NPTEL Programming, Data Structures And Algorithms Using Python (Week 2 Programming Assignment) 2024

NPTEL Week 2 Programming Assignment Solutions

Problem 1: threesquares(m)

A positive integer m can be expressed as the sum of three squares if it is of the form p + q + r where p, q, r ≥ 0, and p, q, r are all perfect squares. Write a Python function threesquares(m) that takes an integer m as input and returns True if m can be expressed as the sum of three squares and False otherwise. (If m is not positive, your function should return False.)

Examples:

>>> threesquares(6)
True

>>> threesquares(188)
False

>>> threesquares(1000)
True
                

Problem 2: repfree(s)

Write a function repfree(s) that takes as input a string s and checks whether any character appears more than once. The function should return True if there are no repetitions and False otherwise.

Examples:

>>> repfree("zb%78")
True

>>> repfree("(7)(a")
False

>>> repfree("a)*(?")
True

>>> repfree("abracadabra")
False
                

Problem 3: hillvalley(l)

A list of numbers is said to be a hill if it consists of an ascending sequence followed by a descending sequence, where each of the sequences is of length at least two. Similarly, a list of numbers is said to be a valley if it consists of a descending sequence followed by an ascending sequence. You can assume that consecutive numbers in the input sequence are always different from each other. Write a Python function hillvalley(l) that takes a list l of integers and returns True if it is a hill or a valley, and False otherwise.

Examples:

>>> hillvalley([1,2,3,5,4])
True

>>> hillvalley([1,2,3,4,5])
False

>>> hillvalley([5,4,1,2,3])
True

>>> hillvalley([5,4,3,2,1])
False
                

Programming Assignment Solutions

Python

def threesquares(n):
    while n > 0 and n % 4 == 0:
        n =n// 4
    return(n % 8 != 7)

def repfree(s):
    return(len(set(s))==len(s))
  
  
def hillvalley(l):
    dect = False
    inc = False
    c = 0
    for i in range(len(l)-1):
        if c > 1:
            return False
        right = l[i+1]
        middle = l[i]
        diff = right - middle
        if diff > 0:
            if dect:
                c += 1
            inc = True
            dect = False
        elif diff < 0:
            if inc:
                c += 1
            dect = True
            inc = False
    if c == 1:
        return True
    return False  
import ast

def tolist(inp):
  inp = "["+inp+"]"
  inp = ast.literal_eval(inp)
  return (inp[0],inp[1])

def parse(inp):
  inp = ast.literal_eval(inp)
  return (inp)

fncall = input()
lparen = fncall.find("(")
rparen = fncall.rfind(")")
fname = fncall[:lparen]
farg = fncall[lparen+1:rparen]

if fname == "threesquares":
   arg = parse(farg)
   print(threesquares(arg))
elif fname == "repfree":
   arg = parse(farg)
   print(repfree(arg))
elif fname == "hillvalley":
   arg = parse(farg)
   print(hillvalley(arg))
else:
   print("Function", fname, "unknown")