Given an interval, the task is to count numbers which have same first and last digits. For example, **1**23**1** 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++

// 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; }

## Java

// Java program to get count of numbers with // same start and end digit in an interval import java.util.*; class Digits { // Utility method to get first digit of x public static 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 public static 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 public static int getCountWithSameStartAndEnd(int start, int end) { return getCountWithSameStartAndEndFrom1(end) - getCountWithSameStartAndEndFrom1(start - 1); } // driver code public static void main(String[] args) { int start = 5, end = 40; System.out.print(getCountWithSameStartAndEnd(start, end)); } } // This code is contributed by rishabh_jain

## Python3

# Python3 program to get count of numbers with # same start and end digit in an interval # Utility method to get first digit of x def getFirstDigit(x) : while (x >= 10) : x /= 10 return x # method to return count of numbers with same # starting and ending digit from 1 upto x def getCountWithSameStartAndEndFrom1(x) : if (x < 10): return x # get ten-spans from 1 to x tens = x / 10 # add 9 to consider all 1 digit numbers res = tens + 9 # Find first and last digits firstDigit = getFirstDigit(x) lastDigit = x % 10 # If last digit is greater than first digit # then decrease count by 1 if (lastDigit < firstDigit) : res = res - 1 return res # Method to return count of numbers with same starting # and ending digit between start and end def getCountWithSameStartAndEnd(start, end) : return (getCountWithSameStartAndEndFrom1(end) - getCountWithSameStartAndEndFrom1(start - 1)) # Driver Code start = 5 end = 40 print(getCountWithSameStartAndEnd(start, end)) # This code is contributed by rishabh_jain

## C#

// C# program to get count of numbers with // same start and end digit in an interval using System; class GFG { // Utility method to get first digit // of x public static 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 public static 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 public static int getCountWithSameStartAndEnd( int start, int end) { return getCountWithSameStartAndEndFrom1(end) - getCountWithSameStartAndEndFrom1(start - 1); } // driver code public static void Main() { int start = 5, end = 40; Console.Write(getCountWithSameStartAndEnd(start, end)); } } // This code is contributed by nitin mittal.

## PHP

<?php // PHP program to get count of numbers with // same start and end digit in an interval // method to get first digit of x function getFirstDigit($x) { while ($x >= 10) $x /= 10; return $x; } // method to return count // of numbers with same // starting and ending // digit from 1 upto x function getCountWithSameStartAndEndFrom1($x) { if ($x < 10) return $x; // get ten-spans from 1 to x $tens = $x / 10; // add 9 to consider all // 1 digit numbers $res = $tens + 9; // Find first and last digits $firstDigit = getFirstDigit($x); $lastDigit = $x % 10; // If last digit is greater // than first digit // then decrease count by 1 if ($lastDigit < $firstDigit) $res--; return $res; } // Method to return count of // numbers with same starting // and ending digit between // start and end function getCountWithSameStartAndEnd($start, $end) { return getCountWithSameStartAndEndFrom1($end) - getCountWithSameStartAndEndFrom1($start - 1); } // Driver Code $start = 5; $end = 40; echo getCountWithSameStartAndEnd($start, $end); // This code is contributed by nitin mittal. ?>

Output:

8

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