will see an existing contract named . Migration.sol Create a new solidity contract named . Inside of the store, define the following structures. Store.sol // SPDX-License-Identifier: MIT
pragma solidity ^0.8.4;

contract Store {
  // All codes goes in here!
} This is a typical structure of a solidity smart contract, let’s code this smart contract one step at a time. // Defining store variables
address public immutable storeOwner;
uint256 public storeAcc;
string public storeName;
uint256 public immutable feePercent;
uint256 public storeSales; These are the variables our smart contract will use to perform store sales. The and variables are , once the smart contract is deployed it can no longer be changed in the course of the program. store owner fee percent immutable Variables with address type mean that they can only hold data types of wallet address. Whereas variables with or mean unsigned integers, they can be used to hold only positive numbers with or without decimals. uint uint256 // Tracking users number of sales
mapping(address => uint256) public salesOf; The code above describes a solidity variable with a key-value type of association. It's similar to the python hash method in that it returns a value if the argument passed in the parameter finds a match. // Declaring Events within each sale
event Sale(
    address indexed buyer,
    address indexed seller,
    uint256 amount,
    uint256 timestamp
);
event Withdrawal(
    address indexed receiver,
    uint256 amount,
    uint256 timestamp
); Events are useful for storing the arguments passed into the smart contract on the blockchain network. It’s an essential ingredient for writing a professional smart contract. // Structuring the sales object
struct SalesStruct {
    address buyer;
    address seller;
    uint256 amount;
    string purpose;
    uint256 timestamp;
}
SalesStruct[] sales; We're describing a structure for collecting sales data in the code above. We want to collect the buyer and seller's addresses, the number of ethers transacted, the purpose of the transaction, and the time the transaction was completed for each sale made through our smart contract. Solidity provides us with a struct method, which is the best practice for ensuring that these records are correctly entered. // Initializing the store
constructor(
    string memory _storeName,
    address _storeOwner,
    uint256 _feePercent
) {
    storeName = _storeName;
    storeOwner = _storeOwner;
    feePercent = _feePercent;
    storeAcc = 0;
} These are the information passed during the deployment of the smart contract. // Performing sales payment
function payNow(address seller, string memory purpose)
    public
    payable
    returns (bool success)
{
    // Validating payments
    require(msg.value > 0, "Ethers cannot be zero!");
    require(msg.sender != storeOwner, "Sale Not allowed");

    // Calculating up cost and fee
    uint256 fee = (msg.value / 100) * feePercent;
    uint256 cost = msg.value - fee;

    // Assigning sales and payment to store and product owner
    storeAcc += msg.value;
    storeSales += 1;
    salesOf[seller] += 1;

    // Cashing out to sales party
    withdrawMoneyTo(storeOwner, fee);
    withdrawMoneyTo(seller, cost);

    // Recording sales in smart contract
    sales.push(
        SalesStruct(msg.sender, seller, cost, purpose, block.timestamp)
    );

    // Captures sales data on event
    emit Sale(msg.sender, seller, cost, block.timestamp);
    return true;
} This function collects payment from a buyer and sends the seller of the sales and to the store owner as the fee for utilizing their platform. 90% 10% // Sends ethers to a specified address
function _payTo(address _to, uint256 _amount) internal {
    (bool success1, ) = payable(_to).call{value: _amount}("");
    require(success1);
} This is an internal method for transferring ethers to a specified address, it works in conjunction with the withdrawal function. It can only be called by another function within our smart contract. // Performs ethers transfer
function withdrawMoneyTo(address receiver, uint256 amount)
    internal
    returns (bool success)
{
    require(storeAcc >= amount, "Insufficent Fund!");
    _payTo(receiver, amount);
    storeAcc -= amount;

    // Captures transfer data on event
    emit Withdrawal(receiver, amount, block.timestamp);
    return true;
} This is a function that performs the sending of money to a specified address. It makes sure that it checks for balances before carrying out the transaction. // Retreives all processed sales from smart contract
function getAllSales() public view returns (SalesStruct[] memory) {
    return sales;
} Lastly, this function returns an array of all the sales that have taken place on our smart contract. The full code looks like this… // SPDX-License-Identifier: MIT
pragma solidity ^0.8.4;

contract Store {
    // Defining store variables
    address public immutable storeOwner;
    uint256 public storeAcc;
    string public storeName;
    uint256 public immutable feePercent;
    uint256 public storeSales;

    // Tracking users number of sales
    mapping(address => uint256) public salesOf;

    // Declaring Events within each sale
    event Sale(
        address indexed buyer,
        address indexed seller,
        uint256 amount,
        uint256 timestamp
    );

    event Withdrawal(
        address indexed receiver,
        uint256 amount,
        uint256 timestamp
    );

    // Structuring the sales object
    struct SalesStruct {
        address buyer;
        address seller;
        uint256 amount;
        string purpose;
        uint256 timestamp;
    }

    SalesStruct[] sales;

    // Initializing the store
    constructor(
        string memory _storeName,
        address _storeOwner,
        uint256 _feePercent
    ) {
        storeName = _storeName;
        storeOwner = _storeOwner;
        feePercent = _feePercent;
        storeAcc = 0;
    }

    // Performing sales payment
    function payNow(address seller, string memory purpose)
        public
        payable
        returns (bool success)
    {
        // Validating payments
        require(msg.value > 0, "Ethers cannot be zerro!");
        require(msg.sender != storeOwner, "Sale Not allowed");

        // Calculating up cost and fee
        uint256 fee = (msg.value / 100) * feePercent;
        uint256 cost = msg.value - fee;

        // Assigning sales and payment to store and product owner
        storeAcc += msg.value;
        storeSales += 1;
        salesOf[seller] += 1;

        // Cashing out to sales party
        withdrawMoneyTo(storeOwner, fee);
        withdrawMoneyTo(seller, cost);

        // Recording sales in smart contract
        sales.push(
            SalesStruct(msg.sender, seller, cost, purpose, block.timestamp)
        );

        // Captures sales data on event
        emit Sale(msg.sender, seller, cost, block.timestamp);
        return true;
    }

    // Sends ethers to a specified address
    function _payTo(address _to, uint256 _amount) internal {
        (bool success1, ) = payable(_to).call{value: _amount}("");
        require(success1);
    }

    // Performs ethers transfer
    function withdrawMoneyTo(address receiver, uint256 amount)
        internal
        returns (bool success)
    {
        require(storeAcc >= amount, "Insufficent Fund!");

        _payTo(receiver, amount);
        storeAcc -= amount;

        // Captures transfer data on event
        emit Withdrawal(receiver, amount, block.timestamp);
        return true;
    }

    // Retreives all processed sales from smart contract
    function getAllSales() public view returns (SalesStruct[] memory) {
        return sales;
    }
} Now that we are done with coding this smart contract, it's time to test it programmatically. Setting up the Migration Scripts Before we proceed with testing out the smart contract, let’s set up the migration script in the folder. migrations Head to the migrations folder and create a new file called . Paste the following codes inside the file. 2_deploy_contracts.js 2_deploy_contracts.js const Store = artifacts.require('Store')
module.exports = async (deployer) => {
  const [_feeAccount] = await web3.eth.getAccounts()
  const _name = 'Fresher'
  const _feePercent = 10
  await deployer.deploy(
    Store,
    _name,
    _feeAccount,
    _feePercent
  )
} This will be necessary when we start testing out the smart contract. Testing the Smart Contract Spin up Ganache and ensure that it’s live and accessible. Next, locate the folder and create a file called . test Store.test.js Paste the code snippet inside of it. const Store = artifacts.require('Store')

require('chai').use(require('chai-as-promised')).should()

const toWei = (num) => web3.utils.toWei(num.toString())
const fromWei = (num) => web3.utils.fromWei(num.toString())

contract('Store', ([storeOwner, buyer, seller]) => {
  const feePercent = 10
  const storeName = 'Freshers'

  let store

  beforeEach(async () => {
    store = await Store.new(storeName, storeOwner, feePercent)
  })

  describe('deployment', () => {
    it('confirms store name', async () => {
      const result = await store.storeName()
      result.should.equal(storeName)
    })

    it('confirms store owner', async () => {
      const result = await store.storeOwner()
      result.should.equal(storeOwner)
    })

    it('confirms sales fee', async () => {
      const result = await store.feePercent()
      result.toString().should.equal(feePercent.toString())
    })
  })

  describe('Sales process', () => {
    const amount = fromWei(toWei(4))
    const purpose = 'Sales on dippers'

    it('confirms increase in sales of store and seller', async () => {
      // Sales of seller before purchase
      let result = await store.salesOf(seller)
      result.toString().should.equal('0')

      // Sales of store before purchase
      result = await store.storeSales()
      result.toString().should.equal('0')

      // Perform sales
      await store.payNow(seller, purpose, { from: buyer, value: amount })

      // Sales of after after purchase
      result = await store.salesOf(seller)
      result.toString().should.equal('1')

      // Sales of store after purchase
      result = await store.storeSales()
      result.toString().should.equal('1')
    })
  })
}) The above test is designed to check that our smart contract can perform sales. An extra measure to ensure that your smart contract runs accordingly is to write a script that will interact with it. Let’s do that next. Interacting with the Smart Contract This is the best way to validate the functionalities of your smart contract. We want to write a script to simulate the sales process. Head to the and create a file called . Next, paste the following codes inside of it. scripts folder performSales.js const Store = artifacts.require("Store");

module.exports = async (callback) => {
  const [storeOwner, seller, buyer] = await web3.eth.getAccounts()
  const amount = web3.utils.toWei('4', 'ether')
  const purpose = 'Sales on dippers'

  const store = await Store.deployed()

  let buyerBal = await web3.eth.getBalance(buyer)
  let sellerBal = await web3.eth.getBalance(seller)
  let storeOwnerBal = await web3.eth.getBalance(storeOwner)

  console.log(`Initial balance of buyer | ${web3.utils.fromWei(buyerBal.toString(), 'ether')}`)
  console.log(`Initial balance of seller   | ${web3.utils.fromWei(sellerBal.toString(), 'ether')}`)
  console.log(`Initial balance of storeOwner   | ${web3.utils.fromWei(storeOwnerBal.toString(), 'ether')}`)

  console.log(`\n ${purpose} for ${web3.utils.fromWei(amount.toString(), 'ether')} ethers... \n`)

  await store.payNow(seller, purpose, {from: buyer, value: amount})

  buyerBal = await web3.eth.getBalance(buyer)
  sellerBal = await web3.eth.getBalance(seller)
  storeOwnerBal = await web3.eth.getBalance(storeOwner)

  console.log(`Balance of buyer after sales | ${web3.utils.fromWei(buyerBal.toString(), 'ether')}`)
  console.log(`Balance of seller after sales | ${web3.utils.fromWei(sellerBal.toString(), 'ether')}`)
  console.log(`Balance of storeOwner after sales | ${web3.utils.fromWei(storeOwnerBal.toString(), 'ether')}`)

  callback()
} Cool, after creating and pasting the codes above, run the following command on the terminal. Please make sure that your ganache is up and running. truffle migrate --reset You will observe the following result on your terminal. If you reached here, you’re awesome, let’s run the script by running this code on the terminal. perfomSales truffle exec scripts/performSales.js You should have something like this on your terminal… Fantastic, we can be happy that our smart contract is certified and fully functional. Let’s deploy it to the . rinkeby test net Deploying the Smart Contract To do this deployment, configure your truffle config file in the order below: require('dotenv').config()
const HDWalletProvider = require('@truffle/hdwallet-provider')
module.exports = {
  // Configure networks (Localhost, Kovan, etc.)
  networks: {
    development: {
      host: '127.0.0.1',
      port: 7545,
      network_id: '*', // Match any network id
    },
    rinkeby: {
      provider: () =>
        new HDWalletProvider(process.env.SECRET_KEY, process.env.ENDPOINT_URL),
      network_id: 4, // Rinkeby's id
      gas: 5500000, // Rinkeby has a lower block limit than mainnet
      confirmations: 2, // # of confs to wait between deployments. (default: 0)
      timeoutBlocks: 200, // # of blocks before a deployment times out  (minimum/default: 50)
      skipDryRun: true, // Skip dry run before migrations? (default: false for public nets )
    },
  },
  contracts_directory: './contracts/',
  contracts_build_directory: './src/shared/abis/',
  // Configure your compilers
  compilers: {
    solc: {
      version: '0.8.11',
      optimizer: {
        enabled: true,
        runs: 200,
      },
    },
  },
} Deploying to Alchemy At the moment, our smart contract can only run on our computer, and no one else can connect to it. We will use alchemy to make it available to everyone at no cost. Sign up with them now, or if you already have an account. log in When you log in, you will see the dashboard page, which allows you to create a new blockchain application. Click on the button and enter the information shown in the image below, making sure to include the network. Creating an Alchemy App CREATE APP Rinkeby test After you've created the app, you can view its information by clicking on the app's name or the view the details button. Copy the as shown in the image below by clicking on the button. WSS URL VIEW KEY Amazing, now proceed as shown in the images below to obtain your account. Please keep in mind that we are not using the regular account address, but rather the private key to that account. Rinkeby ENDPOINT_URL=<YOUR_ALCHEMY_WSS_URL>
SECRET_KEY=<YOUR_METAMASK_SECRET_PHRASE>
DEPLOYER_KEY=<YOUR_METAMASK_PRIVATE_KEY> Please do not use your real ; these keys must be kept secret. That's why we put them in the environment file and tell git to ignore them. Metamask details After you've entered the above keys into their respective variables, execute the commands below. truffle migrate --reset --network rinkeby As we can see below, your smart contract will be deployed on the Rinkeby test net. Wow, you've worked hard to get to this point. You've just finished deploying an eye-catching smart contract to the Ethereum blockchain network. We'll connect it to a ReactJs frontend in of this tutorial. PART-TWO Conclusion You've completed the first part of this tutorial; next, we'll learn how to connect the solidity smart contract we just deployed to our React frontend. You can see the finished version of this application , and you can also check out the , which you should star. live here git repo here I'll see you again in of this tutorial. PART-TWO About the Author Gospel Darlington kick-started his journey as a software engineer in 2016. Over the years, he has grown full-blown skills in JavaScript stacks such as React, ReactNative, VueJs, and more. He is currently freelancing, building apps for clients, writing technical tutorials teaching others how to do what he does. Gospel Darlington is open and available to hear from you. You can reach him on , , , or on his . LinkedIn Facebook Github website Also published here

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And what if you could turn the problem of making money into the problem of finding the shortest-path? We can do that in at least one particular way: by exploiting arbitrage opportunities. Who doesn’t like to make money? What is arbitrage? is the act of buying or selling things across different markets, or in different forms, to profit from differences in prices. And the people who engage in it? They’re known as a fancy title indeed. Arbitrage arbitrageurs — Let’s start with an example. Say Paul, Peter, and Bob live in a village, where they barter carrots, potatoes, and lettuce. Bob trades potatoes for carrots, Peter trades lettuce for potatoes, and Paul trades lettuce for carrots. Furthermore, Bob will trade 2 potatoes for a carrot, Peter will trade 1 lettuce for 2 potatoes, and Paul will trade 2 carrots for 1 lettuce. If we were to treat each individual as a market for their respective goods, what would the exchange rates look like? Do you sense an opportunity? Being the enterprising individual that you are, you may try to exploit it. Starting with 5 carrots, you approach Bob, and trade your 5 carrots for 10 potatoes, at the rate at which he is willing to trade. Next, you approach Peter with your potatoes, knowing that he’ll trade you 5 lettuce for them. Then you approach Paul with your 5 lettuce, and he trades 10 carrots for your lettuce. After a few smart trades, you’ve doubled your carrot wealth. You turned 5 carrots into 10, by exploiting an arbitrage opportunity. Later on, the villagers may develop more sophisticated markets where Bob, Peter, and Paul aren’t the only traders. Instead this little village might develop a carrot/lettuce market, a lettuce/potato market, and a potato/carrot market, where the going rate for each trade will fluctuate based on what people are willing to trade. But the arbitrage principle remains the same. And the opportunity can be exploited until the traders offering to exchange at those rates run out of carrots, lettuce, and potatoes to trade. The arbitrage opportunity is exploited until the market reaches an equilibrium. Arbitrage in Modern Times When you think of modern markets, you probably don’t think of trading carrots, potatoes, and lettuce. If you’re into forex, you’re more likely thinking of trading dollars, pounds, and yen. And in that case, we would be dealing with a dollar/pound market, a pound/yen market, and a yen/dollar market, with many traders acting on each market. From now on, let’s use those currencies as examples of things to trade, but keep in mind the principles can apply to all sorts of trade-able things. Say at a given time, the exchange rates are as follows: If you learned anything from Bob, Peter, and Paul trading carrots, lettuce, and potatoes, you’d sense an opportunity here. If you trade $1 for pounds, you’ll end up with £0.8. Trading that for yen, you’ll end up with ¥80. You take your yen to the yen/dollar exchange where you trade it back for dollars… but now you have $1.04! But you have to act quickly, before another arbitrageur beats you to the punch. These opportunities only exist temporarily, until the liquidity is used up and the rates equalize. The perceptive among you may notice that we haven’t considered exchange fees in our example. Of course, you’d have to take those into account to calculate if a profitable arbitrage opportunity actually exists. Acting Quickly Hopefully you have some intuition to understand why acting fast is paramount. Exchange rates fluctuate quickly, and there is only a limited amount of “thing” available at that exchange rate. While we’ve worked with relatively simple examples here, arbitrage opportunities can span many trades, becoming incredibly complex. Our examples used 3 trades, but what if you needed 10? And in a network of 20 currencies with a market for each pair, how quickly could you find an opportunity? Using a computer is an obvious answer. But we need an efficient algorithm, lest someone else beat us to the opportunity. To achieve that, we can leverage a few clever insights in mathematics and computer science. Markets as a Graph Graphs are an incredibly important structure that has found its uses in numerous applications. Many social and natural structures can be modeled with graphs, and it turns out that markets are one of them. In our case, let’s treat each currency as a node. Moving from node to node corresponds to trading one currency for another. So moving along an edge, between nodes, should transform the amount of currency by the exchange rate. That means moving from the dollar node to the pound node corresponds to multiplying by 0.8 pounds/dollar. Let’s assign the exchange rate as the weight of each edge. Note that the exchange rate in each direction will be the reciprocal of each other. That means if the rate to convert pounds to dollars is 0.8 pounds/dollar, the rate in the other direction will be 1/(0.8 pounds/dollar) = 1.25 dollars/pound. The consequence for us is that we need to be careful to treat buying and selling on each market as distinct, directed edges, with different weights. approximately The reason that the exchange rates in both directions are only reciprocal is due to small differences in the prices to buy and sell currencies, known as the buy-sell spread. For example, if at a given moment you can buy pounds at 0.8 pounds/dollar (the current price somebody will sell to you), but can sell dollars for pounds at 0.82 pounds/dollar (or 1.22 dollars/pound, and the current price somebody will buy from you), your graph model will look like this (excluding the other exchange rates for simplicity): approximately A series of trades can be modeled by moving along edges in this graph, and the result of the trades is computed by the edge weights as you move along them. multiplying Seeing the Opportunity Now that we have a working model, what are we looking for in our graph that corresponds to an arbitrage opportunity? To determine whether a series of trades is profitable, we need a consistent metric of profitability. In other words, if we begin our series of trades in dollars, then we’ll need to end it in dollars, too. And by comparing the amount of dollars we ended up with to the amount we started with, we’ll know if it was profitable or not. In our graph, that means that our series of trades must end at the same node from which it started. In our case, we started at the dollar node, and ended in the dollar node. In graph terminology, we call that a cycle. So we know we’re looking for some sort of cycle- but what kind of cycle makes it profitable? Notice that if we multiply along the edges of a cycle, we transform the units of the effective exchange rate. However, when we return to our starting node, the quantity becomes unit-less. It transforms from a rate of exchange, to a ratio of return! Traversing a cycle on our graph and computing the product of exchange rates along the way corresponds to calculating the ratio of return we would get after completing the series of trades. If the market is perfectly efficient, our return ratio, will be 1, because the exchange rates have equalized. If the product of weights is greater than 1, say 1.02, then our arbitrage opportunity would have made us a 2% return. abc, Therefore, generalizing to an arbitrary number of trades, an arbitrage opportunity corresponds to the following inequality: where corresponds to the ’th exchange rate, for each trade , over trades. e_i i i n So what we need is an algorithm that will find a cycle on the graph of markets, where the product of edge weights is greater than 1. You might be able to invent an algorithm to do that - but in computer science, as in life in general, it’s useful to reduce problems to ones you already know how to solve. The Bellman-Ford Algorithm The problem of finding shortest paths is a common and fundamental problem in computer science, which can be applied to many different scenarios. An obvious one, by drawing a correspondence between a graph and a map, is that of finding the shortest route on a map. But with some cleverness, many other kinds of problems can be transformed into a shortest-path problem, as well. What I’m going to prove to you is that the problem of finding arbitrage opportunities is one such problem. First, let’s establish what the shortest path problem is. Given two nodes in a graph, and , the shortest path is that path which minimizes the of edge weights. In other words, we move along the path from to , adding up edge weights along the way, the path with the minimum sum is the shortest path — the path with the smallest cost. s t sum s t Next, it will be helpful to understand that there are different classes of shortest-path problems. In the obvious example — like the shortest route on a map — edge weights must be positive. There’s no way, barring a time machine, that driving down a road will reduce your travel time. In a graph with only positive edge weights, Dijkstra’s famous algorithm will compute the shortest path to all nodes in the graph. However, there is no reason a graph cannot have negative edge weights. In that case, moving along that edge reduces the total cost of the path. But, if you have a which has a negative weight, then you can keep traversing that cycle forever — every time, lowering your overall cost of the path — and your shortest path will have a cost approaching -∞. In that case, it would be very useful for our shortest-path algorithm to have a mechanism to identify negative weight cycles. Otherwise the shortest path would get stuck circling the negative weight cycle, forever. cycle The Bellman-Ford algorithm is exactly that algorithm. A more general version of Dijkstra’s shortest-path algorithm, it can handle negative weights. To do so, it detects cycles in a graph along which up the weights produces a negative value. negative weight cycles — adding But how does an algorithm which can find cycles where the of edges is less than 0 help us, when we need an algorithm that can detect cycles where the of edges is greater than 1? sum product Log to the Rescue The next insight is that a product can be turned into a sum by applying the logarithmic function, thanks to the identity: Thereby we can transform our problem of finding a cycle with a greater than 1, to a problem of finding a cycle with a greater than 0! We do that by taking the log of each exchange rate, and using that as the weight of each edge. product sum Let’s show that by taking the log of both sides of our inequality. First, taking the log of the left-hand side transforms the problem of computing a product into computing a sum: The log of the right side just transforms the 1 to a 0: We’re close, but not quite there. The final step, to reduce our problem to one that we can solve with this known algorithm, is to multiply each edge weight by -1. This turns the problem of finding a positive weight cycle, into finding a negative one: Which we know the Bellman-Ford algorithm can do! Constructing a graph as specified and executing the Bellman-Ford algorithm on it will quickly and efficiently find arbitrage opportunities for us, because we’ve turned the arbitrage problem into the problem of finding the shortest path — . the infinitely shortest path In hindsight, it’s obvious that there should be a correspondence between a negative weight cycle — which lowers the cost of the path every time you traverse it — to an arbitrage opportunity, which makes you a profit every time you traverse it. The key insight is transforming a problem of finding a product greater than 1 into finding a sum less than 0, by applying -log to the edge weights. Prove It Let’s run this algorithm on our exchange rates to see if it correctly identifies the arbitrage opportunity. Transforming the exchange rates by -log, we get: Summing over the trades, our equality holds- we found a negative weight cycle! We can undo the logarithmic operation to restore the product, and calculate the return: Which is exactly the 4% return we calculated earlier. In the Real World Since an arbitrage opportunity corresponds to a negative weight cycle, it seems that we could traverse the cycle forever to make infinite money. Of course, that is not the case. The liquidity — the volume available before the price changes significantly- available for any arbitrage opportunity is limited, and is quickly exploited by algorithmic traders pushing the boundaries of computing technology and the laws of physics to beat each other. That being said, I hope you found this exercise in applying graph theory and a well known shortest path algorithm to solving a problem in the finance domain — and making money — as interesting as I always have.

Arbitrage as a Shortest-Path Problem

El arbitraje como un problema de ruta más corta

A quick overview and comparison of shortest and longest path algorithms in graphs. There are so many little points to remember about innocent looking shortest and longest path problems in graphs. Questions on this topic are very common in technical job interviews for computer programmers. However, it is often hard to keep your memory fresh and remember all details about these problems and their algorithms. For example: (if not, see the section for longest path below) Did you know finding the shortest simple path in a graph is NP-hard? Did you know in some graphs shortest path can be found in linear time? Here I provide a quick summary and important points about each of the famous algorithms in one place, which can be reviewed quickly before each interview. Before we begin: First, we assume the graph is has , where G(V, E) V = {1, 2, … , n} , |V| = n |E| = m For the shortest path problem, we assume we are after the shortest path, i.e., vertices can repeat. Also, we assume the edge weights can be an integer value, i.e., positive, negative, or zero. non-simple problem only requires the shortest distance between nodes, whereas requires the actual shortest path between nodes. We discuss the shortest distance problem here. The shortest path can usually be found with minor enhancement in the algorithm. The Shortest Distance The Shortest Path Problem Floyd-Warshall Algorithm Floyd-Warshall is the simplest algorithm: : We calculate the shortest possible path from node to using nodes only from the set between them. d(i,j,k) represents the shortest distance between i, j using only k nodes. We can write: Quick Intuition i j {1, 2, …, k} as intermediate points d(i,j,k) = min(d(i,j,k-1), d(i,k,k-1)+ d(k,j,k-1)) The following picture shows the intuition: Shortest path from i,j using k nodes can be calculated by comparing the shortest path from i to j using k-1 nodes and the sum of i to k and k to j using k-1 nodes Below is a video clearly explaining the Floyd-Warshall Algorithm: Below is the implementation in C++: < < >> floydWarshal( < < >> &graph) { < < >> d(graph.size(), < >(graph.size())); ( i = ; i < graph.size(); ++i) { ( j = ; j < graph.size(); ++j) {
            d[i][j] = graph[i][j];
        }
    } ( k = ; k < graph.size(); k++) ( i = ; i < graph.size(); ++i) ( j = ; j < graph.size(); ++j)
        d[i][j] = ::min(d[i][j], d[i][k] + d[k][j]); d;
} // Floyd-Warshall Algorithm for finding the shortest distance vector vector long long vector vector int vector vector long long vector long long //Initialize d for int 0 for int 0 for int 0 for int 0 for int 0 std return View gist on Github What You Need to Know about Floyd-Warshal Algorithm: It finds the shortest distance between all pairs of nodes. It is O(n³) It is a dynamic programming algorithm The graph CAN have negative edges It CAN have negative cycles Dijkstra Algorithm Dijkstra algorithm finds the shortest path between a single source and all other nodes. Keep a list of visited nodes. At each step: Intuition: Find the unvisited node with shortest distance u Relax the distance of neighbors of u Add to the visited list and repeat u Below is Dijkstra’s implementation in C++: < > dijkstra( < < >> &graph, source) { < > d(graph.size()); < > s; ( i = ; i < graph.size(); i++) {
        d[i] = graph[source][i];
    }

    s.push_back(source); (s.size() < graph.size()) { u = findMinInDButNotInS(d, s);
        s.push_back(u); ( j = ; j < graph.size(); j++) {
            d[j] = ::min(d[j], d[u] + graph[u][j]);
        }
    } d;
} // Dijkstra shortest distance vector long vector vector int int vector long vector int for int 0 while //Find minimum int //Relax for int 0 std return View gist on Github What You Need to Know about Dijkstra’s Algorithm: The run-time is: ² simple form. With min-heap: With Fibonacci heap: O(n ) O( (m+n)log(n) ). O(m+n log n) It’s a greedy algorithm It CANNOT handle negative edges or negative cycles Below is Dijkstra’s algorithm using a priority queue in C++: < > dijkstraPriorityQueue( < < >> &graph, source) { priority_queue<pair< , >, <pair< , >>,
                   greater<pair< , >>>
            q; < > d(graph.size(), INT_MAX);
    d[source] = ;

    q.push(make_pair( , source)); (!q.empty()) { u = q.top().second;
        q.pop(); ( j = ; j < graph.size(); j++) { (d[j] > d[u] + graph[u][j]) {
                d[j] = d[u] + graph[u][j];
                q.push(make_pair(d[j], j));
            }
        }
    } d;
} // Dijkstra shortest distance vector long vector vector int int // Queue of pairs of distance to node number int int vector int int int int vector long 0 0 while // Find minimum int // Relax distances // Rather than decreasing the values in the queue, // we just add the updated distance to the queue again. for int 0 if return View gist on Github Bellman-Ford Algorithm This algorithm finds shortest distance from source to all other nodes. We have two loops: Intuition: We have two loops: Intuition: The inner loop: We iterate on all edges. At each iteration we relax the distances by using edges from to . 0 j The outer loop: We repeat the inner loop times n-1 Bellman-Ford Algorithm. Picture taken from here . After the iteration of the outer loop, the shortest paths with at most edges are calculated. There can be maximum edges in any simple path, so we repeat times. i-th i n - 1 n - 1 Below is an implementation of Bellman-Ford algorithm in C++. < > bellmanFord( < < >> &graph, source) { < > d(graph.size(), INT_MAX);
    d[source] = ; ( i = ; i < graph.size() - ; i++) { ( u = ; u < graph.size(); u++) ( v = ; v < graph.size(); v++)
                d[v] = ::min(d[v], d[u] + graph[u][v]);
    } d;
} // BellmanFord Algorithm vector long vector vector int int vector long 0 for int 0 1 for int 0 for int 0 std return Bellman-Ford Algorithm. Notice that we use an adjacency matrix to iterate edges View gist on Githu What you need to know about Bellman-Ford Algorithm Run Time: O(m.n). If we use the adjacency matrix (as in the above code) to iterate edges, the run time is O(n³) It CAN handle negative edges It CAN report negative cycles Shortest Distance in DAGs Shortest distance in a DAG (Directed Acyclic Graph) can be calculated in a linear time. We use topological sort to find the distance of a single source to all other nodes. Iterate nodes of the graph in topological order. For each node that is a neighbor of , relax Intuition: u v u d[v] using the following: d[v]=min(d[v], d[u] + w(u,v)) What you need to know: Run Time: O(m+n) It CAN handle negative edges It CANNOT handle negative cycles (there is no cycle in DAGs) Below is the implementation of shortest path in DAG using topological sort: < > shortestPathTopo( < < >> &graph, source) { < > d(graph.size(), INT_MAX);
    d[source] = ; < > sorted = topologicalSortDFS(graph); ( n : sorted) { ( j = ; j < graph.size(); j++) { (graph[n][j] != INT_MAX) {
                d[j] = min(d[j], d[n] + graph[n][j]);
            }
        }
    } d;
} // Shortest path using topological sort vector long vector vector int int vector long 0 vector int for auto for int 0 // Relax outgoing edges of n if return View gist on Github Detailed implementation of topological sort in C++ is as follows: < > topologicalSortDFS( < < >> &graph) { < > result; < , > visited; < > unvisited; ( i = ; i < graph.size(); i++) {
        unvisited.insert(i);
    } (!unvisited.empty()) {
        DFS(graph, visited, unvisited, result, *(unvisited.begin()));
    } ::reverse(result.begin(), result.end()); result;
} { (visited[n] == ) { << << ; ;
    } (visited[n] == ) { ;
    }

    visited[n] = ; ( j = ; j < graph.size(); j++) { (j != n && graph[n][j] != INT_MAX) {
            DFS(graph, visited, unvisited, sorted, j);
        }
    }
    unvisited.erase(n);
    visited[n] = ;
    sorted.push_back(n);
} // Topological Sort Using DFS vector int vector vector int vector int // map of node to 0: not visited, 1: being visited, 2: visited unordered_map int int set int for int 0 // While there is unvisited nodes while std return //----------------------------------------------------- // Recursively visits nodes // If all children of a node is visited, adds it to sorted // Marks nodes 0: not visited, 1: being visited, 2: visited void DFS ( < < >> &graph, < , > &visited, < > &unvisited, < > &sorted, n) vector vector int unordered_map int int set int vector int int if 1 cout "Detected cycle!" endl return if 2 return 1 for int 0 if 2 View gist on Github Breadth First Search Algorithm Breadth First Search, BFS, can find the shortest path in a non-weighted graphs or in a weighted graph if all edges have the same non-negative weight. Without loss of generality, assume all weights are . 1 BFS levelizes a graph, i.e., at each iteration it visits the nodes at distance from the source. Therefore, if the shortest path from source to a node is , we will definitely find it in iteration Intuition: i i i i. What you need to know about BFS: Run Time: O(m+n) All weights should be equal It CANNOT handle negative weights It CANNOT handle negative cycles The Longest Distance Problem The sister problem to finding the shortest path is to find the longest path. But first notice that there is a huge confusion when we talk about the longest path: The longest path problem commonly means finding the longest path. simple The shortest path problem (as discussed above), however, focuses on finding the shortest (simple or non-simple) path. So, in the literature even when people talk about finding the longest path, they usually mean finding the longest path. simple Transformation to -G The longest simple path problem can be solved by converting to inverting the sign of the weight of each edge in the original ), and then calculate the . G -G (i.e. G shortest simple path Notice that if has no negative cycles, finding the shortest simple path is the same as finding the shortest path which can be solved in polynomial time using above algorithms. -G What you need to know about the longest simple path problem Finding the longest simple path in general is NP-Hard. This can easily be shown by reducing from the Hamiltonian Cycle problem. It follows that finding the longest simple path in the presence of positive cycles in is NP-hard. G If there is no positive cycles in , the longest simple path problem can be solved in polynomial time by running one of the above shortest path algorithms on . G -G And here comes an interesting point about finding the shortest path in a graph that we don’t hear often: simple Finding the shortest path in a graph is NP-hard. simple This can be proved by using transformation to the problem of finding the longest simple path. -G To understand it better, suppose there is a negative cycle in . In this case none of our famous algorithms can find a shortest path simple because it doesn’t exit. However, there is still a shortest path in the graph where no vertices repeat. Finding that shortest simple path is NP-hard! G simple Longest Path in DAGs If is a DAG, because there is no cycles, the problem of finding longest simple path can be solved using topological sort in linear time. The solution is similar to the solution for finding the shortest distance in DAGs except that we take the maximum value as we relax the distances. G Please let me know if you heard about interesting questions about shortest and longest path algorithms during job interviews. Good luck on your interview! Check my video on  Graph representation in C++:

Shortest and Longest Path Algorithms: Job Interview Cheatsheet

The Noob Guides: Your Shortest Path on Becoming a Developer (Full Stack) A step by step series from zero to hero on becoming a fully independent developer. Possible Outcomes Save Lots of MoneyConvert your Ideas to RealityCater to Ideas of othersCreate your own Digital StartupSolve problems and setups of yourself and others Key Facts According to Indeed.com, as of 2018 the average salary for a full-stack developer in the United States is $111,644.As of 2018, the average front-end developer salary according to Indeed is $102,799.The average back-end developer salary in 2018 is, according to Indeed, $121,071. Introduction Hello Readers, My name is Muhammad and I was never supposed to be in this profession but somehow as a child, in the early 90s when the computer gaming industry started to take it toll, the new form of entertainment ot a child`s eye was as bright as twinkling of the morning star in the midst of sunrise. It was a drug, a really addictive one and getting exposed to it meant, parenthood had to put on restrictions that a child might not understand due to its feeble mind, but what can you say, a child's mind is a beautiful universe of possibilities, possibilities that are endless. So your restrict a child and in time what one gets, is a child trying to find alternatives to bypass the restriction. Your training a child to become a hacker by not providing the basis for the security protocol a parent has put upfront. Then it happened, fiddling here and there, having the time of the whole world, the path to discovery of a toy took place and that toy is what a personal computer. I remember, it was a pentium 1, 200mhz Processor with a MMX processor and gosh!, i had 128mb of RAM, that sure did put a smile on my face. When I was bought the computer, i remember the seller saying “Man this child is getting 4GBs of Hard Drive space, how the hell is he actually gonna fill that up?” the sellers said, It was magic in reality, i think of it today, so as time went by, the exterior was researched, upgraded and discovered and then when it was no more to be explored, the interior discovery started. This is in the simplest of words, i could reiterate how it all started. What I have in my mind, these guides will cover? FrontendHTML, CSS, Javascript, Typescript, Angular, Ionic, Bootstrap, Font Awesome, Node, NPMBackendNodeJS, MySQL, MariaDB, CentOS, Ubuntu, Apache, NGINXDatabaseMySQL, MariaDB, MongoDBSoftwaresVisual Studio Code, Putty, Iterm, MySQL Workbench, WAMP, Android Studio, XCode, Table PlusOS EnvironmentsWindows, PopOS (Linux), MacOS (Mojave, High Sierra) Overview I started my path from prebuilt CMS`s which we will highlight, such as Wordpress, Joomla and Magento which are in PHP then I shifted from these CMS to my own custom CMS from scratch in PHP which at first seemed impossible but eventually it was just my fear of the impossible that hindered it. I think what you start fearing is what becomes your impossible. I will give my experience with PHP and why I shifted completely to the Java side of things. Some pros were way better than the cons of it. I will include some exercises, following maybe some assessments if people would like that and then will also guide on using git, I prefer GitLab. The contents will be created as we move on. So Good luck to me and Cheers!. Always welcoming contributors. Next coming: The Noob Index

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