Münchhausen Number

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.

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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 using namespace std;     // pwr[i] is going to store i raised to // power i. unsigned pwr;    // 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 Code int main() {     int n = 10000;     printMunchhausenNumbers(n);     return 0; }

Java

 // Java code for Munchhausen Number    import 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;        // 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 Number import math    # pwr[i] is going to  # store i raised to # power i. pwr =  * 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 Code n = 10000 printMunchhausenNumbers(n)    # This code is contributed by Nikita Tiwari.

C#

 // C# code for Munchhausen Number using 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;            // 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



Output:

1
3435

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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