Fibonacci Algorithms and Networking Concepts
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Questions and Answers

Which of the following Fibonacci algorithms provides both accuracy and efficiency?

  • Fibonacci1
  • Fibonacci2
  • Fibonacci4
  • Fibonacci3 (correct)

Fibonacci1 provides both accuracy and efficiency.

False (B)

What value is stored in the first two elements of the Fibonacci array when calculating Fibonacci3?

1

In the Fibonacci3 algorithm, Fib[i] is calculated as Fib[i-1] + Fib[___].

<p>i-2</p> Signup and view all the answers

Match the following terms with their definitions:

<p>Fibonacci1 = Lacks accuracy Fibonacci2 = Provides accuracy but not efficiency Fibonacci3 = Provides both accuracy and efficiency Fibonacci loop = Repeats instructions based on an index variable</p> Signup and view all the answers

What does Moore's Law state?

<p>The number of transistors on a computer chip doubles approximately every 18 months. (A)</p> Signup and view all the answers

The instruction 'For i=3 to n do' indicates that the loop starts at index 1.

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

When using Fibonacci3 with n=6, what will the final value returned be?

<p>8</p> Signup and view all the answers

Nielsen's Law states that users' bandwidth grows by 25% per year.

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

What is the maximum theoretical speed of 5G?

<p>10 gigabits per second</p> Signup and view all the answers

In this framework, the value of a telecommunications network is proportional to the square of the number of connected users, according to __________ law.

<p>Metcalfe's</p> Signup and view all the answers

Match the concepts with their definitions:

<p>Moore's Law = Transistor growth rate Nielsen's Law = Bandwidth growth rate Metcalfe's Law = Network value based on users Multicore = Multiple processors in one computer</p> Signup and view all the answers

What is meant by 'network bandwidth'?

<p>The maximum amount of data that can be transmitted over a network in a given time. (A)</p> Signup and view all the answers

Computer systems are becoming larger, more expensive, and slower over time.

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

What technology allows a computer to have multiple cores?

<p>Multicore technology</p> Signup and view all the answers

What is the main issue with using recursion for calculating Fibonacci numbers?

<p>It calculates the same values multiple times. (B)</p> Signup and view all the answers

The technique of memorization helps in avoiding repeated calculations of the same subproblem.

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

What is the purpose of a for loop in programming?

<p>To execute code repeatedly for a specified number of iterations.</p> Signup and view all the answers

The Fibonacci sequence is calculated using the two previous _______ in the sequence.

<p>numbers</p> Signup and view all the answers

When n is equal to 1000, the complexity of calculating Fibonacci numbers recursively results in a time complexity close to which of the following?

<p>$O(2^n)$ (B)</p> Signup and view all the answers

The third method for calculating Fibonacci numbers is described as the least accurate.

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

What does the header of a for loop specify?

<p>The iteration details and often declares a loop counter.</p> Signup and view all the answers

What is the value stored in the fifth position of the Fibonacci sequence?

<p>3 (A)</p> Signup and view all the answers

The running time of Fibonacci 2 is faster than Fibonacci 3.

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

What technique is used in Fibonacci to avoid recomputing previously computed values?

<p>Memorization</p> Signup and view all the answers

The running time of Fibonacci 3 is measured as _____ in terms of the number of lines of code executed.

<p>T(n)</p> Signup and view all the answers

Match the Fibonacci algorithm with its running time complexity:

<p>Fibonacci 2 = Exponential time Fibonacci 3 = Linear time Fibonacci 1 = Constant time Fibonacci 4 = Polynomial time</p> Signup and view all the answers

How many times are lines 1, 2, and 5 executed in Fibonacci 3?

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

When n equals 8, the total number of instructions for Fibonacci 3 is 19.

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

What is the Big O notation used for in relation to running time?

<p>It describes the growth rate of the running time.</p> Signup and view all the answers

What does Big O notation help ignore in algorithm analysis?

<p>Low-level details (B)</p> Signup and view all the answers

The Tribonacci number for N=2 is 2.

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

Who proposed the Stable Marriage Algorithm?

<p>Shapley</p> Signup and view all the answers

In the Stable Marriage Algorithm, a pair (m, w) is a blocking pair if __________.

<p>m and w are not partners in M, but prefer each other over their current partners.</p> Signup and view all the answers

Match the following concepts with their descriptions:

<p>Big O notation = Upper bound performance of an algorithm Fibonacci algorithm = Algorithm that runs in O(n) Stable Marriage Algorithm = Solves matching problems Gale-Shapley algorithm = A method for stable matching</p> Signup and view all the answers

Which property defines a stable marriage in the Stable Marriage Algorithm?

<p>No blocking pairs exist. (A)</p> Signup and view all the answers

Fibonacci2 has a better runtime complexity than Fibonacci3.

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

What is the initial condition for calculating the Tribonacci number?

<p>The initial conditions are T(0) = 0, T(1) = 1, and T(2) = 1.</p> Signup and view all the answers

What is the time complexity of binary search?

<p>O(log n) (D)</p> Signup and view all the answers

The algorithm always takes the same amount of time to execute in constant time complexity O(1).

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

What will be the result if the target value is not found in a binary search?

<p>NOT FOUND</p> Signup and view all the answers

The number of comparisons done by binary search can be described by the recurrence T(n) = T(n/2) + _____ .

<p>1</p> Signup and view all the answers

Which algorithm has a better running time than a linear search?

<p>Logarithmic algorithm (B)</p> Signup and view all the answers

Match the following algorithm complexities with their descriptions:

<p>O(1) = Constant time - execution time remains the same regardless of input size O(log n) = Logarithmic time - grows logarithmically with size O(n) = Linear time - grows directly with input size O(n^2) = Quadratic time - grows with the square of input size</p> Signup and view all the answers

Sequential search has a better running time than binary search.

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

What happens to the search space during each step of the binary search if the midpoint is greater than the target value?

<p>The right part of the list is discarded.</p> Signup and view all the answers

Flashcards

Moore's Law

The number of transistors on a computer chip doubles approximately every 18 months, leading to exponential growth in processing power.

Network Bandwidth

A measure of how much data can be sent over a network connection within a specific time, often expressed in bits per second (bps) or its multiples.

Metcalfe's Law

A principle stating that the value of a telecommunications network increases proportionally to the square of the number of connected users.

Connectivity Value

Refers to the perceived or actual benefits derived from being connected to a network, often influenced by the number of users and the speed of the connection.

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What is an algorithm?

A set of instructions or rules that a computer follows to perform a specific task. Algorithms are essential for processing and analyzing data.

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Multicore

A technology that allows for multiple processing units (cores) to operate simultaneously within a single computer, increasing overall performance.

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5G

A type of wireless network that offers significantly faster data transfer speeds and lower latency compared to previous generations, like 4G.

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Nielsen's Law

Nielsen's law states that users' bandwidth (the amount of data we can send on a network) grows by 50% per year. This means we can send double the data in two years compared to two years prior.

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Recursion

A way to solve a problem by breaking it down into smaller, similar problems.

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Memorization

A method of solving a problem by storing the results of previous calculations to avoid repeating them.

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Fibonacci Sequence

A sequence of numbers where each number is the sum of the two preceding numbers. It starts with 0 and 1.

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For Loop

A control flow statement that repeats a block of code a specified number of times.

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Loop Counter

The variable that keeps track of the current iteration in a for loop.

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Array

A data structure that holds a sequence of values of the same data type.

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Iterative Fibonacci Algorithm

The process of calculating the Fibonacci sequence using a for loop.

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Efficient Fibonacci Algorithm

The most efficient and accurate way to calculate the Fibonacci sequence by storing previous values in an array and using a for loop to iterate through the sequence.

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Loop

A programming construct that executes a block of code repeatedly for a specified number of times. It's essential for iterating through data structures and performing tasks repeatedly.

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Loop Index

A variable used within a loop to keep track of the current iteration. It typically increments or decrements with each loop iteration.

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Loop Body

The block of code that is executed repeatedly within a loop. It contains instructions that are repeated for each iteration.

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Fibonacci3 Algorithm

An algorithm that calculates Fibonacci numbers efficiently. It utilizes an array to store previous Fibonacci numbers and uses them to calculate the next one.

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Store values

The process of storing a value in a specific memory location, often within an array. It's used in the Fibonacci3 algorithm to keep track of calculated values during iterations.

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Fibonacci3

A faster algorithm for calculating Fibonacci numbers by storing calculated values in a table, avoiding redundant computations.

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Return value

The value returned by a function after it has completed its execution. In the Fibonaci3 algorithm, it refers to the calculated Fibonacci number at a specific index.

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Fibonacci2

A slower algorithm for calculating Fibonacci numbers by recursive function calls. Every number requires recalculating previous numbers, leading to redundant computations.

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Running time

A measure of how an algorithm's runtime grows with increasing input size. It describes the relationship between the size of the input and the number of steps required by the algorithm.

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Big-O notation

A mathematical notation used to describe the growth rate of an algorithm's running time. It focuses on the dominant term in the runtime expression and ignores constant factors.

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Number of instructions

The number of instructions executed by an algorithm. It is a simplified way to estimate an algorithm's runtime.

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Bottleneck

The part of an algorithm that has the most significant impact on its runtime. It is the operation that takes the longest to complete, causing a bottleneck.

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Linear time

The number of steps required by an algorithm grows linearly with the input size. For example, if the input size doubles, the runtime also doubles.

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Stable Marriage Algorithm

An algorithm that finds stable pairings between two sets of equal size. This applies to matching problems like assigning students to internships, professors to courses, or rooms to events.

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Blocking Pair

A pair of individuals (e.g., a man and a woman in a matching problem) who are not currently matched but would prefer each other to their current partners.

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Gale-Shapley Algorithm

An algorithm used to find stable matchings in the Stable Marriage Problem. It involves a series of proposals and acceptances, where individuals propose to their most preferred partners and accept or reject offers depending on their preferences.

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Stable Matching

The concept that there exists a matching where no pair of individuals from opposite sets would prefer each other to their current partners. It is a fundamental goal in matching problems like the Stable Marriage Problem.

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Complexity Analysis

A method for analyzing the efficiency of algorithms and data structures, focusing on how their performance changes with the size of the input. It provides a way to compare and categorize algorithms based on their growth rate.

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Binary Search

A technique for finding a specific value within a sorted list by repeatedly dividing the search space in half. It compares the target value with the middle element of the list and eliminates half of the list based on the comparison.

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Constant Algorithm - O(1)

An algorithm with a constant running time, meaning it takes the same amount of time to execute regardless of the input size.

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Logarithmic Algorithm - O(log n)

An algorithm whose running time grows logarithmically with the input size. It's faster than linear algorithms but slower than constant algorithms.

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Linear Algorithm - O(n)

An algorithm with a running time that grows directly proportional to the input size. It's slower than logarithmic algorithms.

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Quadratic or Polynomial Algorithm - O(nc)

An algorithm with a running time that grows faster than linear algorithms. It's the slowest type we discussed.

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Sequential Search

A method for searching through a list of elements one by one until the desired element is found.

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T(n) - Number of Comparisons in Binary Search

The number of comparisons made by binary search to find an element in a sorted list of size n. It's logarithmic, meaning T(n) = O(log n).

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Study Notes

Computer Power

  • The capacity and capability of a computer system to perform tasks efficiently and effectively is referred to as computer power.
  • Moore's Law states that the number of transistors on a computer chip doubles approximately every 18 months.
  • Improvements in computer technology, such as multicore processors, result in faster, smaller, and more efficient computers.

Network Bandwidth

  • Network bandwidth measures the maximum amount of data transferrable through a network connection per given time period.
  • Data transfer rate is typically measured in bits per second (bps), kilobits per second (kbps), megabits per second (Mbps), or gigabits per second (Gbps).
  • Nielsen's Law describes how user bandwidth doubles approximately every two years.
  • 5G technology promises extremely high bandwidth (10 Gbps).

Connectivity Value

  • Perceived or actual benefits and advantages resulting from network connectivity are refered to as Connectivity value.
  • Metcalfe's Law states that the value of a network is proportional to the square of the number of users. A greater number of users generally increases the value of the network.

Algorithms

  • An algorithm is a set of step-by-step instructions that produces a desired result.
  • The Eratosthenes' sieve is an algorithm used to find all prime numbers up to a specified whole number.
  • Artificial neural networks are computing systems inspired by biological neural networks that constitute animal brains. Their goal is to "learn" to perform tasks through various examples, often without any explicit programming rules involved.

Big Data

  • Big data refers to exceptionally large, intricate, and varied datasets that are difficult to manage and analyze conventionally.
  • Data is structured according to a certain format, otherwise it can be unstructured or semi-structured, depending on the case.
  • The main characteristic features are described using the 3 V's model to assess the volume, velocity, and variety.
  • The characteristics include Volume, Variety, Velocity, and Value.

Fibonacci Sequence

  • The Fibonacci sequence is based on a series of numbers beginning with 0 and 1, in which each subsequent number is the sum of the two preceding ones.
  • Fibonacci sequence examples can be found in nature, art, and certain patterns.

Big Data - 3+n V's

  • Volume: size of data that is difficult to manage.
  • Variety: different types of data, structured, semi-structured, and/or unstructured.
  • Velocity: rate of data generation (how fast data is created).
  • Value: insights and potential advantages to be derived from this data.
  • Veracity: accuracy, authenticity, trustworthiness, and consistency of data.
  • Variability: data flows that can fluctuate and have periodic peaks.
  • Visualization: presenting data in a visual format suitable for our perception.

Algorithm Fibonacci 2

  • An algorithm for calculating Fibonacci numbers using a recursive approach.
  • It is less efficient than Algorithm Fibonacci 3, particularly when computing a large number of Fibonacci numbers.

Algorithm Fibonacci 3

  • An algorithm for calculating Fibonacci numbers using memoization (dynamic programming).
  • This approach results in significantly improved efficiency, compared to the recursive method.

Algorithm for Big O Notation

  • Analysis of how the running time of a program/algorithm scales with the input size.
  • Ignore lower order terms and constants.

Algorithm for K-means

  • An iterative algorithm used for clustering data points into k groups.
  • The algorithm will calculate the centroids and reassign the data points to the closest cluster until it converges.

Hashing

  • A technique to convert values of any length into small indices, used to quickly find entries in very large datasets.
  • Hash Tables use a hash function to map keys to array indices.
  • Separate chaining: storing values with same hash index in a linked list.
  • Open addressing: finding the next empty index if the hash index is already set.

Recommender Systems

  • A filter that selects items relevant to a user’s tastes.
  • Personalized recommender systems use user profiles and context to suggest items.
  • Collaborative filtering relies on the preferences of other users with similar tastes.
  • Content-based recommender systems suggest items with similar content.

Social Networks

  • A network representation of relationships among individuals or entities.
  • Measures such as diameter and clustering coefficients are used to evaluate the characteristics of a social network.

Introduction to Cybersecurity Attacks

  • Cybersecurity attacks include backdoors, denial of service (DoS) attacks, distributed denial-of-service (DDoS) attacks, and direct access attacks as well as eavesdropping, tampering, and social engineering attacks.
  • These attacks focus on gaining unauthorized access, stealing data, disrupting services, or causing damage to systems.

Cryptography

  • The process of converting readable data (plaintext) into an unreadable format (ciphertext) to keep the data safe and secure during transmission.
  • Symmetric cryptography uses one key for both encryption and decryption, while public-key cryptography uses two separate keys—one for encryption and one for decryption.

Digital Signatures

  • A unique message digest is produced for every message, this is then encrypted by the sender's private key.
  • The resulting encryption is the digital signature.
  • The receiver can use the sender's public key to decrypt the signature and recreate the message digest.
  • The message received can be verified if there is a match in the original message's digest in order to confirm the integrity.

Federated Learning

  • A collaborative machine learning approach that trains models on decentralized data.
  • Training occurs on multiple devices (Clients) without transferring raw data to a central server.
  • The central server only receives processed data (Updates).

Bitcoin and Blockchain

  • A decentralized cryptocurrency that uses blockchain technology for transactions.
  • Blocks containing transactions are linked together in a blockchain.
  • Processes such as “mining” are used to validate and confirm transactions.

Clustering

  • A technique used to group similar data points together into clusters.
  • Different methods (e.g. hierarchical clustering, K-means) are used to identify and build clusters.
  • Distance metrics are used to measure the similarity between data points.

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Description

This quiz covers Fibonacci algorithms, specifically accuracy and efficiency, as well as networking concepts like Moore's and Nielsen's Laws. Participants will answer questions on algorithm calculations, terms and their definitions, and the significance of network bandwidth. Test your knowledge on these critical topics in computer science and telecommunications.

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