Understanding Algorithmic Complexity

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Questions and Answers

What is something found in nature that humans can use?

  • An artificial creation
  • A natural resource (correct)
  • A manufactured product
  • A synthetic material

Where do the vegetables you eat come from?

  • Created in factories
  • Made from oil
  • Growing plants (correct)
  • Mined from underground

What raw material is glass made from?

  • Metal
  • Oil
  • Sand (correct)
  • Plastic

How can natural resources be classified?

<p>Based on how available they are (B)</p> Signup and view all the answers

Which type of resource has a limited supply?

<p>Nonrenewable resource (A)</p> Signup and view all the answers

How long does it take for nonrenewable resources to form?

<p>Millions of years (A)</p> Signup and view all the answers

Which of the following is an example of a nonrenewable resource?

<p>Coal (A)</p> Signup and view all the answers

What makes a resource renewable?

<p>It is replaced as quickly as people use it (B)</p> Signup and view all the answers

Which of the following is a renewable resource because plants constantly produce oxygen?

<p>Air (A)</p> Signup and view all the answers

What do resources need to be to remain renewable?

<p>Used at a rate slower than they are produced (A)</p> Signup and view all the answers

What do we use land for?

<p>To build houses (B)</p> Signup and view all the answers

What would happen without soil?

<p>We would have very few kinds of food to eat (C)</p> Signup and view all the answers

How long can it take for soil to form?

<p>Hundreds of years (D)</p> Signup and view all the answers

What do forests provide?

<p>Habitats for many organisms (A)</p> Signup and view all the answers

What role do forests play in controlling the amount of carbon dioxide?

<p>An important role (C)</p> Signup and view all the answers

Wetlands are examples of what?

<p>California land environments (C)</p> Signup and view all the answers

About how many acres of forest land does California have?

<p>33 million (B)</p> Signup and view all the answers

Flashcards

Natural resource

Materials from nature used by humans.

Classify

To sort into groups.

Nonrenewable resource

A resource that cannot be replaced quickly.

Renewable resource

Resource that is replaced as quickly as people use it.

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Land

It provide many things we need and want and It is used to build houses and other structures and to grow crops and graze animals.

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Forest

It provide habitats for many organisms and materials for paper, medicines, and foods. It also control the amount of carbon dioxide in the air.

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Study Notes

Algorithmic Complexity: What?

  • It is an approximate measure of the time and/or space an algorithm needs
  • The measure is dependent on the size of the input
  • It is expressed using "Big O" notation as: O(f(n))
    • Where n is the input size
    • f(n) is a function that grows as n grows

Algorithmic Complexity: Why?

  • To compare different algorithms
  • To predict algorithm performance
  • To avoid the use of slow algorithms

Algorithmic Complexity: How?

  • First choose a metric, either time or space
  • Then determine the input size: n
  • Calculate the amount by which the metric changes as "n" increases
    • This may require an inspection of code
    • Ignore any constants
    • Express as O(f(n))

Common complexities

  • Constant: O(1), example is accessing an array element
  • Logarithmic: O(log(n)), example is binary search
  • Linear: O(n), example is searching an unsorted array
  • Linearithmic: O(nlog(n)), example is merge sort
  • Quadratic: O(n^2), example is bubble sort
  • Exponential: O(2^n), example is calculating Fibonacci recursively

Visualized Complexities

  • Constant: Horizontal line at y=1, indicating constant growth
  • Logarithmic: Curve that grows very slowly, starting near the origin and increasing gradually
  • Linear: Straight line that grows proportionally with the input size
  • Linearithmic: Curve that grows faster than linear but slower than quadratic
  • Quadratic: Curve that grows rapidly as the input size increases
  • Exponential: Curve that grows extremely rapidly as the input size increases

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