# Linear Search/ Sequential Search

### Linear/Sequential Search

In computer science, linear search, also known as sequential search, is a method for <mark style="color:red;">locating</mark> a specific value in a list that involves verifying each of the list's members one by one until the desired one is discovered.&#x20;

The <mark style="color:red;">simplest</mark> search algorithm is linear search. It's a type of <mark style="color:red;">brute-force</mark> search with a twist. Its worst-case cost is proportional to the list's amount of items.

### The complexity of Linear Search Technique

* **Time Complexity:** <mark style="color:red;">O(n)</mark>
* **Space Complexity:** <mark style="color:red;">O(1)</mark>

### Linear/ Sequential Search - Algorithm

<div align="center"><img src="https://3717782766-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F60gGuq3OlHvCAPS1ajFy%2Fuploads%2FwbJYutUJuCABLEoLkcrK%2Fimage.png?alt=media&#x26;token=bbff91ae-c67c-41ad-b67c-8db2a26ae477" alt=""></div>

### Linear/ Sequential Search - Example

Search for <mark style="color:red;">**1**</mark> in the given array  ![](https://3717782766-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F60gGuq3OlHvCAPS1ajFy%2Fuploads%2FiCLCeQL20HDZP2uDWHTm%2Fimage.png?alt=media\&token=0abeee8d-0d6c-41ba-a8ab-3406b96abbd9)

Comparing the value of <mark style="color:red;">ith</mark> index with element to be search one by one until we get searched element or end of the array.

![Element found at ith index, i=3](https://3717782766-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F60gGuq3OlHvCAPS1ajFy%2Fuploads%2FbvB0KwA4LOt7gWIlKgoS%2Fimage.png?alt=media\&token=8b933b64-4d1f-440f-8afc-3f35372009a5)

### Example

```
#include<iostream>
using namespace std;

int linSearch(int a[], int size, int key) {
   for(int i = 0; i<size; i++) {
      if(a[i] == key) 
         return i; 
   }
   return -1; 
}

int main() {
   int n, skey, loc;
   cout << "Enter number of items: ";
   cin >> n;
   int arr[n]; 
   cout << "Enter items: " << endl;

   for(int i = 0; i< n; i++) {
      cin >> arr[i];
   }

   cout << "Enter which number to search in the list: ";
   cin >> skey;

   if((loc = linSearch(arr, n, skey)) >= 0)
      cout << "Item found at location: " << loc << endl;
   else
      cout << "Item is not found in the list." << endl;
}
```

### Output

```
Enter number of items: 5
Enter items:
2 9 3 1 8
Enter which number/ to search in the list: 1
Item found at location: 3
```


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