701749. Nth number made of prime digits
Here is the Markdown blog post for the problem "Nth number made of prime digits":
Nth Number Made of Prime Digits
Summary
Given a positive integer n, find the n-th number that can be formed using only prime digits. The numbers are 0-indexed, and the first number is considered to have one digit.
This problem involves mathematical concepts, specifically prime numbers and their manipulation in strings.
Detailed Explanation
To solve this problem, we need to generate all possible combinations of prime digits (2, 3, 5, 7) and count them. We can do this by iterating over the prime digits and appending them to a string. We then increment our counter for each number generated.
Here's a step-by-step breakdown of the solution:
- Initialize a counter
countto 0. - Iterate over all possible combinations of prime digits (2, 3, 5, 7) and append them to a string.
- For each combination, increment the counter
count. - When the counter reaches
n, return the current combination as then-th number.
The time complexity for this solution is O(4^n), where n is the number of digits in the prime number sequence. This is because we are generating all possible combinations of prime digits, which has a factorial time complexity. The space complexity is O(n), as we need to store the combination strings.
Optimized Solutions
Java
public class Main {
public static void main(String[] args) {
int n = 10; // Replace with your desired value of n
System.out.println(findNthNumber(n));
}
public static String findNthNumber(int n) {
StringBuilder sb = new StringBuilder();
int count = 0;
for (char c : "2357".toCharArray()) {
sb.append(c);
count++;
if (count == n) {
return sb.toString();
}
}
return "";
}
}