Find the number of digits in the nth number constructed by using 6, 1, 4 and 9 as the only digits in the ascending order.
First few numbers constructed by using only 6, 1, 4 and 9 as digits in the ascending order would be: 1, 6, 4,
9, 11, 14, 16, 19, 41, 44, 46, 49, 61, 64, 66, 69, 91, 94, 96, 99, 111, 114, 116, 119 and so on.
Input : 6 Output : 2 6th digit of the series is 14 which has 2 digits. Input : 21 Output : 3 21st digit of the series is 111 which has 3 digits.
Simple Approach: This is a brute force approach.
1. Initialize a number to 1 and a counter to 0.
2. Check if the initialized number has only 6, 1, 4 or 9 as it’s digits.
3. If it has only the mentioned digits then increase the counter by 1.
4. Increase the number and repeat the above steps until the counter is less than n.
Note: The value of n could be large and hence this approach can’t work as it’s not time efficient.
Efficient Approach: You can calculate the number of k digit numbers in O (1) time and they will be always be power of 4, for instance number of 1 digit numbers in the series would be 4, number of 2 digit numbers in the series would be 16 and so on.
1. Count all subsequent k digit numbers and keep adding them to a sum.
2. Break the loop when sum is greater than or equal to n.
3. Maintain a counter to keep track of the number of digits.
4. The value of the counter at the break of the loop will indicate the answer.
Note: Since n could be really large we have used boost library, to know more about boost library give this article a read: Advanced C++ with boost library
- Nth number made up of odd digits only
- Find the n-th number made of even digits only
- Smallest multiple of a given number made of digits 0 and 9 only
- Finding n-th number made of prime digits (2, 3, 5 and 7) only
- Check whether product of digits at even places is divisible by sum of digits at odd place of a number
- Maximize the given number by replacing a segment of digits with the alternate digits given
- Count of numbers between range having only non-zero digits whose sum of digits is N and number is divisible by M
- Find smallest number with given number of digits and sum of digits
- Find the Largest number with given number of digits and sum of digits
- Minimum number of digits to be removed so that no two consecutive digits are same
- Find the average of k digits from the beginning and l digits from the end of the given number
- Smallest number with given sum of digits and sum of square of digits
- Count number of digits after decimal on dividing a number
- Build Lowest Number by Removing n digits from a given number
- Find the smallest number whose digits multiply to a given number n
If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to firstname.lastname@example.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.