Programming, Data Structures And Algorithms Using Python - Assignment 1 | NPTEL | [Jan 2023]

Programming, Data Structures And Algorithms Using Python - Assignment 1 | NPTEL |Answer with Explanation

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What is the value of f(2343) for the function below?
def f(x):
d=0
y=1
while y <= x:
d=d+1
y=y*3
return(d)

Answer

8
y = 1 < 2343
=> d = 0 + 1 = 1
y = 1 * 3 = 3

3 < 2343
=> d = 1 + 1 = 2
y = 3 * 3 = 9

9 < 2343
=> d = 2 + 1 = 3
y = 9 * 3 = 27

27 < 2343
=> d = 3 + 1 = 4
=> y = 27 * 3 = 81

81 < 2343
=> d = 4 + 1 = 5
=> y = 81 * 3 = 243

243 < 2343
=> d = 5 + 1 = 6
=> y = 243 * 3 = 729

729 < 2343
=> d = 6 + 1 = 7
y = 729 * 3 = 2187

2187 < 2343
=> d = 7 + 1 = 8
y = 2187 * 3 = 6561

6561 > 2343
Hence d = 8
f(2343) Returns 8 value of f(2343) = 8

What is h(53)-h(52), given the definition of h below?
def h(n):
s = 0
for i in range(1,n+1):
if n%i > 0:
s = s+1
return(s)

Answer

5

For what integer value n would g(92,n) return 13?
def g(m,n):
res = 0
while m >= n:
res = res+1
m = m-n
return(res)

Answer

7

Consider the following function mys:
def mys(m):
if m == 1:
return(1)
else:
return(m*mys(m-1))
Which of the following is correct, assuming we always pass an integer argument to mys?

a. The function always terminates with mys(n) = factorial of n
b. The function always terminates with mys(n) = 1+2+...+n
c. The function terminates for non-negative n with mys(n) = factorial of n
d. The function terminates for positive n with mys(n) = factorial of n

Answer

d. The function terminates for positive n with mys(n) = factorial of n
The correct statement is "The function terminates for positive n with mys(n) = factorial of n" This is because the function uses recursion to calculate the factorial of the input number. The recursion stops when the input number reaches 1, and then it starts returning the calculated factorial. If the input number is 0 or negative, it will not terminate as the recursion never stops.

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