Page 24 - Data Structures Interactive Book

Chapter 2

2.1 Algorithm Efficiency

Algorithm efficiency refers to how effectively an algorithm uses computational

resources such as time and memory. Since different algorithms can solve the same problem

in varying ways, efficiency provides a framework for comparing them. A highly efficient
algorithm minimizes execution time and memory usage, making it suitable for large-scale

applications. Understanding efficiency is crucial in data structures, as the choice of algorithm

directly impacts performance.

2.1.1 Time Complexity

Time complexity measures the amount of time an algorithm takes to run as a function

of the input size. It provides a theoretical estimate of performance rather than exact

execution time. For example, searching an element in an unsorted array requires checking

each element, resulting in a time complexity of ( ). In contrast, binary search on a sorted

array reduces the complexity to ( ⁡ ). Time complexity helps programmers predict how
algorithms will scale as input size increases.

2.1.2 Time Complexity

Time complexity measures the amount of time an algorithm takes to run as a function

of the input size. It provides a theoretical estimate of performance rather than exact
execution time. For example, searching an element in an unsorted array requires checking

each element, resulting in a time complexity of ( ). In contrast, binary search on a sorted

array reduces the complexity to ( ⁡ ). Time complexity helps programmers predict how
algorithms will scale as input size increases.

2.2 Big-O Notation

Big-O notation is a mathematical representation used to describe the upper bound of

an algorithm’s growth rate. It abstracts away machine-specific details and focuses on how
performance scales with input size. By categorizing algorithms into classes such as constant

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