Define the concepts of logarithm, linear, and quadratic when analyzing algorithms. What are some of the pros and cons associated with utilizing Big$-$Oh notation to analyze an algorithm? How can analyzing the efficiency of an algorithm lead to improvements in the initial design?

In your answer, specifically, think of and give a real$-$life scenario where:

Algorithm analysis is important

Algorithm efficiency is paramount

After your initial post, be sure respond to at least two peers in this discussion.

Requirements:

Be sure to post an initial, substantive response by Thursday at $11$:$59$ p$.$m$.$ MT and respond to $2$ or more peers with substantive responses by Sunday at $11$:$59$ p$.$m$.$ MT$.$ A substantive initial post answers the question presented completely and$/$or asks a thoughtful question pertaining to the topic. Substantive peer responses ask a thoughtful question pertaining to the topic and$/$or answers a question $($in detail$)$ posted by another student or the instructor.