Prime Time Problem (TCS Codevita)

July 15, 2021

Prime Time Problem

Prime Time Problem is a simple coding problem which was asked in one of the sample problem of TCS CodeVita coding competition. TCS organizes this global level coding competition in order to promote Programming-As-a-Sport and in the search of world’s best Coder. This is the solution for the Codevita Question, Prime Time Problem.

Problem Description

Here on earth, our 24-hour day is composed of two parts, each of 12hours. Each hour in each part has a corresponding hour in the other partseparated by 12 hours: the hour essentially measures the duration sincethe start of the day part. For example, 1 hour in the first part of the day is equivalent to 13, which is 1 hour into the second part of the day.Now, consider the equivalent hours that are both prime numbers.

We have 3 such instances for a 24-hour 2-part day:

5~17
7~19
11~23

Accept two natural numbers D, P >1 corresponding respectively to numberof hours per day and number of parts in a day separated by a space. D should be divisible by P, meaning that the number of hours per part (D/P) should be a natural number. Calculate the number of instances of equivalent prime hours. Output zero if there is no such instance.

Note – That we require each equivalent hour in each part in a day to be a prime number.

Example:

Input:

24 2

Output:

3 (We have 3 instances of equivalent prime hours: 5~17, 7~19 and 11~23.)

Constraints:

10 <= D < 500
2 <= P < 50

Input:

Single line consists of two space separated integers, D and P corresponding to number of hours per day and number of parts in a day respectively.

Output:

Output must be a single number, corresponding to the number of instances of equivalent prime number, as described above

Time Limit:

Examples

Example 1

Input

36 3

Output

Explanation

In the given test case D = 36 and P = 3

Duration of each day part = 12

2~14~X

3~15~X

5~17~29 – instance of equivalent prime hours

7~19~31 – instance of equivalent prime hours

11~23~X

Hence the answers is 2.

Example 2

Input

49 7

Output

Explanation

Duration of each day part = 7

2~9~X~23~X~37~X

3~X~17~X~31~X~X

5~X~19~X~X~X~47

7~X~X~X~X~X~X

Hence there are no equivalent prime hours.

Solution for Prime Time Problem

Python

Python (Optimized)

Python

#  To check prime you do not need run the loop till N, rather SQRT(N)
import math
def prime(n):
    if n == 1:
        return False
    for i in range(2, int(math.sqrt(n) + 1)):
        if n % i == 0:
            return False

    return True


d, p = map(int, (input().split()))
n = int(d / p)
count = 0
# as 0, 1 not prime so starting from 2
for i in range(2, n):
    prime_time = True
    for j in range(p):
        num = i + j*n
        if not prime(num):
            prime_time = False
            break

    if prime_time:
        count += 1

print(count)

Python (Optimized)

import math
n = 505
prime_list = [True for i in range(n + 1)]
pr = 2
# Sieve of Eratosthenes
while pr * pr <= n:
    if prime_list[pr] == True:
        for i in range(pr * 2, n + 1, pr):
            prime_list[i] = False
    pr += 1
prime_list[0] = False
prime_list[1] = False

d, p = map(int, (input().split()))
n = int(d / p)
count = 0
# as 0, 1 not prime so starting from 2
for i in range(2, n):
    prime_time = True
    for j in range(p):
        num = i + j * n
        if not prime_list[num]:
            prime_time = False
            break

    if prime_time:
        count += 1

print(count)