Find last five digits of a given five digit number raised to power five

Given a five-digit number N., The task is to find the last five digits of the given number raised to the power of 5 after modifying it by arranging the digits as: 

first digit, third digit, fifth digit, fourth digit, second digit.

Examples:

Input : N = 12345
Output : 71232
Explanation : 
After modification the number becomes 13542. (13542)5 is 
455422043125550171232

Input : N = 10000
Output : 00000

Approach: In this problem, just implementation of the actions described in the statement is required. However, there are two catches in this problem.
The first catch is that the fifth power of a five-digit number cannot be represented by a 64-bit integer. But we do not actually need the fifth power, we need the fifth power modulo 10⁵. And mod operation can be applied after each multiplication.
The second catch is that you need to output five digits, not the fifth power modulo 10⁵. The difference is when the fifth digit from the end is zero. To output, a number with the leading zero one can either use corresponding formatting (%05d in printf) or extract digits and output them one by one.

Below is the implementation of the above approach :

C++

// CPP program to find last five digits
// of a five digit number raised to power five

#include <bits/stdc++.h>
using namespace std;

// Function to find the last five digits
// of a five digit number raised to power five
int lastFiveDigits(int n)
{
    n = (n / 10000) * 10000
        + ((n / 100) % 10)
              * 1000
        + (n % 10)
              * 100
        + ((n / 10) % 10)
              * 10
        + (n / 1000) % 10;

    long long ans = 1;
    for (int i = 0; i < 5; i++) {
        ans *= n;
        ans %= 100000;
    }

    printf("%05d", ans);
}

// Driver code
int main()
{
    int n = 12345;

    lastFiveDigits(n);

    return 0;
}

Java

// Java program to find last five digits
// of a five digit number raised to power five

class GfG {

    // Function to find the last five digits
    // of a five digit number raised to power five
    static void lastFiveDigits(int n)
    {
        n = (n / 10000) * 10000
            + ((n / 100) % 10)
                  * 1000
            + (n % 10)
                  * 100
            + ((n / 10) % 10)
                  * 10
            + (n / 1000) % 10;

        int ans = 1;
        for (int i = 0; i < 5; i++) {
            ans *= n;
            ans %= 100000;
        }

        System.out.println(ans);
    }

    // Driver code
    public static void main(String[] args)
    {
        int n = 12345;

        lastFiveDigits(n);
    }
}

Python3

# Python3 program to find last five digits
# of a five digit number raised to power five

# Function to find the last five digits
# of a five digit number raised to power five
def lastFiveDigits(n):
    n = ((int)(n / 10000) * 10000 +
        ((int)(n / 100) % 10) * 1000 + (n % 10) * 100 +
        ((int)(n / 10) % 10) * 10 + (int)(n / 1000) % 10)
    ans = 1
    for i in range(5):
        ans *= n
        ans %= 100000
    print(ans)

# Driver code
if __name__ == '__main__':
    n = 12345

    lastFiveDigits(n)

# This code contributed by PrinciRaj1992

C#

// C# program to find last five
// digits of a five digit number
// raised to power five
using System;

class GFG
{

    // Function to find the last
    // five digits of a five digit
    // number raised to power five
    public static void lastFiveDigits(int n)
    {
        n = (n / 10000) * 10000 +
           ((n / 100) % 10) * 1000 +
            (n % 10) * 100 +
           ((n / 10) % 10) * 10 +
            (n / 1000) % 10;

        int ans = 1;
        for (int i = 0; i < 5; i++)
        {
            ans *= n;
            ans %= 100000;
        }

        Console.WriteLine(ans);
    }

    // Driver code
    public static void Main(string[] args)
    {
        int n = 12345;

        lastFiveDigits(n);
    }
}

// This code is contributed
// by Shrikant13

PHP

<?php
// PHP program to find last five digits
// of a five digit number raised to power five

// Function to find the last five digits
// of a five digit number raised to power five
function lastFiveDigits($n)
{
    $n = (int)($n / 10000) * 10000 +
        ((int)($n / 100) % 10) * 1000 +
              ($n % 10) * 100 +
        ((int)($n / 10) % 10) * 10 +
         (int)($n / 1000) % 10;

    $ans = 1;
    for ($i = 0; $i < 5; $i++)
    {
        $ans *= $n;
        $ans %= 100000;
    }

    echo $ans;
}

// Driver code
$n = 12345;

lastFiveDigits($n);

// This code is contributed
// by Akanksha Rai
?>

Javascript

<script>
// JavaScript program to find last five digits
// of a five digit number raised to power five

// Function to find the last five digits
// of a five digit number raised to power five
function lastFiveDigits(n)
{
    n = (Math.floor(n / 10000)) * 10000
        + (Math.floor(n / 100) % 10)
            * 1000
        + (n % 10)
            * 100
        + (Math.floor(n / 10) % 10)
            * 10
        + Math.floor(n / 1000) % 10;

    let ans = 1;
    for (let i = 0; i < 5; i++) {
        ans *= n;
        ans %= 100000;
    }

    document.write(ans);
}

// Driver code

    let n = 12345;

    lastFiveDigits(n);

// This code is contributed by Manoj.

</script>

Output

71232

Time Complexity: O(1)
Auxiliary Space: O(1)

Approach: Modified Digit Arrangement and Modulo Operation” 

The “Modified Digit Arrangement and Modulo Operation” approach to finding the last five digits of a five-digit number raised to power five consists of the following steps:

1. Modify the number as per the given arrangement of digits.
2. Calculate the power of 5 of the modified number.
3. Take modulo with 100000 (10^5) to get the last five digits.

The key idea behind this approach is to use the given arrangement of digits to modify the original number in such a way that the resulting number has the same last five digits as the original number when raised to power five. Then, by taking modulo with 100000, we can obtain the last five digits of the resulting number.

Python3

def find_last_five_digits(N):
    # Modify the number as per the given arrangement of digits
    new_N = int(str(N)[0] + str(N)[2] + str(N)[4] + str(N)[3] + str(N)[1])
    print(f"Modified number: {new_N}")

    # Calculate the power of 5 of the modified number
    power = new_N ** 5
    print(f"Power of 5: {power}")

    # Take modulo with 100000 to get the last five digits
    last_five_digits = power % 100000
    print(f"Last five digits: {last_five_digits}")

    return last_five_digits

print(find_last_five_digits(12345))
print(find_last_five_digits(10000))

Output

Modified number: 13542
Power of 5: 455422043125550171232
Last five digits: 71232
71232
Modified number: 10000
Power of 5: 100000000000000000000
Last five digits: 0
0

The time complexity  is O(1)

The auxiliary space is also O(1)