The document provides information on various sorting and searching algorithms, including bubble sort, insertion sort, selection sort, quick sort, sequential search, and binary search. It includes pseudocode to demonstrate the algorithms and example implementations with sample input data. Key points covered include the time complexity of each algorithm (O(n^2) for bubble/insertion/selection sort, O(n log n) for quick sort, O(n) for sequential search, and O(log n) for binary search) and how they work at a high level.
Divide and Conquer Algorithms - D&C forms a distinct algorithm design technique in computer science, wherein a problem is solved by repeatedly invoking the algorithm on smaller occurrences of the same problem. Binary search, merge sort, Euclid's algorithm can all be formulated as examples of divide and conquer algorithms. Strassen's algorithm and Nearest Neighbor algorithm are two other examples.
Merge sort is a sorting technique based on divide and conquer technique. With worst-case time complexity being Ο(n log n), it is one of the most respected algorithms.
Merge sort first divides the array into equal halves and then combines them in a sorted manner.
In computer science, divide and conquer is an algorithm design paradigm based on multi-branched recursion. A divide-and-conquer algorithm works by recursively breaking down a problem into two or more sub-problems of the same or related type until these become simple enough to be solved directly.
Data Structures, which is also called as Abstract Data Types (ADT) provide powerful options for programmer. Here is a tutorial which talks about various ADTs - Linked Lists, Stacks, Queues and Sorting Algorithms
Divide and Conquer Algorithms - D&C forms a distinct algorithm design technique in computer science, wherein a problem is solved by repeatedly invoking the algorithm on smaller occurrences of the same problem. Binary search, merge sort, Euclid's algorithm can all be formulated as examples of divide and conquer algorithms. Strassen's algorithm and Nearest Neighbor algorithm are two other examples.
Merge sort is a sorting technique based on divide and conquer technique. With worst-case time complexity being Ο(n log n), it is one of the most respected algorithms.
Merge sort first divides the array into equal halves and then combines them in a sorted manner.
In computer science, divide and conquer is an algorithm design paradigm based on multi-branched recursion. A divide-and-conquer algorithm works by recursively breaking down a problem into two or more sub-problems of the same or related type until these become simple enough to be solved directly.
Data Structures, which is also called as Abstract Data Types (ADT) provide powerful options for programmer. Here is a tutorial which talks about various ADTs - Linked Lists, Stacks, Queues and Sorting Algorithms
while some elements unsorted:
Using linear search, find the location in the sorted portion where the 1st element of the unsorted portion should be inserted
while some elements unsorted:
Using linear search, find the location in the sorted portion where the 1st element of the unsorted portion should be inserted
while some elements unsorted:
Using linear search, find the location in the sorted portion where the 1st element of the unsorted portion should be inserted
while some elements unsorted:
Using linear search, find the location in the sorted portion where the 1st element of the unsorted portion should be inserted
while some elements unsorted:
Using linear search, find the location in the sorted portion where the 1st element of the unsorted portion should be inserted
while some elements unsorted:
Using linear search, find the location in the sorted portion where the 1st element of the unsorted portion should be inserted
while some elements unsorted:
Using linear search, find the location in the sorted portion where the 1st element of the unsorted portion should be inserted
while some elements unsorted:
Using linear search, find the location in the sorted portion where the 1st element of the unsorted portion should be inserted
while some elements unsorted:
Using linear search, find the location in the sorted portion where the 1st element of the unsorted portion should be inserted
while some elements unsorted:
Using linear search, find the location in the sorted portion where the 1st element of the unsorted portion should be inserted
while some elements unsorted:
Using linear search, find the location in the sorted portion where the 1st element of the unsorted portion should be inserted
while some elements unsorted:
Using linear search, find the location in the sorted portion where the 1st element of the unsorted portion should be inserted
while some elements unsorted:
Using linear search, find the location in the sorted portion where the 1st element of the unsorted portion should be inserted
while some elements unsorted:
Using linear search, find the location in the sorted portion where the 1st element of the unsorted portion should be inserted
while some elements unsorted:
Using linear search, find the location in the sorted portion where the 1st element of the unsorted portion should be inserted
while some elements unsorted:
Using linear search, find the location in the sorted portion where the 1st element of the unsorted portion should be inserted
while some elements unsorted:
Using linear search, find the location in the sorted portion where the 1st element of the unsorted portion should be inserted
while some elements unsorted:
Using linear search, find the location in the sorted portion where the 1st element of the unsorted portion should be inserted
while some elements unsorted:
Using linear search, find the location in the sorted portion where the 1st element of the unsorted portion
Decimal Long Double Double Double. Represents double-precision floating-point...Anwar Patel
Decimal
Long
Double
Double
Double. Represents double-precision floating-point numbers. It can store decimal values and provides a wider range than the Integer data type. Dim price As ...
The role of Software Quality Assurance (SQA) has transformed significantly in the context of modern software development life cycle, particularly with the rise of Agile and Scrum methodologies. SQA teams are now integrated into the development process from the beginning, working collaboratively with developers to identify and address quality issues. This agility is critical in ensuring high-quality software products that meet the needs of end-users.
DevOps practices have also played a significant role in the transformation of SQA. By integrating development and operations, DevOps enables SQA teams to work more closely with both teams and ensure that quality is maintained throughout the entire software development life cycle.
To ensure agility in SQA, teams can also implement test automation, continuous integration and delivery, and other DevOps practices. These strategies help to reduce the time and effort required to test software, while also improving accuracy and reliability.
In the future, emerging technologies such as artificial intelligence and machine learning will create new opportunities for innovation in SQA, and new challenges for SQA teams to overcome. However, by embracing agility and DevOps practices, SQA teams will be well-equipped to meet these challenges and continue to ensure the high-quality software products that users demand.
In summary, this presentation will cover the transformation of SQA in modern software development life cycle, with a particular focus on agility, Agile and Scrum methodologies, DevOps practices, and emerging technologies. Attendees will gain a clear understanding of the strategies and technologies that can be used to ensure high-quality software products in an increasingly fast-paced and complex development landscape.
Increasing the company's profitability and impact is the dream of every company. Nowadays Agility / Agile is the buzz word and the whole world want's it but most of the time companies are confused about how we can achieve the agility dream.
The written material provides a visible how, why and what of agility and what the best practices we need to execute to achieve agility.
Software Development Guide To Accelerate PerformanceZaid Shabbir
Scrum is the most widely used framework across all software and business industries. By following complete scrum framework you can improve the quality product deliver in more adaptive way.
Slides contents content guidelines related to scrum framework and how some one become a certified scrum master. Slides elaborate scrum framework by using user friendly diagrams and bulleted points. After grasping the slides any one can easily pass certified scrum examination.
I am sure you will enjoy the contents and its really helpful to become a certified scrum practitioner.
It covers the Agile software development and how effectively use testing technique in Agile environment.
Its helps to understand what is agility in software testing and the roll of whole team in agile software development.
Without automation software testing agility not completed, slides covers when we go for automation and when need aware.
Slides present data and information system. In any information system security and integrity is the prime concern. How we can make sure stored data is more secure and generated information should be accurate, reliable and consistent.
In Cloud computing we explain the basics of cloud and its model. It contain contents which distinguish between different types of clouds and its characteristics. With the help of presented point you will able to select your required cloud solution that can meet your company requirements.
3. Bubble Sort
● In bubble sort repeatedly move the largest
element to the highest index position of the array
and on each iteration to reduce the effective size
of the array.
● In Bubble sort we compare the adjacent item and
swap if required.
● In a bubble sorting algorithm, the elements of the
list "gradually 'bubble' (or rise) to their proper
location in the array, like bubbles rising in a glass
of soda"
4. Algorithm of Bubble Sort
● Declare array on n items
items[n]={4,5,1,8,54,32...32}
● Compare each pair of item and swap if required.
for(int pass=0; pass<n-1; pass ++)
for(int i=0; i<n-pass-1; i++)
If (item[ i ] > item [i+1]) {
tempvar = item[i]
Item[ i ] = item [i+1]
Item[ i+1]=tempvar
}
}
}
5. Bubble Sort
512354277 101
0 1 2 3 4 5
512354277 10142 77
512357742 10135 77
512773542 10112 77
577123542 101
77123542 5 101
Note: In phase 1 Largest element in the correct position
77 101
6. Bubble Sort
0 1 2 3 4 5
Note: In phase 2 Largest element place in the correct position
42 35 7712 5 101
42 12 77 5 10135
42 77 5 10135 12
77 5 10135 12 42
10135 12 42 5 77
10. Analysis of Bubble Sort
● Works best when array is already nearly sorted
● Worst case number of comparisons is O(n2)
– e.g. input array values are 10,9,8,7,6,5,4,3,2,1
– On each step comparison required 9+8+7+... +1
– (n-1)*n /2
– O(n2)
● Best case occurs when the array is already sorted and
its complexity is O (n)
– input is in order (1,2,3,4,5,6,7,8,9,10)
– the algorithm still goes over each element once and
checks if a swap is necessary.
11. Insertion Sort
● Sort the elements in range[0,m] form = 0,...,n−1
● No action need form=0
● When going from m to m+1, insert the element
in index m+1, to its appropriate location
12. Algorithm of Insertion Sort
● This algorithm sorts the array a with n elements.
Set a[n] ={ 2,7,5,8,43,23..99}
● for (int i = 1; i < n; i++) //Array start from 0
{
Item tmp = a[i];
for (int j=i; j>0 && tmp < a[j-1]; j--)
a[j] = a[j-1];
a[j] = tmp;
}
17. Selection Sort
● Find smallest element in the array and
exchange it with the element in the first
position.
● Find second smallest element and
exchange it with the element in the second
position
● Do this (n-1) times.
● Efficiency is O(n2)
18. Selection Sort Algorithm
● Declare array on n items
Set items[n] = { 2,7,5,8,43,23..99}
● Find the min item and and iteratively swap with
first item if required.
for (int i = 0; i < n-1; i++) {
int min = i;
for (int j = i+1; j < n; j++)
if (a[j] < a[min]) min = j;
swap(a[i], a[min]);
}
19. Selection Sort
512354277 101 Min=77
512354277 101
512354277 101
42 Min > 42
Min=42
Min > 35
Min=35
35
512354277 10112
512354277 101101
512354277 101 5
Min > 12
Min=12
Min < 101
Min (12)
Min > 5
Min=5
771235425 1015
Min > 5
Min=5
0 1 2 3 4 5
20. Selection Sort ...
771235425 1015 Min=4242
771235425 1015 35
Min > 35
Min=35
771235425 1015 12
Min > 12
Min=12
771235425 1015 101
Min < 101
Min (12)
771235425 1015 77
Min < 77
Min (12 )
774235425 1015 12
Min=12
0 1 2 3 4 5
21. Selection Sort ...
774235425 1015 12
Min=35
35
774235425 1015 12
Min < 42
Min (35 )
42
774235425 1015 12
Min < 101
Min (35 )
101
774235425 1015 12
Min < 77
Min (35 )
77
774235425 1015 12
Min = 42
4235
774235425 1015 12 10135
774235425 1015 12 7735
Min < 101
Min (42 )
Min < 77
Min (42 )
0 1 2 3 4 5
23. Quick Sort
● The main concept of this sort is divide and
conquer
● Pick an element, say P (the pivot) Re-
arrange the elements into 3 sub-blocks,
● Repeat the process recursively for the left-
and right- sub-blocks.
● those less than or equal to (≤) P (the left-
block S1) P (the only element in the
middle-block)
● those greater than or equal to (≥) P (the
right- block S2)
24. Quick Sort Algorithm
● Set pivot = a[left], l = left + 1, r = right;
● while l < r, do
– while l < right & a[l] < pivot , set l = l + 1
– while r > left & a[r] >= pivot , set r = r – 1
– if a[l] < a[r], swap a[l] and a[r]
● Set a[left] = a[r], a[r] = pivot
● Terminate
25. Quick Sort
65 70 75 80 85 60 55 50 45
Pass 1
P = 65
65 45 75 80 85 60 55 50 70
l r
65 45 50 80 85 60 55 75 70
l r
65 45 50 55 85 60 80 75 70
l r
65 45 50 55 60 85 80 75 70
r l
65 70 75 80 85 60 55 50 45
l r
Unsorted Numbers
45 < 70
swap
50 < 75
swap
55 < 80
swap
60 < 85
swap
l >= r break
Swap r
with P
60 45 50 55 65 85 80 75 70
On left hand side of P=65 all
items are smaller and on right
hand side all items are greater
26. Quick Sort
Pass 2a
P = 60
60 45 50 55 65 85 80 75 70 Pass 2b
P = 85
60 45 50 55 65 85 80 75 70
l r l r
l value < p
l++
l value < p
l++
60 45 50 55 65 85 80 75 70
l r l r
I value < p
l++
I value < p;
l++
l>=r break
Swap p with r
l>=r break
Swap p with r
r < p
60 45 50 55 65 85 80 75 70
lr lr
55 45 50 60 65 70 80 75 85
27. Quick Sort
Pass 3a
P = 55
Pass 3b
P = 70
l value < p
l++ r value >= p; r --
l>=r break
Swap p with r
l>=r break
Swap p with r
r < p
55 45 50 60 65 70 80 75 85
55 45 50 60 65 70 80 75 85
l r l r
55 45 50 60 65 70 80 75 85
l r l r
50 45 55 60 65 70 80 75 85
r l
50 45 55 60 65 70 80 75 85
r value >= p; r --
28. Quick Sort
Pass 4a
P = 50
Pass 4b
P = 80
l value < p
l++ l value < p; l ++
l>=r break
Swap p with r
l>=r break
Swap p with r
r < p
50 45 55 60 65 70 80 75 85
l r l r
50 45 55 60 65 70 80 75 85
r l r l
45 50 55 60 65 70 75 80 85
r l r i
45 50 55 60 65 70 75 80 85
Sorted
29. Sorting Complicity Table
Sorting Algorithm Worst Case Best Case Average Case
Bubble Sort O(n^2) O(n) O(n^2)
Insertion Sort O(n^2) O(n) O(n^2)
Selection Sort O(n^2) O(n^2) O(n^2)
Quick Sort O(n^2) O(n log(n)) O(n log(n))
31. Sequential Search
● Search key is compared with all elements
in the list,
● O(n) time consuming for large datasets
● Time can reduced if data is sorted.
32. Sequential Search Algorithm
● Declare array on n items
Set items[n] = { 2,7,5,8,43,23..99}
● Find a number into provided items array.
bool found = false;
for(int loc = 0; loc < n; loc++)
if(items[loc] == item) {
found = true;
break; }
if(found)
return loc;
else
return -1;
34. Binary Search
● Use divide and conquer technique to search item.
● Complexity of binary search is O(log n)
● Can only be performed on sorted list.
● Searching criteria:
– Search item is compared with middle element of list.
– If search item < middle element of list, search is
restricted to first half of the list.
– If search item > middle element of list, search second
half of the list.
– If search item = middle element, search is complete.
35. Binary Search Algorithm
● Declare array of n items
Set items[n] = { 2,7,5,8,43,23..99}
● Find a number into provided items
array.
● int first = 0; int mid; int last=n -1
● bool found = false;
● while(first <= last && !found) {
– mid = (first + last) / 2 ;
– if(items[mid] ==item)
found=true;
else
if(items[mid] > item)
last=mid-1;
else
first= mid+1;
}
if(found)
return mid;
else
return -1;