Intro

Linear search is a very common searching algorithm; It is implemented under the hood in the JavaScript built-in methods indexOf(), includes(), find(), and findIndex().

It is also the most straight-forward searching algorithm: it simply loops over each element in an array and stops if that element equals our target value.

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Linear Search steps

I think that with this algorithm, the gif below explains it all. But here are the steps in words:

1. Linear search will accept an array and a target value.
2. Start searching from the beginning of the array.
3. Check if that value equals the target:

• If so, stop and return that values index.
• If not, move onto the next element.

4. Repeat step 3 until all elements are checked. If target not found, return -1.

Source of the above gif: bournetocode.com

And if you ever find yourself looking for a specific length of French fry:

Linear Search in JavaScript

function linearSearch(arr, target) {
  for (let i in arr) {
    if (arr[i] === target) return i
  }
  return -1
}
console.log(linearSearch([1, 2, 3, 4], 1)) // 0
console.log(linearSearch([1, 2, 3, 4], 4)) // 3
console.log(linearSearch([1, 2, 3, 4], 6)) // -1
console.log(linearSearch([3, 4, 1, 6, 3], 6)) // 3

We simply loop over each element in the array, and check to see if the current element is equal to the target; if so, we return that elements index. If the target isn’t found, then we simply return -1 at the end of the function.

Time complexity of Linear Search

Best-case time complexity of Linear Search

If our target value is at the beginning of the array, the algorithm will always run at constant time, O(1). The algorithm will always only have to perform one comparison, no matter what the size of the array.

Worst-case time complexity of Linear Search

If our target is the last element in the array, then the algorithm will have to make n comparisons (n being the length of the input array). This means that the Big O notation of Linear Search is Big O(n) – linear time complexity.

Average-case time complexity of Linear Search

If our target element is somewhere in the middle of the array, then the time complexity will be approximately O(n/2), which simplifies to O(n) – linear time.

Space complexity of Linear Search

Linear Search has a space complexity of O(1) – constant space. It uses no auxiliary data structures to find the target value.

Performance summary table

When to use Linear Search

Linear search is the best we can do when searching in unsorted arrays, such as [2, 3, 1].

Whilst there are searching algorithms that can perform faster, such as Binary Search, they can only search through sorted arrays.

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