Q1. Find the nature and roots of the quadratic equation.

Algorithm :-
1. Start
2. Input values of the variables a, b and c.
3. Calculate the discriminant D = b2 – 4ac
4. To determine the nature :
 If D>0D > 0D>0: The equation has two distinct real roots.
 If D=0D = 0D=0: The equation has one real and repeated root.
 If D<0D < 0D<0: The equation has two complex conjugate roots.

5. To calculate the roots : x = (-b+math.sqrt(D))/(2*a)

, (-b-math.sqrt(D))/(2*a)
6. Obtain the output.
7. Stop.

Psuedocode-
START
INPUT a, b, c
COMPUTE D = b² - 4ac
IF D > 0 THEN
PRINT "Roots are real and distinct"
COMPUTE r1 = (-b + sqrt(D)) / (2a)
COMPUTE r2 = (-b - sqrt(D)) / (2a)
PRINT r1, r2
ELSE IF D = 0 THEN
PRINT "Roots are real and equal"
COMPUTE root = -b / (2a)
PRINT root
ELSE
PRINT "Roots are complex"
COMPUTE real_part = -b / (2a)
COMPUTE imaginary_part = sqrt(-D) / (2a)
PRINT real_part, imaginary_part
STOP

Q2. To find sum of n numbers.

Algorithm :-
 1. Start
2. Take input n.
3. Create a list l and a variable s.
4. Create a for loop to get input of all numbers in the list.
for i in range(n):
a=int(input())
l.append(a)
5. Create another for loop to add all the numbers.
for i in range(n):
s=s+l[i]
6. Display sum.
7. Stop.

Psuedocode-

BEGIN
INPUT n
INITIALIZE list l as empty
INITIALIZE s = 0

FOR i = 1 TO n DO
INPUT a
APPEND a TO l
ENDFOR

FOR i = 1 TO n DO
s = s + l[i]
ENDFOR

PRINT s
END

Q3. To reverse a string.

Algorithm :-
1. Start.
2. Input a string and name it str.
3. Store the length of the string in a variable str_len.
4. Take another variable n and its value at -1.
5. Create a for loop from 0 to str_len.
6. Use str and n to store the value in the reversed form in a new variable.
7. Display the reversed string.
8. Stop.
 Psuedocode-
BEGIN
INPUT str
str_len = LENGTH(str)
n = -1
reversed_str = ""

FOR i = 0 TO str_len - 1 DO
reversed_str = reversed_str + str[n]
n=n-1
ENDFOR

PRINT reversed_str
END

Q4. To Find palindrome number

Answer:-

1. Start.
2. Take an input as a.
3. Create a for loop to reverse the integer with the body:
a = n%10
n=n//10
s=s*10+a
4. Check if the integer n matches the reversed integer.
5. Display result.
6. Stop.

Psuedocode

BEGIN
INPUT n
original_n = n
s=0

WHILE n > 0 DO
a = n % 10
n = n // 10
s = s * 10 + a
ENDWHILE

IF original_n = s THEN
PRINT "Palindrome"
 ELSE
PRINT "Not a Palindrome"
ENDIF
END

Q5 To Find Leap Year or not

1. Start.
2. Take an input integer as n.
3. Check if the number is divisible by 4.
4. If so, check if the number is divisible by 100.
5. If yes, check if the number is divisible by 400.
6. Display leap year if the number is divisible by 4, 100 and 400.
7. Display not a leap year if the number is not divisible by 4 or if divisible by 4 and
100 but not by 400.
8. Stop.

Psuedocode
BEGIN
INPUT n

IF n MOD 4 = 0 THEN
IF n MOD 100 = 0 THEN
IF n MOD 400 = 0 THEN
PRINT "Leap Year"
ELSE
PRINT "Not a Leap Year"
ENDIF
ELSE
PRINT "Leap Year"
ENDIF
ELSE
PRINT "Not a Leap Year"
ENDIF

END

Q6. To Swap Two Numbers with temporary variable

Algorithm.
1. Start.
2. Take two numbers as inputs a and b.
3. Now enter the algorithm:
c=a
 a=b
b=c
4. Display the reversed numbers.
5. Stop.

Psuedocode

BEGIN
INPUT a, b

c=a
a=b
b=c

PRINT a, b
END

Q7. To Count vowels in a string

Answer:

1. Start.
2. Take an input string as str.
3. Declare integer variable i=0.
4. Use a for loop to check for each index if there is a, e, i, o or u.
5. If there is , i = i+1.
6. Display i.
7. Stop.

Pseudocode-
BEGIN
INPUT str
i=0
vowels = "aeiouAEIOU"

FOR each character IN str DO

IF character IN vowels THEN
i=i+1
ENDIF
ENDFOR

PRINT i
END
Q8. To Find the Anagrams of the given string
1. Start.
2. Input the string (s).
3. Generate all possible permutations of the characters in str.
4. Store each permutation in a list or set.
5. Output all unique anagrams.
6. End.

Psuedocode-

BEGIN

INPUT s

SET anagrams = EMPTY SET

FUNCTION PERMUTE(current, remaining):

IF LENGTH(remaining) = 0 THEN

ADD current TO anagrams

ELSE

FOR i = 0 TO LENGTH(remaining) - 1 DO

NEW_CURRENT = current + remaining[i]

NEW_REMAINING = remaining WITHOUT remaining[i]

CALL PERMUTE(NEW_CURRENT, NEW_REMAINING)

ENDFOR

ENDIF

END FUNCTION
 CALL PERMUTE("", s)

PRINT anagrams

END

Q9 Decimal to binary conversion

1. Start.
2. Take an input of decimal integer as n.
3. Use the command;
m= bin(n)
4. Display m.
5. Stop.

Psuedocode-

BEGIN

INPUT n

m = CONVERT n TO BINARY

PRINT m

END

Bubble sort

1. Start.
2. Ask for input for the number of elements to be entered.
3. Enter all the elements in a list a.
4. Create the first for loop with the range x.
5. Create another nested loop with range x – i – 1.
 6. Use the following commands:
if(a[j]>a[j+1]):
a[j]=a[j]+a[j+1]
a[j+1]=a[j]-a[j+1]
a[j]=a[j]-a[j+1].
7. Close both the active loops.
8. Display a.
9. Stop.

Psuedocode-

BEGIN
INPUT x // Number of elements
CREATE list a

FOR i = 0 TO x - 1 DO
INPUT a[i] // Enter elements
ENDFOR

FOR i = 0 TO x - 1 DO
FOR j = 0 TO x - i - 2 DO
IF a[j] > a[j+1] THEN
a[j] = a[j] + a[j+1]
a[j+1] = a[j] - a[j+1]
a[j] = a[j] - a[j+1]
ENDIF
ENDFOR
ENDFOR

PRINT a // Sorted list

END