Given a range [L, R], the task is to count the numbers which have even number of odd digits and odd number of even digits. For example,
- 8 has 1 even digit and 0 odd digit – Satisfies the condition since 1 is odd and 0 is even.
- 545 has 1 even digit and 2 odd digits – Satisfies the condition since 1 is odd and 2 is even.
- 4834 has 3 even digits and 1 odd digit – Does not satisfy the condition since there are odd numbers(i.e 1) of odd digits.
Input: L = 1, R = 9
2, 4, 6 and 8 are the only integers from the
given range that satisfy the given conditions.
Input: L = 1, R = 19
Input: L = 123, R = 984
- Case 1
There is a pattern in which these numbers occur between and (where 1<=k<=18).
Number of occurrences from
- 1 – 10 and 1 – 100 are 4
- 1 – 1000 and 1 – 10000 are 454
- 1 – 10000 and 1 – 100000 are 45454
and so on…
- Case 2
- If the number of digits in a number is even then it cannot satisfy the given condition because we need an odd number(of digits) and an even number(of digits) to satisfy our condition and odd number + even number is always odd
- So if the number of digits for a given number(say n) is even then its number of occurrences from 1 is equal to the number of occurrences from to largest (1<=k<=18) which is less than n
Let n = 19, number of digits in 19 are 2
Therefore number of occurrences from 1 – 19 = number of occurrences from 1 – 10 (since 10 the largest less than 19)
- Case 3
If number of digits for a given number(say n) are odd then number of occurrences between and n is equal to
where is the largest less than n.
Implementation: Now we now how to calculate the number of occurrences from 1 to given n. Therefore,
Number of occurrences from L to R = NumberOfOccurrencesUpto(R) – NumberOfOccurrencesUpto(L – 1) where L is not equal to 1.
Below is the implementation of the above approach:
Time Complexity: O(logn)
- Count of numbers between range having only non-zero digits whose sum of digits is N and number is divisible by M
- Number of integers in a range [L, R] which are divisible by exactly K of it's digits
- Count of Numbers in Range where the number does not contain more than K non zero digits
- Count numbers in given range such that sum of even digits is greater than sum of odd digits
- Find the number of positive integers less than or equal to N that have an odd number of digits
- Number of n-digits non-decreasing integers
- Find the number of integers from 1 to n which contains digits 0's and 1's only
- Find smallest possible Number from a given large Number with same count of digits
- Find smallest number with given number of digits and sum of digits under given constraints
- Count number of digits after decimal on dividing a number
- Count of prime digits of a Number which divides the number
- Find count of digits in a number that divide the number
- Find the number in a range having maximum product of the digits
- 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
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