Given an integer N where 1 ≤ N ≤ 105, the task is to find the number of positive integers less than or equal to N that have an odd number of digits without leading zeros.
Input: N = 11
1, 2, 3, …, 8 and 9 are the numbers ≤ 11
with odd number of digits.
Input: N = 893
Naive approach: Traverse from 1 to N and for each number check if it contains odd digits or not.
Efficient approach: For the values:
- When N < 10 then the count of valid numbers will be N.
- When N / 10 < 10 then 9.
- When N / 100 < 10 then 9 + N – 99.
- When N / 1000 < 10 then 9 + 900.
- When N / 10000 < 10 then 909 + N – 9999.
- Otherwise 90909.
Below is the implementation of the above approach:
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- Count of integers in a range which have even number of odd digits and odd number of even digits
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- Count of integers of length N and value less than K such that they contain digits only from the given set
- Count number of integers less than or equal to N which has exactly 9 divisors
- Smallest odd digits number not less than N
- Find maximum product of digits among numbers less than or equal to N
- Find K distinct positive odd integers with sum N
- Greatest number less than equal to B that can be formed from the digits of A
- Highest and Smallest power of K less than and greater than equal to N respectively
- Count positive integers with 0 as a digit and maximum 'd' digits
- Count of digits after concatenation of first N positive integers
- Count numbers in given range such that sum of even digits is greater than sum of odd digits
- Find Largest Special Prime which is less than or equal to a given number
- Find all powers of 2 less than or equal to a given number
- Print a number strictly less than a given number such that all its digits are distinct.
- Find all factorial numbers less than or equal to n
- Find unique pairs such that each element is less than or equal to N
- Find Multiples of 2 or 3 or 5 less than or equal to N
- Find all possible subarrays having product less than or equal to K
- Smallest even digits number not less than N
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