Prime Time Again Problem Statement
You are given two integers DAY_HOURS
and PARTS
. Consider a day with DAY_HOURS
hours, which can be divided into PARTS
equal parts. Your task is to determine the total instances of equivalent prime groups, where a prime group is defined as a set of hour values that are prime and occur at the same position in different parts of the day.
Example:
Input:
DAY_HOURS = 20
PARTS = 2
Output:
2
Explanation:
If we divide the day into 2 parts, we have:
Part 1: 1 2 3 4 5 6 7 8 9 10
Part 2: 11 12 13 14 15 16 17 18 19 20
3-13
is a prime group, as both numbers are prime.7-17
is a prime group, as both numbers are prime.
There are 2 prime groups in total.
Constraints:
1 <= T <= 100
10 <= DAY_HOURS <= 5 * 10^3
2 <= PARTS <= 10^3
- Time Limit: 1 second
Input:
The first line of input contains an integerT
representing the number of test cases.
The first and only line of each test case contains two space-separated integersDAY_HOURS
andPARTS
.
Output:
Output a single integer for each test case, representing the number of equivalent prime groups.
Note:
- The day starts with hour 1 and ends with hour
DAY_HOURS
. - Each hour in a prime group must be in a different part of the day.
- If there is no prime group, return zero.
DAY_HOURS
should be divisible byPARTS
.
AnswerBot
1d
Calculate total instances of equivalent prime groups in a day divided into equal parts.
Divide the day into equal parts and check for prime groups at the same position in different parts.
Each prime gro...read more
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