Design and Analysis of Algorithms - Sohail Aslam January 2004
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Questions and Answers

What is the origin of the word 'Algorithm'?

  • Created by a group of computer scientists in the 20th century
  • Derives from the Arabic word 'al-Khwarizmi' (correct)
  • Derived from the name of a famous mathematician
  • Adapted from an ancient Greek term

    • Which section discusses the 'Merge Sort' algorithm?

  • Sorting
  • Linear Time Sorting
  • Divide and Conquer Strategy (correct)
  • Dynamic Programming

    • What is an example of a 'Slow Sorting Algorithm' discussed in the text?

  • Heap Sort (correct)
  • Radix Sort
  • Bucket or Bin Sort
  • Counting Sort

    • Which algorithm uses the 'Sieve Technique'?

    <p>Selection Problem</p> Signup and view all the answers

    Which section discusses the 'Edit Distance' algorithm?

    <p>Dynamic Programming</p> Signup and view all the answers

    What is the time complexity of 'Heapsort' algorithm?

    <p>$O(n ext{ log } n)$</p> Signup and view all the answers

    'Counting Sort', 'Bucket or Bin Sort', and 'Radix Sort' all belong to which category of sorting algorithms?

    <p>Linear Time Sorting</p> Signup and view all the answers

    Which problem is solved using the '0/1 Knapsack Problem: Dynamic Programming Approach'?

    <p>'Selection Problem'</p> Signup and view all the answers

    'Divide and Conquer Strategy' is used in which sorting algorithm?

    <p>'Quicksort'</p> Signup and view all the answers

    'Edit Distance Algorithm' uses which approach for solving problems?

    <p>Dynamic Programming Approach</p> Signup and view all the answers

    What does the term $O(n!)$ represent in relation to sorting algorithms?

    <p>Worst-case time complexity</p> Signup and view all the answers

    What is a characteristic of 'In-place, Stable Sorting' algorithms?

    <p>They may change the relative order of elements with equal keys</p> Signup and view all the answers

    Study Notes

    The Origin of 'Algorithm'

    • The word "algorithm" originates from the name of the 9th-century Persian mathematician, Muhammad ibn Musa al-Khwarizmi.

    Merge Sort Algorithm

    • Discussion of the Merge Sort algorithm occurs in the section dedicated to "Divide and Conquer Strategies in Sorting."

    Slow Sorting Algorithm

    • Bubble Sort is an example of a slow sorting algorithm discussed in the text.

    Sieve Technique

    • The Sieve of Eratosthenes algorithm uses the "Sieve Technique" to determine prime numbers.

    Edit Distance Algorithm

    • The "Edit Distance Algorithm" is explored in the section dedicated to "Dynamic Programming Techniques."

    Heapsort Algorithm

    • The time complexity of the Heapsort algorithm is $O(n\log n)$.

    Sorting Algorithms

    • Counting Sort, Bucket or Bin Sort, and Radix Sort all belong to the category of Non-Comparison-based Sorting Algorithms.

    0/1 Knapsack Problem

    • The "0/1 Knapsack Problem: Dynamic Programming Approach" is a method used to solve the classic knapsack problem, where the objective involves maximizing the total value of items that can fit in a knapsack with a limited weight capacity.

    Divide and Conquer Strategy

    • Merge Sort, Quick Sort, and Binary Search are sorting algorithms that utilize the "Divide and Conquer Strategy."

    Edit Distance Algorithm Approach

    • The Edit Distance Algorithm employs the "Dynamic Programming Approach" to solve problems.

    O(n!)

    • $O(n!)$ represents the worst-case time complexity for sorting algorithms, particularly those using brute force approaches. This means that as the input size 'n' increases, the time required to sort the data grows incredibly fast, exhibiting factorial growth.

    In-place, Stable Sorting

    • Algorithms categorized as "In-place, Stable Sorting" have the following characteristics:
      • In-place: they modify the input array directly without requiring extra memory.
      • Stable: they preserve the relative order of equal elements after sorting.

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    Test your knowledge of the contents of the 'Design and Analysis of Algorithms' by Sohail Aslam from January 2004, including topics like the origin of the word 'algorithm', informal definitions, programming, implementation issues, analyzing algorithms, and model of computation.

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