Project Euler #73: Counting fractions in a range
Question
Answer : 7295372
Hacker Rank Problem
Solution
Consider the fraction, n/d, where n and d are positive integers. If n<d and HCF(n,d)=1, it is called a reduced proper fraction.
If we list the set of reduced proper fractions for d ≤ 8 in ascending order of size, we get:
How many fractions lie between 1/3 and 1/2 in the sorted set of reduced proper fractions for d ≤ 12,000?
If we list the set of reduced proper fractions for d ≤ 8 in ascending order of size, we get:
1/8, 1/7, 1/6, 1/5, 1/4, 2/7, 1/3, 3/8, 2/5, 3/7, 1/2, 4/7, 3/5, 5/8, 2/3, 5/7, 3/4, 4/5, 5/6, 6/7, 7/8
It can be seen that there are 3 fractions between 1/3 and 1/2.How many fractions lie between 1/3 and 1/2 in the sorted set of reduced proper fractions for d ≤ 12,000?
Answer : 7295372
Hacker Rank Problem
Solution
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 | import java.util.Scanner; public class Solution { private static int A; private static long rank(int n, long d) { long[] data = new long[A + 1]; for(int i = 0; i < data.length; i++) { data[i] = i * n / d; } for(int i = 1; i < data.length; i++) { for(int j = 2 * i; j < data.length; j+= i) { data[j] -= data[i]; } } long sum = 0; for(long x : data) { sum += x; } return sum; } public static void main(String[] args) { try(Scanner sc = new Scanner(System.in)) { long D = sc.nextInt(); A = sc.nextInt(); long fromD = D + 1; System.out.println(rank(1, D) - rank(1, fromD) - 1); } } } |
Comments
Post a Comment