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A number that has only 2, 3 or 5 as prime factors is called an ugly number. Some ugly numbers include: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, etc.
We have a number N, and the task is to find the Nth ugly number in the sequence of ugly numbers.
For example:
Input-1:
N = 5
Output:
5
Explanation:
The 5th ugly number in the sequence of ugly numbers [1, 2, 3, 4, 5, 6, 8, 10, 12, 15] is 5.
Input-2:
N = 7
Output:
8
Explanation:
In the ugly number sequence [1, 2, 3, 4, 5, 6, 8, 10, 12, 15], the seventh ugly number is 8.
A simple way to solve this problem is to check if the given number is divisible by 2, 3 or 5 and follow the sequence until the given number. Now find if the number satisfies the conditions for all ugly numbers and return that number as output.
Demo
public class UglyN { public static boolean isUglyNumber(int num) { boolean x = true; while (num != 1) { if (num % 5 == 0) { num /= 5; } else if (num % 3 == 0) { num /= 3; } // To check if number is divisible by 2 or not else if (num % 2 == 0) { num /= 2; } else { x = false; break; } } return x; } public static int nthUglyNumber(int n) { int i = 1; int count = 1; while (n > count) { i++; if (isUglyNumber(i)) { count++; } } return i; } public static void main(String[] args) { int number = 100; int no = nthUglyNumber(number); System.out.println("The Ugly no. at position " + number + " is " + no); } }
The Ugly no. at position 100 is 1536.
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