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Assignment No. 01
SEMESTER Spring 2020

CS502- Fundamentals of Algorithms

Total Marks: 20

Due Date: 28/05/2020

Instructions

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.

·         Assignment should be in .doc or .docx format.

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:

·          Font style: “Times New Roman”

·          Font color: “Black”

·          Font size: “12”

·          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 - 08

Assignment Statement:

Palindrome is a number which does not change even if we reverse its digits. For example, 121, 1331, 16561 etc, while 122, 2354, 25486 etc are not palindromes.

There may be many algorithms which can be written for the identification of a number to be palindrome or not palindrome.

Question No  01:   (Marks:  10)

You are required to design (write) a simple algorithm (Only Pseudo code) which can identify a number to be Palindrome or Not Palindrome.

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 CS502@vu.edu.pk

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CS502_Assignment_No_01_Solution_Spring_2020

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CS502 Assignment 1 Solution SPring 2020

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CS502 Fundamentals of Algorithms Assignment 1 Solution & Dicussion Spring 2020

Solution Credit: @mc190203271

Question No 01:   (Marks:  10)

You are required to design (write) a simple algorithm (Only Pseudo code) which can identify a number to be Palindrome or Not Palindrome.

Solution:

int x;

reverse = 0:

while (x>0)

reverse = reverse + x % 10);

x / = 10;

if ( x = reverse )

then

number is palindrome

Else

number is not palindrome

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:

frequency

int n;                                                                           1

reverse = 0;                                                                 1

while (n>0)                                                                  n

reverse = reverse + n % 10;                                         n

n / = 10;                                                                      n

if ( n = reverse)                                                            1

then                                                                             1

number is palindrome                                                    1

else                                                                              1

number is not palindrome                                               1

so time complexity of above algorithm would be as follows:

T(n) = 1+1+n+n+n+1+1+1+1+1

T(n) = n + 9

From the above equation the highest degree is n so its complexity is linear. This is the worst case time complexity of the above algorithm is T(n).

How sum of T(n) = 1+1+n+n+n+1+1+1+1+1 can be  n + 9?

Cs502 Assignment 1 Solution

Cs502 Assignment 1 Solution

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Correct Solution For CS502 Assignment No.1 Spring 2020 uploaded by VU

Solution:

Question No. 01:  The algorithm for the identification of Palindrome number is as follows,

1. PALINDROME (num)
2. Define variables: orignum, reverse, remainder
3. orignum = num
4. while (num is not equal to 0)
5.     remainder = num % 10    //  % operator calculate remainder.
6.     reverse  = (reverse *10 ) + remainder
7.     num = num /10
8. if (reverse is equal to orignum)
9. print “ number is palindrome”
10. else
11. print “ number is not palindrome”

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:   C3                                      // Execute only 1 time or Constant Time or  O (1)

Step 4:   [log(num)/log(10)] +1        // Execute [log(num)/log(10)] +1 times

Step 5:   [log(num)/log(10)] +1        // Execute [log(num)/log(10)] +1 times

Step 6:   [log(num)/log(10)] +1        // Execute [log(num)/log(10)] +1 times

Step 7:   [log(num)/log(10)] +1        // Execute [log(num)/log(10)] +1 times

Step 8:    C4                                                  // Execute only 1 time or Constant Time or  O (1)

Step 9:    C5                                                          // Execute only 1 time or Constant Time or  O (1)

Step 10:  C6                                                          // Execute only 1 time or Constant Time or  O (1)

Step 11:  C7                                                  // Execute only 1 time or Constant Time or  O (1)

Total time T(n) can be calculated as follows,

T(n)    = C1 + C2 + C3 + [log(num)/log(10)] +1  +[log(num)/log(10)] +1 +[log(num)/log(10)]

1 + [log(num)/log(10)] +1  + C4 + C5 + C6 + C7

T(n)    = C1 + C2 + C3 + C4 + C5 + C6 + C7+ 4+ 4[log(num)/log(10)]

T(n)    = C8 + 4[log(num)/log(10)]         //  C8  = (C1 + C2   + C3 + C4 + C5 + C6 + C7 +4)

T(n)    =  log(num) / log(10)                  //   Ignoring constant terms

T(n)    =  log(n) / log(10)                                 //   If   num = n  ( or replace num with n)

Or      T(n)   =  O (log (n) / log (10)

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