# Analysis of Algorithm

There are the three cases to analyze an algorithm i.e

- Worst Case
- Average Case
- Best Case

The implementation of Linear Search:

## Worst Case Analysis (Commonly Performed)

From the worst case analysis, most of us analyze upper bound with running time of an algorithm. We should understand the actual case that causes maximum number of operations to become executed. With regard to Linear Search, the actual worst case occurs when the element to be searched (x in the above code) isn't contained in the array. Whenever x isn't existing, the search() functions even comes close this with the elements associated with arr[] one by one. Consequently, the worst case time complexity associated with linear search would be Θ(n).

## Average Case Analysis (Sometimes Performed)

From the average case analysis, all of us consider just about all possible inputs as well as determine computing time with regard to all the inputs. Sum all the calculated values as well as divide the sum by total number of inputs. We should understand distribution associated with cases. For that linear search problem, let's presume that instances tend to be uniformly distributed (such as the situation associated with x not being present in array). Therefore we sum all the cases and divide the sum by (n+1). The value of average case time complexity.

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### Best Case Analysis (Bogus)

From the best case analysis, all of us determine lower bound on running time of an algorithm. We should understand the actual case that causes minimum number of operations to become executed. Within the linear search problem, the best case occurs when x exists in the first location. The number of operations within the best case is constant (not really determined by n). Therefore time complexity within the best case will be Θ(1).