Count numbers with same first and last digits

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 <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 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 <stdio.h>
// 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

<?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 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

<script>

// JavaScript program to get count of numbers with
// same start and end digit in an interval

    // Utility 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
        let tens = x / 10;

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

        // Find first and last digits
        let firstDigit = getFirstDigit(x);
        let 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
      let start = 5, end = 40;
      document.write(getCountWithSameStartAndEnd(start,
                                                     end));
</script>

Output: 

8

Time Complexity: O(log₁₀N)

Auxiliary Space: O(1)
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