Given two integers L and R denoting a range [L, R]. The task is to find the total count of numbers in the given range [L,R] whose sum of even digits is greater than the sum of odd digits.
Input : L=2 R=10
Output : 4
Numbers having the property that sum of even
digits is greater than sum of odd digits are: 2, 4, 6, 8
Input : L=2 R=17
Output : 7
Firstly, count the required numbers up to R i.e. in the range [0, R]. To reach the answer in the range [L, R] solve for the range from zero to R and then subtracting the answer for the range from zero to L – 1. Define the DP states as follows:
- Consider the number as a sequence of digits, one state is the position at which we are currently at. This position can have values from 0 to 18 if we are dealing with the numbers up to 10^18. In each recursive call, try to build the sequence from left to right by placing a digit from 0 to 9.
- First state is the sum of the even digits that has been placed so far.
- Second state is the sum of the odd digits that has been placed so far.
- Another state is the boolean variable tight which tells the number we are trying to build has already become smaller than R so that in the upcoming recursive calls we can place any digit from 0 to 9. If the number has not become smaller, the maximum limit of digit we can place is the digit at the current position in R.
Below is the implementation of the above approach:
Time Complexity : There would be at max 18*(180)*(180)*2 computations when 0 < a,b < 1018
- Count of numbers between range having only non-zero digits whose sum of digits is N and number is divisible by M
- Count of numbers from range [L, R] whose sum of digits is Y
- Count numbers in range L-R that are divisible by all of its non-zero digits
- Count of Numbers in Range where the number does not contain more than K non zero digits
- Count of all even numbers in the range [L, R] whose sum of digits is divisible by 3
- Count Numbers in Range with difference between Sum of digits at even and odd positions as Prime
- Count of integers in a range which have even number of odd digits and odd number of even digits
- Total numbers with no repeated digits in a range
- Numbers of Length N having digits A and B and whose sum of digits contain only digits A and B
- Numbers with sum of digits equal to the sum of digits of its all prime factor
- Count numbers with same first and last digits
- Count Numbers with N digits which consists of even number of 0’s
- Count numbers formed by given two digit with sum having given digits
- Count different numbers that can be generated such that there digits sum is equal to 'n'
- Count of n digit numbers whose sum of digits equals to given sum
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