Linear search algorithm
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The linear search algorithm involves checking all elements of an array or data structure sequentially until the target element is found. In the worst case, all elements must be checked, resulting in O(n) time complexity where n is the number of elements. However, if the target is the first element, it requires only constant O(1) time. The algorithm is simple to implement but does not scale well to large data sets as the search time grows linearly with the number of elements.
![C++ code [Iterative]
void iterSearch(const double data [ ],int n,double key) //const for safety ,we want to keep array unchanged
{
for(int i=0;i<=n-1;i++)
//looping through all elements of the array
{
if(data[i]==key)
{
cout<<key<<" found at index "<<i<<" of the array"<<endl;
break;
//if element is found,come out of the loop
}
if(i==n-1)
//searched through the array,still not found
cout<<"n Element not found n";
}
}](https://image.slidesharecdn.com/linearsearchalgorithm-131212155548-phpapp01/85/Linear-search-algorithm-6-320.jpg)
![Recursive Linear Search
bool recursiveSearch (const double data[ ],int n,double key)
{
static int i=0;
//static will prevent i being initialised to 0 every time we enter the function
if(data[i]==key)
{
cout<<key<<" found at index "<<i<<" of the array"<<endl;
return true; //this will end recursion which is desired as the element has been found
}
else
{ ++i;
if(i==n)
{
cout<<"nElemnent not foundn";
}
recursiveSearch(data,n,key);
}
}
i=0;
return false; //i=0 to reset i for next search.](https://image.slidesharecdn.com/linearsearchalgorithm-131212155548-phpapp01/85/Linear-search-algorithm-7-320.jpg)
Linear search algorithm
- 1. LINEAR SEARCH ALGORITHM Algorithm involves checking all the elements of the array(or any other structure) one by one and in sequence until the desired result is found.
- 2. Daily life example If you are asked to find the name of the person having phone number say “1234” with the help of a telephone directory . Since telephone directory is sorted by name not by numbers,we have to go through each and every number of the directory
- 3. Best case ● If the first number in the directory is the number you were searching for ,then lucky you!!. ● Since you have found it on the very first page,now its not important for you that how many pages are there in the directory. ● Whether if it is of 1000 pages or 2000 pages it will take u same time to find you the number ,if it is at the very beginning . ● So it does not depends on no. on elements in the directory.Hence constant time . InBig O notation : 0(1)
- 4. Worst Case It may happen that the number you are searching for is the last number of directory or if it is not in the directory at all. In that case you have to search the whole directory. Now number of elements will matter to you.if there are 500 pages ,you have to search 500;if it has 1000 you have to search 1000. Your search time is proportional to number of elements in the directory. In big O notation O(n) No of elements No of comparisons to be done 15 15 600 600
- 5. Pseudocode For all elements Check if it is equal to element being searched for. If it is ,return its position. else continue.
- 6. C++ code [Iterative] void iterSearch(const double data [ ],int n,double key) //const for safety ,we want to keep array unchanged { for(int i=0;i<=n-1;i++) //looping through all elements of the array { if(data[i]==key) { cout<<key<<" found at index "<<i<<" of the array"<<endl; break; //if element is found,come out of the loop } if(i==n-1) //searched through the array,still not found cout<<"n Element not found n"; } }
- 7. Recursive Linear Search bool recursiveSearch (const double data[ ],int n,double key) { static int i=0; //static will prevent i being initialised to 0 every time we enter the function if(data[i]==key) { cout<<key<<" found at index "<<i<<" of the array"<<endl; return true; //this will end recursion which is desired as the element has been found } else { ++i; if(i==n) { cout<<"nElemnent not foundn"; } recursiveSearch(data,n,key); } } i=0; return false; //i=0 to reset i for next search.
- 8. Discussions 1.Sorted array is not needed. 2.Works fine for small number of elements .Search time increases with number of elements. 3.Elements with higher probability of being searched should be kept in the beginning. 4.Trick: Get completely rid of the end-check, namely putting a sentinel value after the end of the last valid array element.