Design & Analysis of Algorithms - Vol 1 | 6. Input Size and Running Time by Abraham | Learn Smarter
Students

Academic Programs

AI-powered learning for grades 8-12, aligned with major curricula

Professional

Professional Courses

Industry-relevant training in Business, Technology, and Design

Games

Interactive Games

Fun games to boost memory, math, typing, and English skills

6. Input Size and Running Time

6. Input Size and Running Time

Efficiency in algorithm performance is evaluated based on input size and basic operations to compute running time functions. Worst-case analysis provides an upper bound on resource consumption while understanding input characteristics is crucial for algorithm design. Average case analysis, although appealing, presents challenges in estimation, rendering worst-case analysis a practical focus in algorithm evaluation.

9 sections

Enroll to start learning

You've not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take practice test.

Sections

Navigate through the learning materials and practice exercises.

  1. 6.1
    Input Size And Running Time

    This section discusses the relationship between input size and the running...

  2. 6.1.1
    Definition Of Input Size

    This section explores the significance of input size in algorithm...

  3. 6.1.2
    Examples Of Input Sizes

    This section discusses the importance of input size in measuring algorithm...

  4. 6.1.3
    Special Case: Input Size For Numbers

    This section discusses the concept of input size when analyzing algorithms,...

  5. 6.1.4
    Ignoring Constants In Analysis

    This section discusses the importance of input size in algorithm analysis...

  6. 6.2
    Worst Case And Average Case Analysis

    This section explores the concepts of worst case and average case analysis...

  7. 6.2.1
    Definition Of Worst Case

    This section discusses the concept of the worst-case scenario in algorithm...

  8. 6.2.2
    Understanding Average Case Analysis

    This section discusses how the efficiency of an algorithm can be measured...

  9. 6.2.3
    Summary Of Worst Case Vs. Average Case

    This section explores the concepts of worst-case and average-case scenarios...

What we have learnt

  • The running time of an algorithm depends on the size of the input.
  • Worst-case the analysis is essential to determine the maximum time an algorithm may take.
  • Input size can vary depending on the nature of the problem and can be defined in terms of properties such as number of digits in arithmetic operations.

Key Concepts

-- Input Size
The measure of the amount of space needed to represent the problem's distribution, typically correlated with the number of elements such as in an array.
-- Worst Case Analysis
An evaluation of the maximum time an algorithm can take, based on the least favorable input condition.
-- Average Case Analysis
An assessment of the expected time taken by an algorithm when inputs are distributed uniformly, often difficult to compute accurately.

Additional Learning Materials

Supplementary resources to enhance your learning experience.