An algorithm is a set of instructions or steps that can be used to solve a problem or complete a task. It can be written in any programming language and can range from a simple sequence of operations to a complex process involving different data structures and logic. The purpose of an algorithm is to take in input, process it, and produce the desired output. Algorithms can be categorized based on the time and space complexity, the method used to solve the problem, and the type of problem it solves. Examples of algorithms include sorting, searching, graph traversals, string manipulations, mathematical operations, and many more.

Algorithms we will be talking about:

1. Sorting algorithms are methods used to organize data in a certain order, such as from smallest to largest. Examples of sorting algorithms include quicksort, merge sort and heap sort.
2. Search algorithms are used to find a specific item in a large dataset. Examples of search algorithms include binary search and hash tables.
3. Graph algorithms are used to solve problems related to graphs, such as finding the shortest path between two nodes or determining if a graph is connected.
4. Dynamic programming is a technique for solving problems by breaking them down into smaller subproblems and storing the solutions to these subproblems to avoid redundant computation.
5. Greedy algorithms are used to solve optimization problems by making the locally optimal choice at each step with the hope of finding a global optimum.
6. Divide and Conquer is an algorithm design paradigm based on multi-branched recursion. It breaks down a problem into sub-problems of the same or related type, until these become simple enough to be solved directly.
7. Backtracking is a general algorithmic technique that considers searching every possible combination in a systematic manner, and abandons a particular path as soon as it determines that it cannot be part of the solution.
8. Randomized algorithms use randomness to solve a problem. It can be useful to solve problems that cannot be solved deterministically or to improve the average case complexity of a problem.

It is important for a programmer to have a good understanding of algorithms because they are used in many different types of applications. I will do my best to explain them.

Sorting algorithms:

Quicksort:

Quicksort is a way of sorting an array of items by first picking one item (the "pivot") and then dividing the other items into two groups: those that are smaller than the pivot and those that are larger. The two groups are then sorted using the same method, and this is repeated until all items are sorted.

function quickSort(arr) {
  if (arr.length < 2) {
    return arr;
  } else {
    let pivot = arr[0];
    let left = [];
    let right = [];

    for (let i = 1; i < arr.length; i++) {
      arr[i] < pivot ? left.push(arr[i]) : right.push(arr[i]);
    }

    return quickSort(left).concat(pivot, quickSort(right));
  }
}

console.log(quickSort([5, 8, 1, 3, 7, 9, 2])); // [1, 2, 3, 5, 7, 8, 9]

Merge Sort:

The merge sort algorithm takes an array and splits it into two halves. It then sorts each of the halves and combines them back together into one sorted array.

// Merge Sort Algorithm in Javascript
// Merge Sort is a divide and conquer algorithm.
// It divides input array in two halves, calls itself for the two halves and then merges the two sorted halves.
// The merge() function is used for merging two halves. The merge(arr, l, m, r) is key process that assumes that arr[l..m] and arr[m+1..r] are sorted and merges the two sorted sub-arrays into one.
// A function that sorts an array of integers using Merge Sort algorithm.
function mergeSort(arr) {
  if (arr.length === 1) {
    // return once we hit an array with a single item
    return arr;
  }

  const middle = Math.floor(arr.length / 2); // get the middle item of the array rounded down
  const left = arr.slice(0, middle); // items on the left side
  const right = arr.slice(middle); // items on the right side

  return merge(mergeSort(left), mergeSort(right));
}

// compare the arrays item by item and return the concatenated result
function merge(left, right) {
  let result = [];
  let indexLeft = 0;
  let indexRight = 0;

  while (indexLeft < left.length && indexRight < right.length) {
    if (left[indexLeft] < right[indexRight]) {
      result.push(left[indexLeft]);
      indexLeft++;
    } else {
      result.push(right[indexRight]);
      indexRight++;
    }
  }

  return result.concat(left.slice(indexLeft)).concat(right.slice(indexRight));
}

const list = [2, 5, 1, 3, 7, 2, 3, 8, 6, 3];
console.log(mergeSort(list)); // [ 1, 2, 2, 3, 3, 3, 5, 6, 7, 8 ]

Heap Sort:

The heap sort algorithm is a comparison-based sorting algorithm that builds a heap from the input elements and then repeatedly extracts the maximum element from the heap and places it at the end of the sorted output array.

function heapSort(arr) {
  let n = arr.length;
  // Build heap (rearrange array)
  for (let i = Math.floor(n / 2) - 1; i >= 0; i--) {
    heapify(arr, n, i);
  }
  // One by one extract an element from heap
  for (let i = n - 1; i > 0; i--) {
    // Move current root to end
    let temp = arr[0];
    arr[0] = arr[i];
    arr[i] = temp;
    // call max heapify on the reduced heap
    heapify(arr, i, 0);
  }
  return arr;
}

// To heapify a subtree rooted with node i which is
// an index in arr[]. n is size of heap
function heapify(arr, n, i) {
  let largest = i; // Initialize largest as root
  let l = 2 * i + 1; // left = 2*i + 1
  let r = 2 * i + 2; // right = 2*i + 2
  // If left child is larger than root
  if (l < n && arr[l] > arr[largest]) largest = l;
  // If right child is larger than largest so far
  if (r < n && arr[r] > arr[largest]) largest = r;
  // If largest is not root
  if (largest !== i) {
    let swap = arr[i];
    arr[i] = arr[largest];
    arr[largest] = swap;
    // Recursively heapify the affected sub-tree
    heapify(arr, n, largest);
  }
}

console.log(heapSort([3, 6, 8, 10, 1, 2, 1]));

Search algorithms:

Binary Search:

Binary search is a way of quickly finding an item in a sorted list by cutting the list in half and looking in the correct half until the item is found.

//A function that takes in an array and a value and returns the index of the value if it is present in the array
function binarySearch(arr, val) {
  let start = 0;
  let end = arr.length - 1;
  let middle = Math.floor((start + end) / 2);

  while (arr[middle] !== val && start <= end) {
    if (val < arr[middle]) {
      end = middle - 1;
    } else {
      start = middle + 1;
    }
    middle = Math.floor((start + end) / 2);
  }

  if (arr[middle] === val) {
    return middle;
  }
  return -1;
}

console.log(binarySearch([1, 2, 3, 4, 5, 6, 7], 4));

Hash Tables:

A hash table is a way of storing data that uses a function to link keys (like a name) to a specific value (like a phone number). It does this by taking the key and using it to calculate an index which points to a place in an array where the value is stored.

// This example shows the implementation of a Hash Table in JavaScript using an array.
// Create an array to store the hash table
var hashTable = [];

// Create a function to hash each key
function hashString(key) {
  var hash = 0;
  for (var i = 0; i < key.length; i++) {
    hash += key.charCodeAt(i);
  }
  return hash % 10;
}

// Create a function to add a key/value pair to the hash table
function add(key, value) {
  var index = hashString(key);
  if (hashTable[index] === undefined) {
    hashTable[index] = [[key, value]];
  } else {
    var inserted = false;
    for (var i = 0; i < hashTable[index].length; i++) {
      if (hashTable[index][i][0] === key) {
        hashTable[index][i][1] = value;
        inserted = true;
      }
    }
    if (inserted === false) {
      hashTable[index].push([key, value]);
    }
  }
}

// Create a function to retrieve a value from the hash table
function get(key) {
  var index = hashString(key);
  if (hashTable[index] === undefined) {
    return undefined;
  } else {
    for (var i = 0; i < hashTable[index].length; i++) {
      if (hashTable[index][i][0] === key) {
        return hashTable[index][i][1];
      }
    }
  }
}

// Add a key/value pair to the hash table
add("name", "John");

// Retrieve the value from the hash table
console.log(get("name")); // "John"

Graph Algorithm :

Dijkstra’s shortest path algorithm:

Dijkstra's shortest path algorithm is a way to find the quickest route between two points in a network.

// create a graph object
let graph = {
  start: { A: 5, B: 2 },
  A: { C: 4, D: 2 },
  B: { A: 8, D: 7 },
  C: { D: 6, finish: 3 },
  D: { finish: 1 },
  finish: {},
};

// create a distance object
let distance = {
  A: 5,
  B: 2,
  C: Infinity,
  D: Infinity,
  finish: Infinity,
};

// create a parent object
let parent = {
  A: "start",
  B: "start",
  C: null,
  D: null,
  finish: null,
};

// create an array of visited nodes
let visited = [];

// define a function to find the node with the lowest distance
let findLowestDistanceNode = (distance, visited) => {
  let lowestDistance = Infinity;
  let lowestDistanceNode = null;

  for (let node in distance) {
    if (distance[node] < lowestDistance && !visited.includes(node)) {
      lowestDistance = distance[node];
      lowestDistanceNode = node;
    }
  }

  return lowestDistanceNode;
};

// define a function to find the shortest path between two nodes
let dijkstra = (graph, start, finish) => {
  let node = findLowestDistanceNode(distance, visited);

  while (node !== null) {
    let dist = distance[node];
    let neighbors = graph[node];
    for (let neighbor in neighbors) {
      if (neighbors.hasOwnProperty(neighbor)) {
        let newDist = dist + neighbors[neighbor];
        if (distance[neighbor] > newDist) {
          distance[neighbor] = newDist;
          parent[neighbor] = node;
        }
      }
    }

    visited.push(node);
    node = findLowestDistanceNode(distance, visited);
  }

  let shortestPath = [finish];
  let parentNode = parent[finish];
  while (parentNode !== "start") {
    shortestPath.unshift(parentNode);
    parentNode = parent[parentNode];
  }

  shortestPath.unshift("start");

  console.log(`The shortest path from ${start} to ${finish} is ${shortestPath}`);
  console.log(`The total distance is ${distance[finish]}`);
};

// call the function
dijkstra(graph, "start", "finish");

Dynamic Programming:

Fibonacci sequence:

A good example of a problem that can be solved using a technique called dynamic programming is the Fibonacci sequence, which is a sequence of numbers where each number is the sum of the two numbers before it.

function fibonacci(n) {
  if (n <= 1) {
    return n;
  }
  return fibonacci(n - 1) + fibonacci(n - 2);
}

console.log(fibonacci(7)); // 13

Greedy Algorithms:

Huffman coding:

Huffman coding is a way to compress data without losing any information. It uses a special algorithm to create a code for a set of symbols, where the code is made up of shorter and longer sequences.

// node class is the basic structure
// of each node present in the Huffman - tree.
class HuffmanNode {
  constructor() {
    this.data = 0;
    this.c = "";
    this.left = this.right = null;
  }
}

// recursive function to print the
// huffman-code through the tree traversal.
// Here s is the huffman - code generated.
function printCode(root, s) {
  // base case; if the left and right are null
  // then its a leaf node and we print
  // the code s generated by traversing the tree.
  if (root.left == null && root.right == null && root.c.toLowerCase() != root.c.toUpperCase()) {
    // c is the character in the node
    console.log(root.c + ":" + s + "\n");

    return;
  }

  // if we go to left then add "0" to the code.
  // if we go to the right add"1" to the code.

  // recursive calls for left and
  // right sub-tree of the generated tree.
  printCode(root.left, s + "0");
  printCode(root.right, s + "1");
}

// main function
// number of characters.
let n = 6;
let charArray = ["a", "b", "c", "d", "e", "f"];
let charfreq = [5, 9, 12, 13, 16, 45];

// creating a priority queue q.
// makes a min-priority queue(min-heap).
let q = [];

for (let i = 0; i < n; i++) {
  // creating a Huffman node object
  // and add it to the priority queue.
  let hn = new HuffmanNode();

  hn.c = charArray[i];
  hn.data = charfreq[i];

  hn.left = null;
  hn.right = null;

  // add functions adds
  // the huffman node to the queue.
  q.push(hn);
}

// create a root node
let root = null;
q.sort(function (a, b) {
  return a.data - b.data;
});

// Here we will extract the two minimum value
// from the heap each time until
// its size reduces to 1, extract until
// all the nodes are extracted.
while (q.length > 1) {
  // first min extract.
  let x = q[0];
  q.shift();

  // second min extract.
  let y = q[0];
  q.shift();

  // new node f which is equal
  let f = new HuffmanNode();

  // to the sum of the frequency of the two nodes
  // assigning values to the f node.
  f.data = x.data + y.data;
  f.c = "-";

  // first extracted node as left child.
  f.left = x;

  // second extracted node as the right child.
  f.right = y;

  // marking the f node as the root node.
  root = f;

  // add this node to the priority-queue.
  q.push(f);
  q.sort(function (a, b) {
    return a.data - b.data;
  });
}

// print the codes by traversing the tree
printCode(root, "");
// f: 0
// c: 100
// d: 101
// a: 1100
// b: 1101
// e: 111

Divide and Conquer:

Merge Sort:

This has already been explained earlier.

Backtracking:

Solve Sudoku Puzzle:

This backtracking algorithm is perfect for solving problems like a Sudoku puzzle because it allows you to explore all possible solutions and quickly determine which one is the correct one.

function nextEmptySpot(board) {
  for (var i = 0; i < 9; i++) {
    for (var j = 0; j < 9; j++) {
      if (board[i][j] === 0) return [i, j];
    }
  }
  return [-1, -1];
}

function checkRow(board, row, value) {
  for (var i = 0; i < board[row].length; i++) {
    if (board[row][i] === value) {
      return false;
    }
  }

  return true;
}

function checkColumn(board, column, value) {
  for (var i = 0; i < board.length; i++) {
    if (board[i][column] === value) {
      return false;
    }
  }

  return true;
}

function checkSquare(board, row, column, value) {
  boxRow = Math.floor(row / 3) * 3;
  boxCol = Math.floor(column / 3) * 3;

  for (var r = 0; r < 3; r++) {
    for (var c = 0; c < 3; c++) {
      if (board[boxRow + r][boxCol + c] === value) return false;
    }
  }

  return true;
}

function checkValue(board, row, column, value) {
  if (checkRow(board, row, value) && checkColumn(board, column, value) && checkSquare(board, row, column, value)) {
    return true;
  }

  return false;
}

function solve(board) {
  let emptySpot = nextEmptySpot(board);
  let row = emptySpot[0];
  let col = emptySpot[1];

  // there is no more empty spots
  if (row === -1) {
    return board;
  }

  for (let num = 1; num <= 9; num++) {
    if (checkValue(board, row, col, num)) {
      board[row][col] = num;
      solve(board);
    }
  }

  if (nextEmptySpot(board)[0] !== -1) board[row][col] = 0;

  return board;
}

const board = [
  [0, 5, 1, 3, 6, 2, 7, 0, 0],
  [0, 4, 0, 0, 5, 8, 0, 0, 0],
  [0, 0, 0, 4, 0, 0, 0, 2, 5],
  [0, 8, 0, 0, 0, 0, 9, 0, 3],
  [0, 0, 0, 0, 0, 0, 0, 0, 0],
  [7, 0, 5, 0, 0, 0, 0, 8, 0],
  [1, 2, 0, 0, 0, 9, 0, 0, 0],
  [0, 0, 0, 2, 8, 0, 0, 6, 0],
  [0, 0, 8, 5, 3, 4, 2, 9, 0],
];

console.log(JSON.stringify(solve(board)));

// [8, 5, 1, 3, 6, 2, 7, 4, 9]
// [2, 4, 7, 9, 5, 8, 1, 3, 6]
// [9, 6, 3, 4, 1, 7, 8, 2, 5]
// [4, 8, 6, 7, 2, 5, 9, 1, 3]
// [3, 1, 2, 8, 9, 6, 5, 7, 4]
// [7, 9, 5, 1, 4, 3, 6, 8, 2]
// [1, 2, 4, 6, 7, 9, 3, 5, 8]
// [5, 3, 9, 2, 8, 1, 4, 6, 7]
// [6, 7, 8, 5, 3, 4, 2, 9, 1]

Randomized Algorithm:

Randomized QuickSort:

A version of quicksort where the pivot is chosen randomly instead of using a specific method.

function randomizedQuicksort(arr) {
  if (arr.length <= 1) {
    return arr;
  }
  let pivot = arr[Math.floor(Math.random() * arr.length)];
  let left = arr.filter((x) => x < pivot);
  let middle = arr.filter((x) => x === pivot);
  let right = arr.filter((x) => x > pivot);
  return randomizedQuicksort(left).concat(middle).concat(randomizedQuicksort(right));
}

console.log(randomizedQuicksort([3, 6, 8, 10, 1, 2, 1, 1, 1]));

Every programmer should know about these popular algorithms so they can make better decisions when creating efficient solutions.

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