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
- 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 5445Input: 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:
// 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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