Design and Analysis of Algorithms - Sohail Aslam January 2004

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.

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.