# Count numbers with same first and last digits

• Difficulty Level : Medium
• Last Updated : 26 May, 2022

Given an interval, the task is to count numbers that have the same first and last digits. For example, 1231 has the 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 the 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 the 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 numbers) having the 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 the count of numbers with given property in range 1 to x, for this, we divide x by 10, which gives the number of 10-spans. We add 9 to the span for taking one-digit numbers into account. If the last digit of x is smaller than the first digit of x, then 1 should be decreased in the final answer to discard the 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 ``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 smaller 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;``}`

## C

 `// C program to get count of numbers with``// same start and end digit in an interval``#include ``// 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 smaller 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;` `    ``printf``(``"%d"``,getCountWithSameStartAndEnd(start, end));` `    ``return` `0;``}` `// This code is contributed by allwink45.`

## 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 smaller 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 smaller 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``# Improved by cidacoder`

## 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 smaller 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

 `= 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 smaller``    ``// 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.``?>`

## Javascript

 ``

Output:

`8`

Time Complexity: O(log10N)

Auxiliary Space: O(1)
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