Big O Notation, collectively called Bachmann-Landau notation or asymptotic notation, is a way to describe the performance of an algorithm. It is used to describe the worst-case scenario of an algorithm. It is used to compare the performance of different algorithms. It describes the implementation of an algorithm in terms of the input size. Big O notation characterizes functions according to their growth rates: tasks with the same growth rate are considered to be of the same order. It is a mathematical notation that describes the limiting behavior of a function when the argument tends towards a particular value or infinity. It is used to classify algorithms according to how their run time or space requirements grow as the input size grows. The letter O is used because the growth rate of a function is also called its order. Iteration For loop for (let i = 0; i < n; i++) {
  console.log(i)
} The above code will run n times. The time complexity of this code is O(n). While loop let i = 0
while (i < n) {
  console.log(i)
  i++
} The above code will run n times. The time complexity of this code is O(n). Do while loop let i = 0
do {
  console.log(i)
  i++
} while (i < n) The above code will run n times. The time complexity of this code is O(n). Recursion Factorial function factorial(n) {
  if (n === 0) {
    return 1
  }
  return n * factorial(n - 1)
} The above code will run n times. The time complexity of this code is O(n). Fibonacci function fibonacci(n) {
  if (n <= 1) {
    return n
  }
  return fibonacci(n - 1) + fibonacci(n - 2)
} The above code will run n times. The time complexity of this code is O(n). Searching Linear search function linearSearch(arr, value) {
  for (let i = 0; i < arr.length; i++) {
    if (arr[i] === value) {
      return i
    }
  }
  return -1
} The above code will run n times. The time complexity of this code is O(n). Binary search function binarySearch(arr, value) {
  let start = 0
  let end = arr.length - 1
  let middle = Math.floor((start + end) / 2)
  while (arr[middle] !== value && start <= end) {
    if (value < arr[middle]) {
      end = middle - 1
    } else {
      start = middle + 1
    }
    middle = Math.floor((start + end) / 2)
  }
  if (arr[middle] === value) {
    return middle
  }
  return -1
} The above code will run log(n) times. The time complexity of this code is O(log(n)). Sorting Bubble sort function bubbleSort(arr) {
  for (let i = arr.length; i > 0; i--) {
    for (let j = 0; j < i - 1; j++) {
      if (arr[j] > arr[j + 1]) {
        let temp = arr[j]
        arr[j] = arr[j + 1]
        arr[j + 1] = temp
      }
    }
  }
  return arr
} The above code will run n^2 times. The time complexity of this code is O(n^2). Selection sort function selectionSort(arr) {
  for (let i = 0; i < arr.length; i++) {
    let lowest = i
    for (let j = i + 1; j < arr.length; j++) {
      if (arr[j] < arr[lowest]) {
        lowest = j
      }
    }
    if (i !== lowest) {
      let temp = arr[i]
      arr[i] = arr[lowest]
      arr[lowest] = temp
    }
  }
  return arr
} The above code will run n^2 times. The time complexity of this code is O(n^2). Insertion sort function insertionSort(arr) {
  for (let i = 1; i < arr.length; i++) {
    let currentVal = arr[i]
    for (var j = i - 1; j >= 0 && arr[j] > currentVal; j--) {
      arr[j + 1] = arr[j]
    }
    arr[j + 1] = currentVal
  }
  return arr
} The above code will run n^2 times. The time complexity of this code is O(n^2). Merge sort function mergeSort(arr) {
  if (arr.length <= 1) return arr
  let mid = Math.floor(arr.length / 2)
  let left = mergeSort(arr.slice(0, mid))
  let right = mergeSort(arr.slice(mid))
  return merge(left, right)
}

function merge(left, right) {
  let results = []
  let i = 0
  let j = 0
  while (i < left.length && j < right.length) {
    if (left[i] < right[j]) {
      results.push(left[i])
      i++
    } else {
      results.push(right[j])
      j++
    }
  }
  while (i < left.length) {
    results.push(left[i])
    i++
  }
  while (j < right.length) {
    results.push(right[j])
    j++
  }
  return results
} The above code will run n log(n) times. The time complexity of this code is O(n log(n)). Quick sort function pivot(arr, start = 0, end = arr.length + 1) {
  let pivot = arr[start]
  let swapIdx = start
  function swap(array, i, j) {
    let temp = array[i]
    array[i] = array[j]
    array[j] = temp
  }
  for (let i = start + 1; i < arr.length; i++) {
    if (pivot > arr[i]) {
      swapIdx++
      swap(arr, swapIdx, i)
    }
  }
  swap(arr, start, swapIdx)
  return swapIdx
}

function quickSort(arr, left = 0, right = arr.length - 1) {
  if (left < right) {
    let pivotIndex = pivot(arr, left, right)
    quickSort(arr, left, pivotIndex - 1)
    quickSort(arr, pivotIndex + 1, right)
  }
  return arr
} The above code will run n log(n) times. The time complexity of this code is O(n log(n)). Tips for Big O Arithmetic operations are constant Variable assignment is constant Accessing elements in an array (by index) or object (by key) is constant In a loop, the complexity is the length of the loop times the complexity of whatever happens inside the loop Resources Big O Cheat Sheet Big O Notation Big O Notation Originally published . here

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