Given an interval, the task is to count numbers which have same first and last digits. For example, 1231 has same first and last digits.
Input : start = 7, end : 68 Output : 9 Number with same first and last digits are, 7 8 9 11 22 33 44 55 66. Input : start = 5, end : 40 Output : 8
Let us first consider below examples to understand the approach.
From 120 to 130, only 121 has same starting and ending digit From 440 to 450, only 444 has same starting and ending digit From 1050 to 1060, only 1051 has same starting and ending digit
From above examples, we can observe that in each ten number span we have only one number which has the given property except 1 to 10 which has 9 numbers (all one digit number) having same starting and ending digit.
Using above property we can solve given problem, first we break the given interval into two parts that is if interval is l to r, we break this into 1 to l and 1 to r, our answer is obtained by subtracting result of first query from second query.
Now we remain to find count of numbers with given property in range 1 to x, for this we divide x by 10, which gives number of 10-spans. We add 9 to the span for taking one digit numbers into account. If last digit of x is smaller than first digit of x, then 1 should be decreased in final answer to discard last ten span number because that number is out of range.
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- Count of numbers between range having only non-zero digits whose sum of digits is N and number is divisible by M
- Count numbers in given range such that sum of even digits is greater than sum of odd digits
- Count of numbers from range [L, R] that end with any of the given digits
- Count of numbers from range [L, R] whose sum of digits is Y
- Count Numbers with N digits which consists of even number of 0’s
- Count of n digit numbers whose sum of digits equals to given sum
- Count different numbers possible using all the digits their frequency times
- Count numbers in range L-R that are divisible by all of its non-zero digits
- Count of N-digit numbers with all distinct 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 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 Numbers with N digits which consists of odd number of 0's
- Count the number of digits of palindrome numbers in an array
Improved By : nitin mittal