Count numbers with same first and last digits

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.

Examples:

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.

// C++ program to get count of numbers with
// same start and end digit in an interval
#include <bits/stdc++.h>
using namespace std;

//  Utility method to get first digit of x
int getFirstDigit(int x)
{
    while (x >= 10)
        x /= 10;
    return x;
}

// method to return count of numbers with same
// starting and ending digit from 1 upto x
int getCountWithSameStartAndEndFrom1(int x)
{
    if (x < 10)
        return x;

    // get ten-spans from 1 to x
    int tens = x / 10;

    // add 9 to consider all 1 digit numbers
    int res = tens + 9;

    // Find first and last digits
    int firstDigit = getFirstDigit(x);
    int lastDigit = x % 10;

    // If last digit is greater than first digit
    // then decrease count by 1
    if (lastDigit < firstDigit)
        res--;

    return res;
}

// Method to return count of numbers with same starting
// and ending digit between start and end
int getCountWithSameStartAndEnd(int start, int end)
{
    return getCountWithSameStartAndEndFrom1(end) -
           getCountWithSameStartAndEndFrom1(start - 1);
}

//  Driver code to test above methods
int main()
{
    int start = 5, end = 40;

    cout << getCountWithSameStartAndEnd(start, end);

    return 0;
}

Output:

8

This article is contributed by Utkarsh Trivedi. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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