Last Updated: 2 Dec, 2020

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Problem statement

Ninja is good at numbers. So today his friend gave him a task that required him to find out numbers made of 2 and 5 only less than a given limit.

Given an integer N, you need to print all numbers less than N which are having digits only 2 or 5 or both.

For example :

All numbers less than 30 with digits 2 and 5 are 2, 5, 22, 25.

Input format :

The first line contains a single integer ‘T’ denoting the number of test cases to be run. Then the test cases follow.

The first line of each test case contains an integer N representing the number in the problem statement.

Output format :

For each test case, print all the numbers less than N consisting of digits 2 and 5 only in a space-separated format. The numbers should be printed in ascending order.

Output for each test case will be printed in a separate line.

Constraints :

1 <= T <= 10
1 <= N <= 10^16

Time Limit: 1 sec

Note :

You are not required to print anything; it has already been taken care of. Just implement the function.

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Approaches

01 Approach

We can consider a number with digits 2 and 5 as a binary string where 0 represents a 2 in the number and 1 represents the 5. This way our total numbers consisting of 2 and 5 are limited by 2^(D + 1) where D is the total number of digits in the input number N.

So we define a recursive function that takes a current number of length D and either appends a 2 or 5 to the end of this number.

Algorithm:

print(num, result) function takes the current number num and the result array ‘result’ and appends the numbers satisfying the above criteria to the result array.

If the number becomes greater than N we return as a base case.
we append the number to the current list.
We recursively call the print function by appending a 2 and a 5 at the end.

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