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The ________ given by DFS allow us to determine whether the graph contains any cycles. CS502
Order
Time stamps Page 130
BFS traversing
Topological sort
e6ac3d19-c36b-4817-855d-57b85e421b68-image.png
8.1.5 DFS - Cycles
The time stamps given by DFS allow us to determine a number of things about a graph or digraph.
For example, we can determine whether the graph contains any cycles. We do this with the help of the following two lemmas. -
► Optimal
► Non-optimal
► Exponential
► Polynomial -
In graph theory and computer science, an adjacency list is a collection of unordered lists used to represent a finite graph. Each list describes the set of neighbors of a vertex in the graph. This is one of several commonly used representations of graphs for use in computer programs.
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Consider that a tourist wants to travel between Karachi and Hunza cities in minimum possible span. The road map available has marked distance between each pair of adjacent cities. The time available to the tourist has limited and he/she require to find the shortest possible route between Karachi and Hunza.
In the given scenario, the possible solution may be adopted from the following set of algorithms.
Bellman ford’s Algorithm Flyod Warshal’s Algorithm Dijkstra's Algorithm Breadth-first-search algorithmYou are required to select the possible and most reasonable algorithm for the given scenario. Support you answer with solid reasons.
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Assignment No. 03
SEMESTER Fall 2019
CS502- Fundamentals of Algorithms
Total Marks: 20Due Date: 15/01/2020
Instructions
Please read the following instructions carefully before solving & submitting assignment:
It should be clear that your assignment will not get any credit if:
• The assignment is submitted after due date.
• The submitted assignment does not open or file corrupt.
• The assignment is fully or partially copied from (other student or ditto copy from handouts or internet).
• Student ID is not mentioned in the assignment File or name of file is other than student ID.
• The assignment is not submitted in .doc or .docx format.
Uploading instructions
Your submission must include:• Assignment should be in .doc or .docx format.
• Save your assignment with your ID (e.g. bx180200786.doc).
Assignment submission through email is NOT acceptable
Objective
The objective of this assignment is
• To give basic knowledge and understanding of Graphs.
• To develop the understanding between adjacency list and adjacency matrix representations.Note:
Your answer must follow the below given specifications.
• Font style: “Times New Roman”
• Font color: “Black”
• Font size: “12”
• Bold for heading only.
• Font in Italic is not allowed at all.
• No formatting or bullets are allowed to use.
• Your answer should be precise and to the point, avoid irrelevant detail.Lectures Covered: This assignment covers Lecture # 28
Deadline
Your assignment must be uploaded/submitted at or before 15/01/2020.Assignment Statement:
Everywhere we see objects and some sort of interaction between them. If we are needed to model this connection or relationship between them, the graphs is a good way to model it.
A graph G = (V, E) consists of a finite set of vertices V (or nodes) and E, a binary relation on V called edges. E is a set of pairs from V. If a pair is ordered, we have a directed graph. For unordered pair, we have an undirected graph.
There are two ways of representing graphs: using an adjacency matrix and using an adjacency list.Question No 01: (Marks: 10)
Draw an undirected Graph for the following Adjacency list representation as given below,
e5754efc-b6bf-4975-8417-d71e6c4945d6-image.png
Question No 02: (Marks: 10)
Draw a directed graph for the following matrix format representation,
15a35cf7-f143-437f-897d-7c03d0cd4980-image.png=====================================Ended=======================================
For any query about the assignment, contact at [email protected]
GOOD LUCK
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Assignment No. 02
SEMESTER Fall 2019
CS502- Fundamentals of Algorithms
Total Marks: 20Due Date: 27/11/2019
Instructions
Please read the following instructions carefully before solving & submitting assignment:
It should be clear that your assignment will not get any credit if:
• The assignment is submitted after due date.
• The submitted assignment does not open or file corrupt.
• The assignment is full or partially copied from (other student or ditto copy from handouts or internet).
• Student ID is not mentioned in the assignment File or name of file is other than student ID.
• The assignment is not submitted in .doc or .docx format.
Uploading instructions
Your submission must include:• Assignment should be in .doc or .docx format.
• Save your assignment with your ID (e.g. bx180200786.doc).
Assignment submission through email is NOT acceptable
Objective
The objective of this assignment is
• To give basic knowledge and understanding of Algorithms.
• To be able to design sorting algorithms.
• To be able to understand and calculate the complexity of algorithms.Note:
Your answer must follow the below given specifications.
• Font style: “Times New Roman”
• Font color: “Black”
• Font size: “12”
• Bold for heading only.
• Font in Italic is not allowed at all.
• No formatting or bullets are allowed to use.
• Your answer should be precise and to the point, avoid irrelevant detail.Lectures Covered: This assignment covers Lecture # 09 - 14
Deadline
Your assignment must be uploaded/submitted at or before 27/11/2019.Assignment diagram:
0e4a496c-d936-4a99-ac0c-2e198ae8fc43-image.png
Consider the given diagram having an unsorted array and its sorting procedure through dry run. You are required to answer the following questions.Question No 01: (Marks: 5)
You are required to determine (write down the name) the algorithm being used while sorting the above given array.Question No 02: (Marks: 7)
You are required to design (write) the algorithm (Only Pseudo code) determined in Question 1.Question No 03: (Marks: 😎
You are required to calculate (Step by Step) the worst case time complexity T(n) of the algorithm designed in Question No. 02.=====================================Ended=======================================
For any query about the assignment, contact at [email protected]
GOOD LUCK
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Please share your current paper
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Assignment No. 01 SEMESTER Fall 2019
CS502- Fundamentals of Algorithms
Total Marks: 20Due Date: 13/11/2019
Instructions
Please read the following instructions carefully before solving & submitting assignment:
It should be clear that your assignment will not get any credit if:
• The assignment is submitted after due date.
• The submitted assignment does not open or file corrupt.
• The assignment is full or partially copied from (other student or ditto copy from handouts or internet).
• Student ID is not mentioned in the assignment File or name of file is other than student ID.
• The assignment is not submitted in .doc or .docx format.
Uploading instructions
Your submission must include:• Assignment should be in .doc or .docx format.
• Save your assignment with your ID (e.g. bx180200786.doc).
Assignment submission through email is NOT acceptable
Objective
The objective of this assignment is
• To give basic knowledge and understanding of Algorithms.
• To be able to design simple algorithms.
• To be able to understand and calculate the complexity of algorithms.Note:
Your answer must follow the below given specifications.
• Font style: “Times New Roman”
• Font color: “Black”
• Font size: “12”
• Bold for heading only.
• Font in Italic is not allowed at all.
• No formatting or bullets are allowed to use.
• Your answer should be precise and to the point, avoid irrelevant detail.Lectures Covered: This assignment covers Lecture # 01 - 06
Deadline
Your assignment must be uploaded/submitted at or before 13/11/2019.Assignment Statement:
In mathematics Prime is a number which can be only divisible by 1 and itself. Examples of prime numbers are, 1 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 , 29 , 31 etc. When these numbers get large, then it is very difficult to manually identify them as to be prime or not prime. For example the numbers like, 443 and 44371 cannot easily identify as Prime.
There may be many algorithms which can be written for the identification of a number to be prime or not prime.Question No 01: (Marks: 10)
You are required to design (write) a simple algorithm (Only Pseudo code) which can identify a number to be Prime or Not Prime.Question No 02: (Marks: 10)
You are required to calculate (Step by Step) the worst case time complexity T(n) of the algorithm designed in Question No. 01.=====================================Ended=======================================
For any query about the assignment, contact at [email protected]
GOOD LUCK
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Opening Dec 11, 2019
Closing Dec 12, 2019
SOLVED CS502 Assignment No. 01 Solution and Discussion
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@zareen said in CS502 Assignment No. 01 Solution and Discussion:
Question No 02: (Marks: 10)
You are required to calculate (Step by Step) the worst case time complexity T(n) of the algorithm designed in Question No. 01.Solution:
Question No. 02: The step by stem analysis of the algorithm designed in question 1 is as follow,The time taken by each statement (step) is given as follows,
Step 1: C1 // Execute only 1 time or Constant Time or O (1)
Step 2: C2 // Execute only 1 time or Constant Time or O (1)
Step 3: n -2 // Execute n -2 times
Step 4: n -2 // Execute n -2 times
Step 5: n – 2 // Execute n -2 times
Step 6: C3 // Execute only 1 time or Constant Time or O (1)
Step 7: C4 // Execute only 1 time or Constant Time or O (1)
Step 8: C5 // Execute only 1 time or Constant Time or O (1)
Step 9: C6 // Execute only 1 time or Constant Time or O (1)Total time T(n) can be calculated as follows,
T(n) = C1 + C2 + (n -2 ) + (n -2 ) + (n -2 ) + C3 + C4 + C5 + C6
T(n) = C1 + C2 + n -2 + n -2 + n -2 + C3 + C4 + C5 + C6
T(n) = C1 + C2 + n + n + n - 6 + C3 + C4 + C5 + C6
T(n) = 3n + C1 + C2 + C3 + C4 + C5 + C6 -6
T(n) = 3n + (C1 + C2 + C3 + C4 + C5 + C6 -6)
T(n) = 3n + C7 // C7 = (C1 + C2 + C3 + C4 + C5 + C6 -6)
T(n) = n // Ignoring constant termsOr T(n) = O (n )
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@zareen said in CS502 Assignment No. 01 Solution and Discussion:
Question No 01: (Marks: 10)
You are required to design (write) a simple algorithm (Only Pseudo code) which can identify a number to be Prime or Not Prime.Solution:
Question No. 01: The algorithm for the identification of Prime number is as follows,1 PRIME (int Number)
2 int Count ← 0
3 for i ← 2 to Number – 1
4 if ( Number % i equal to 0)
5 Increment Count
6 If (Count is equal to 0)
7 Number is Prime
8 else
9 Number is NOT Prime -
Question No. 02: The step by stem analysis of the algorithm designed in question 1 is as follow,
The time taken by each statement (step) is given as follows,
Step 1: C1 // Execute only 1 time or Constant Time or O (1)
Step 2: C2 // Execute only 1 time or Constant Time or O (1)
Step 3: n -2 // Execute n -2 times
Step 4: n -2 // Execute n -2 times
Step 5: n – 2 // Execute n -2 times
Step 6: C3 // Execute only 1 time or Constant Time or O (1)
Step 7: C4 // Execute only 1 time or Constant Time or O (1)
Step 8: C5 // Execute only 1 time or Constant Time or O (1)
Step 9: C6 // Execute only 1 time or Constant Time or O (1)Total time T(n) can be calculated as follows,
T(n) = C1 + C2 + (n -2 ) + (n -2 ) + (n -2 ) + C3 + C4 + C5 + C6
T(n) = C1 + C2 + n -2 + n -2 + n -2 + C3 + C4 + C5 + C6
T(n) = C1 + C2 + n + n + n - 6 + C3 + C4 + C5 + C6
T(n) = 3n + C1 + C2 + C3 + C4 + C5 + C6 -6
T(n) = 3n + (C1 + C2 + C3 + C4 + C5 + C6 -6)
T(n) = 3n + C7 // C7 = (C1 + C2 + C3 + C4 + C5 + C6 -6)
T(n) = n // Ignoring constant termsOr T(n) = O (n )
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Solution:
Question No. 01: The algorithm for the identification of Prime number is as follows,1 PRIME (int Number)
2 int Count ← 0
3 for i ← 2 to Number – 1
4 if ( Number % i equal to 0)
5 Increment Count
6 If (Count is equal to 0)
7 Number is Prime
8 else
9 Number is NOT Prime -
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