The Big O Notation in JavaScriptby@imamdev
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The Big O Notation in JavaScript

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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 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. Big O Notation characterizes functions according to their growth rates. It describes the implementation of a algorithm in terms of the size of the input. The time complexity of this code is O(n).

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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

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Originally published here.

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