What is the time complexity of a sequential (linear) search in the worst case for a list of n elements?

Introduction / Context:
Sequential search, also called linear search, is one of the simplest searching algorithms. It checks each element in a list one by one until the target is found or the list ends. While easy to implement, it is not the most efficient method for large datasets. This question asks you to recall the standard time complexity of sequential search in the worst case, expressed using Big O notation.

Given Data / Assumptions:

• We have a list or array of n elements.
• Sequential search examines elements from the beginning toward the end.
• The worst case occurs when the element is not present or is located at the last position.
• We measure time in terms of the number of comparisons made.

Concept / Approach:
In sequential search, the algorithm compares the target value with each element of the list in order. In the worst case, it must examine all n elements, resulting in n comparisons. Big O notation captures the growth rate of the running time as n increases, ignoring constant factors. Therefore, if the running time grows proportionally with n, the time complexity is O(n). Any expression such as O(2n) simplifies to O(n), because constant multiplicative factors are not considered significant in Big O notation.

Step-by-Step Solution:
Step 1: Recall the behavior of sequential search, which checks elements one by one.Step 2: In the worst case, the algorithm must inspect all n elements.Step 3: This leads to n comparisons, so the running time is proportional to n.Step 4: In Big O notation, a runtime proportional to n is expressed as O(n).Step 5: Therefore, the worst case time complexity of sequential search is O(n).

Verification / Alternative check:
You can verify this by writing a simple piece of pseudocode for linear search and counting the number of iterations of the loop. The loop runs from index 1 to n, stopping early only if the element is found. In the worst case, the loop does not stop early and runs for all n iterations. Since no other operations dominate this loop, the overall time grows linearly with n, confirming an O(n) complexity.

Why Other Options Are Wrong:
Option B, O(2n), is misleading because Big O notation ignores constant factors, so O(2n) simplifies to O(n), and it is not used as a distinct answer. Option C, O(n^2), suggests quadratic time, which would involve nested loops or repeated passes over the data, which linear search does not have. Option D, O(1), describes constant time, which is not correct because the number of comparisons grows with n in the worst case.

Common Pitfalls:
A common mistake is to be distracted by expressions like O(2n) and think that they represent a different complexity class. Remember that Big O abstracts away constants. Another pitfall is to confuse average and worst case complexities; even though the average case may involve fewer comparisons, the worst case still requires inspecting all elements. Understanding these distinctions is essential for analyzing and comparing algorithms.

Final Answer:
The worst case time complexity of sequential search on n elements is O(n), which corresponds to option A.