Given a number N, output all Munchhausen numbers from 1 to n.
Introduction : A Münchhausen number is a number equal to the sum of its digits raised to each digit’s power. It is similar to that of Narcissistic Number.
For example:
3435 = 33 + 44 + 33 + 55
One can also be considered as Münchhausen Number because when 1 raised to the power 1 is 1 itself.
Since, the number 3435 can be expressed as sum of each digits of the number when each digits of the numbers are raised to power equivalent to the digits itself i.e., ((3 raised to the power 3) + (4 raised to the power 4) + (3 raised to the power 3) + (5 raised to the power 5)) will give output to the same number i.e. 3435, then the number can be called as Münchhausen Number.
Example:
Input : 500 Output : 1 One is the only Münchhausen Number smaller than or equal to 500. Input : 5000 Output : 1 3435 1 and 3435 are the only Münchhausen Numbers smaller than or equal to 5000.
We precompute i raised to power i for every possible digit i where i varies from 0 to 9. After precomputing these values, we traverse through all digits of every number smaller than equal to n and compute sum of digit raised to power digit.
C++
// C++ code for Münchhausen Number#include <bits/stdc++.h>using namespace std; // pwr[i] is going to store i raised to// power i.unsigned pwr[10];// Function to check out whether// the number is Münchhausen// Number or not bool isMunchhausen(unsigned n) { unsigned sum = 0; int temp = n; while (temp) { sum += pwr[(temp % 10)]; temp /= 10; } return (sum == n);}void printMunchhausenNumbers(int n){ // Precompute i raised to power i for every i for (int i = 0; i < 10; i++ ) pwr[i] = (unsigned)pow( (float)i, (float)i ); // The input here is fixed i.e. it will // check up to n for (unsigned i = 1; i <= n; i++) // check the integer for Münchhausen Number, // if yes then print out the number if (isMunchhausen(i)) cout << i << "\n";}// Driver Codeint main() { int n = 10000; printMunchhausenNumbers(n); return 0;} |
Java
// Java code for Munchhausen Numberimport java.io.*;import java.util.*;class GFG {// pwr[i] is going to store i raised to// power i.static long[] pwr; // Function to check out whether// the number is Munchhausen// Number or not static Boolean isMunchhausen(int n) { long sum = 0l; int temp = n; while (temp>0) { int index= temp%10; sum =sum + pwr[index]; temp /= 10; } return (sum == n);} static void printMunchhausenNumbers(int n){ pwr= new long[10]; // Precompute i raised to // power i for every i for (int i = 0; i < 10; i++ ) pwr[i] = (long)Math.pow( (float)i, (float)i ); // The input here is fixed i.e. it will // check up to n for (int i = 1; i <= n; i++) // check the integer for Munchhausen Number, // if yes then print out the number if (isMunchhausen(i)==true) System.out.println(i );} public static void main (String[] args) { int n = 10000; printMunchhausenNumbers(n); }}// This code is contributed by Gitanjali. |
Python3
# Python 3 code for# Münchhausen Numberimport math# pwr[i] is going to # store i raised to# power i.pwr = [0] * 10# Function to check out# whether the number is# Münchhausen Number or# not def isMunchhausen(n) : sm = 0 temp = n while (temp) : sm= sm + pwr[(temp % 10)] temp = temp // 10 return (sm == n)def printMunchhausenNumbers(n) : # Precompute i raised to # power i for every i for i in range(0, 10) : pwr[i] = math.pow((float)(i), (float)(i)) # The input here is fixed # i.e. it will check up to n for i in range(1,n+1) : # check the integer for # Münchhausen Number, if # yes then print out the # number if (isMunchhausen(i)) : print( i )# Driver Coden = 10000printMunchhausenNumbers(n)# This code is contributed by Nikita Tiwari. |
C#
// C# code for Munchhausen Numberusing System;class GFG { // pwr[i] is going to store i // raised to power i. static long[] pwr; // Function to check out whether // the number is Munchhausen // Number or not static bool isMunchhausen(int n) { long sum = 0; int temp = n; while (temp > 0) { int index = temp % 10; sum = sum + pwr[index]; temp /= 10; } return (sum == n); } static void printMunchhausenNumbers(int n) { pwr = new long[10]; // Precompute i raised to // power i for every i for (int i = 0; i < 10; i++) pwr[i] = (long)Math.Pow((float)i, (float)i); // The input here is fixed i.e. // it will check up to n for (int i = 1; i <= n; i++) // check the integer for Munchhausen Number, // if yes then print out the number if (isMunchhausen(i) == true) Console.WriteLine(i); } // Driver Code public static void Main() { int n = 10000; printMunchhausenNumbers(n); }}// This code is contributed by vt_m. |
PHP
<?php// PHP code for Münchhausen Number// pwr[i] is going to store i raised // to power i.$pwr = array_fill(0, 10, 0);// Function to check out whether the // number is Münchhausen Number or not function isMunchhausen($n){ global $pwr; $sm = 0; $temp = $n; while ($temp) { $sm= $sm + $pwr[($temp % 10)]; $temp = (int)($temp / 10); } return ($sm == $n);}function printMunchhausenNumbers($n){ global $pwr; // Precompute i raised to power // i for every i for ($i = 0; $i < 10; $i++) $pwr[$i] = pow((float)($i), (float)($i)); // The input here is fixed i.e. it // will check up to n for ($i = 1; $i < $n + 1; $i++) // check the integer for Münchhausen // Number, if yes then print out the // number if (isMunchhausen($i)) print($i . "\n");}// Driver Code$n = 10000;printMunchhausenNumbers($n);// This code is contributed by mits?> |
Javascript
<script>// Javascript code for Munchhausen Number// pwr[i] is going to store i raised to// power i.var pwr; // Function to check out whether// the number is Munchhausen// Number or not function isMunchhausen(n) { var sum = 0; var temp = n; while (temp > 0) { var index= temp % 10; sum =sum + pwr[index]; temp = parseInt(temp / 10); } return (sum == n);} function printMunchhausenNumbers(n){ pwr = Array.from({length: 10}, (_, i) => 0); // Precompute i raised to // power i for every i for(var i = 0; i < 10; i++) pwr[i] = Math.pow(i, i); // The input here is fixed i.e. it will // check up to n for(var i = 1; i <= n; i++) // check the integer for Munchhausen Number, // if yes then print out the number if (isMunchhausen(i) == true) document.write(i + "<br>");}// Driver codevar n = 10000;printMunchhausenNumbers(n);// This code is contributed by Princi Singh </script> |
Output:
1 3435
Time complexity: O(n logn) n for outer for loop and log n for while loop in function isMunchhausen
Auxiliary space: O(1) because it is using constant space for array pow
Note : If the definition 0^0 = 0 is adopted, then there are exactly four Münchhausen numbers: 0, 1, 3435, and 438579088 [Source : MathWorld]
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