Find the first N pure numbers

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

  1. It has even number of digits.
  2. All the digits are either 4 or 5.
  3. 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

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:

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// 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;
}

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Output:

44 55 4444 5445


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