Find the first N pure numbers

Given an integer N, the task is to print first N^th pure numbers. A number is said to be pure if

It has even number of digits.
All the digits are either 4 or 5.
And the number is a palindrome.

First few pure numbers are 44, 55, 4444, 4554, 5445, 5555, …

Examples:

Input: N = 4
Output: 44 55 4444 5445

Input: N = 10
Output: 44 55 4444 4554 5445 5555 444444 454454 544445 554455

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach: The idea is similar to the approach discussed here. At each step of the queue we can generate the next number by adding 4 and 5 on both of the sides i.e. the ending and the beginning of the previous number:

q.push("4" + temp + "4");
q.push("5" + temp + "5");

Proceeding in this way we can take care of palindromes and even length numbers

Below is the implementation of the above approach:

// C++ implementation of the approach 
#include <bits/stdc++.h> 
using namespace std; 
  
// Function to print the first n pure numbers 
void nPureNumbers(int n) 
{ 
  
    queue<string> q; 
    vector<string> ans; 
  
    // Push the starting two elements 
    q.push("44"); 
    q.push("55"); 
    int total = 2; 
  
    // While generated numbers are less than n 
    while (ans.size() < n) { 
  
        string temp = q.front(); 
        q.pop(); 
        ans.push_back(temp); 
  
        q.push("4" + temp + "4"); 
        q.push("5" + temp + "5"); 
    } 
  
    // Sorting strings based on their value 
    sort(ans.begin(), ans.end(), [](auto s, auto s2) { 
        if (s.size() == s2.size()) 
            return s < s2; 
        else
            return s.size() < s2.size(); 
    }); 
  
    // Print first n pure numbers 
    for (auto i : ans) { 
        cout << i << " "; 
    } 
} 
  
// Driver code 
int main() 
{ 
    int n = 4; 
  
    nPureNumbers(n); 
  
    return 0; 
} 

Output:

44 55 4444 5445

My Personal Notes

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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