Hub 102 - Lesson 5 - Algorithm: Sorting & Searching
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This document discusses algorithms for sorting and searching. It introduces algorithm analysis and why it is important to analyze algorithms to compare different solutions, predict performance, and set parameter values. It discusses analyzing running time by counting primitive operations as a function of input size. Common growth rates like linear, quadratic, and cubic functions are introduced. Big-O notation is explained as a way to classify algorithms by their worst-case running time. Several specific sorting algorithms are described, including bubble sort, insertion sort, merge sort, and quicksort. Their pseudocode and running times are analyzed. Graph traversal algorithms like depth-first search and breadth-first search are also introduced.
![Pseudocode Details
• Control flow
- if … then … [else …]
- while … do …
- repeat … until …
- for … do …
- Indentation replaces braces
• Method declaration
- Algorithm method (arg [, arg…])
Input …
Output …
• Method call
var.method (arg [, arg…])
• Return value
return expression
• Expressions](https://image.slidesharecdn.com/lesson5-150712020950-lva1-app6891/85/Hub-102-Lesson-5-Algorithm-Sorting-Searching-5-320.jpg)
Hub 102 - Lesson 5 - Algorithm: Sorting & Searching
- 1. Lesson 5 Algorithm: Sorting and Searching
- 2. Algorithm Analysis • Motivation • What to do with algorithms? • Programmer needs to develop a working solution • Client wants problem solved efficiently • Theoretician wants to understand • Why analyze algorithms? • To compare different algorithms for the same task • To predict performance in a new environment • To set values of algorithm parameters
- 3. Running Time • We are interested in the design of "good" data structures and algorithms. • Measure of "goodness": - Running time (most important) - Space usage • The running time of an algorithm typically grows with the input size, and is affected by other factors: - Hardware environments: processor, memory, disk. - Software environments: OS, compiler. • Focus: input size vs. running time.
- 4. Pseudocode • High-level description of an algorithm • More structured than English prose • Less detailed than a program source code • Preferred notation for describing algorithms • Hides program design issues
- 5. Pseudocode Details • Control flow - if … then … [else …] - while … do … - repeat … until … - for … do … - Indentation replaces braces • Method declaration - Algorithm method (arg [, arg…]) Input … Output … • Method call var.method (arg [, arg…]) • Return value return expression • Expressions
- 6. Counting Primitive Operations By inspecting the pseudocode, we can determine the maximum number of primitive operations executed by an algorithm, as a function of the input size
- 7. Growth Rates • Growth rates of functions: • Linear n≈ • Quadratic n≈ 2 • Cubic n≈ 3
- 8. Big-Oh Notation • Given functions f(n) and g(n), we say that f(n) is O(g(n)) if there are positive constants c and n0 such that f(n) ≤ cg(n) for n ≥ n0
- 9. Big-Oh Notation Example • Example: 2n + 10 is O(n) • 2n + 10 ≤ cn • (c − 2) n 10≥ • n 10/(≥ c − 2) • Pick c = 3 and n0 = 10
- 10. Big-Oh Notation Example • Example: the function n2 is not O(n) • n2 ≤ cn • n ≤ c • The above inequality cannot be satisfied since c must be a constant
- 13. Sort Algorithm • Bubble Sort • Insertion Sort • Merge Sort • Quick Sort
- 14. Bubble Sort 1. Compare each pair of adjacent elements from the beginning of an array and, if they are in reversed order, swap them 2. If at least one swap has been done, repeat step 1.
- 17. Bubble Sort performance • Worst-case & average-case: O(n2 ) • Best-case: (over an already-sorted list) :O(n)
- 19. Insertion Sort
- 22. Insertion Sort performance • Worst-case & average-case: O(n2 ) • Best-case: (over an already-sorted list) :O(n)
- 25. Merge Sort
- 38. Quick-Sort
- 48. HW 1. Perform the mergesort algorithm with the input sequence: 30, 40, 24, 58, 48, 26, 11, 13. Use a diagram to illustrate the sorting process. 2. Repeat above question but using quicksort instead. 3. Repeat above question but using bubble sort instead. 4. Repeat above question but using insertion sort instead.
- 49. Graph
- 51. Graph Traversal • Depth First Search • Breath First Search
- 53. DFS Example
- 54. DFS Example
- 55. DFS Algorithm
- 57. BFS Example
- 58. BFS Example
- 59. BFS Example
- 60. BFS Algorithm