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Trimorphic Number

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  • Last Updated : 09 Aug, 2022
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Given a number N, the task is to check whether the number is Trimorphic number or not. A number is called Trimorphic number if and only if its cube ends in the same digits as the number itself. In other words, number appears at the end of its cube.

Examples: 

Input : 5 
Output : trimorphic 
Explanation: 5*5*5=125

Input : 24 
Output : trimorphic 
Explanation: 24*24*24=13824 

Input:10 
Output: not trimorphic 
Explanation: 10*10*10=1000
Recommended Practice
Trimorphic Number
Try It!

Approach:  

1. Store the cube of given number.
2. Loop until N becomes 0 as we have to match 
   all digits with its cube.
    i) Check if (n%10 == cube%10) i.e. last digit 
       of number = last digit of cube or not
        a) if not equal, return false.
    ii) Otherwise continue i.e. reduce number and 
        cube i.e. n = n/10 and cube = cube/10;
3- Return true if all digits matched.

Below is the implementation of the approach.  

C++




// C++ program to check if a
// number is Trimorphic
#include <iostream>
using namespace std;
 
// Function to check Trimorphic number
bool isTrimorphic(int N)
{
    // Store the cube
    int cube = N * N * N;
 
    // Start Comparing digits
    while (N > 0)
    {
        // Return false, if any digit
        // of N doesn't match with
        // its cube's digits from last
        if (N % 10 != cube % 10)
            return false;
 
        // Reduce N and cube
        N /= 10;
        cube /= 10;
    }
 
    return true;
}
 
// Driver code
int main()
{
    int N = 24;
 
    isTrimorphic(N) ? cout << "trimorphic" :
                      cout << "not trimorphic";
 
    return 0;
}

Java



// Java program to check if a
// number is Trimorphic
  
class GFG {
  
  // Function to check Trimorphic number
    static boolean isTrimorphic(int N)
    {
        // Store the cube
        int cube = N * N * N;
  
        // Start Comparing digits
        while (N > 0) {
  
         // Return false, if any digit
         // of N doesn't match with
         // its cube's digits from last
         if (N % 10 != cube % 10)
            return false;
  
            // Reduce N and cube
            N /= 10;
            cube /= 10;
        }
  
        return true;
    }
  
// Driver code
public static void main(String[] args)
    {
        int N = 24;
  
        if (isTrimorphic(N) == true)
        System.out.println("trimorphic");
        else
        System.out.println("not trimorphic");
    }
}
  
//This article is contributed by prerna saini.
Python3



# Python 3 program to check
# if a number is Trimorphic
 
  
# Function to check
# Trimorphic number
def isTrimorphic(N) :
     
    # Store the cube
    cube = N * N * N
  
    # Start Comparing digits
    while (N > 0) :
        
        # Return false, if any digit
        # of N doesn't match with
        # its cube's digits from last
        if (N % 10 != cube % 10) :
            return False
  
        # Reduce N and cube
        N = N // 10
        cube = cube // 10
     
    return True
 
 
# Driver code
N = 24
if(isTrimorphic(N)) :
    print("trimorphic")
else :
    print("not trimorphic")
     
     
# This code is contributed by Nikita tiwari.
C#



// C# program to check if
// a number is Trimorphic
using System;
 
class GFG {
 
// Function to check Trimorphic number
    static bool isTrimorphic(int N)
    {
        // Store the cube
        int cube = N * N * N;
 
        // Start Comparing digits
        while (N > 0) {
 
        // Return false, if any digit
        // of N doesn't match with
        // its cube's digits from last
        if (N % 10 != cube % 10)
            return false;
 
            // Reduce N and cube
            N /= 10;
            cube /= 10;
        }
 
        return true;
    }
 
// Driver code
public static void Main()
    {
        int N = 24;
 
        if (isTrimorphic(N) == true)
        Console.Write("trimorphic");
        else
        Console.Write("not trimorphic");
    }
}
 
// This article is contributed
// by Smitha Dinesh Semwal.
PHP



<?php
//PHP program to check if a
// number is Trimorphic
 
// Function to check Trimorphic
// number
function isTrimorphic($N)
{
     
    // Store the cube
    $cube = $N * $N * $N;
 
    // Start Comparing digits
    while ($N > 0)
    {
         
        // Return false, if any digit
        // of N doesn't match with
        // its cube's digits from last
        if ($N % 10 != $cube % 10)
            return -1;
 
        // Reduce N and cube
        $N /= 10;
        $cube /= 10;
    }
 
    return 1;
}
 
// Driver code
    $N = 24;
 
    $r = isTrimorphic($N) ? "trimorphic" :
                      "not trimorphic";
    echo $r;
 
// This code is contributed by aj_36
?>
Javascript



<script>
 
// Javascript program to check if
// a number is Trimorphic
 
// Function to check Trimorphic number
function isTrimorphic(N)
{
     
    // Store the cube
    let cube = N * N * N;
 
    // Start Comparing digits
    while (N > 0)
    {
         
        // Return false, if any digit
        // of N doesn't match with
        // its cube's digits from last
        if (N % 10 != cube % 10)
            return false;
     
        // Reduce N and cube
        N = parseInt(N / 10, 10);
        cube = parseInt(cube / 10, 10);
    }
    return true;
}
 
// Driver code
let N = 24;
 
if (isTrimorphic(N) == true)
    document.write("trimorphic");
else
    document.write("not trimorphic");
     
// This code is contributed by rameshtravel07
 
</script>
Output: 
trimorphic
Find nth Trimorphic Number 
Examples: 
Input  : 10 
Output : 51

Input  : 11
Output : 75
C++



// CPP program to find nth
// Trimorphic number
#include <iostream>
using namespace std;
 
# define INT_MAX 2147483647
// Functions to find nth
// Trimorphic number
bool checkTrimorphic(int num)
{
    int cube = num * num * num;
    // Comparing the digits
    while(num > 0)
    {
        // Return false, if any digit
        // of num doesn't match with
        // its cube's digits from last
        if (num % 10 != cube % 10)
            return false;
 
        // Reduce num and cube
        num /= 10;
        cube /= 10;
    }
    return true;
}
int nthTrimorphic(int n)
{
     
    int count = 0;
    // Check in max int size
    for(int i = 0; i < INT_MAX; i++)
    {
        //check number is Trimorphic or not
        if(checkTrimorphic(i))
            count++;
             
        // if counter is equal to the
        // n then return nth number
        if(count == n)
            return i;
    }
}
 
// Driver code
int main()
{
    int n = 9;
    cout<< nthTrimorphic(n);
    return 0;
}
 
// This code is contributed by jaingyayak.
Java



// Java program to find nth
// Trimorphic number
 
 
class GFG
{
static int INT_MAX = 2147483647;
 
// Functions to find nth
// Trimorphic number
static boolean checkTrimorphic(int num)
{
    int cube = num * num * num;
     
    // Comparing the digits
    while(num > 0)
    {
        // Return false, if any
        // digit of num doesn't
        // match with its cube's
        // digits from last
        if (num % 10 != cube % 10)
            return false;
 
        // Reduce num and cube
        num /= 10;
        cube /= 10;
    }
    return true;
}
 
static int nthTrimorphic(int n)
{
     
    int count = 0;
     
    // Check in max int size
    for(int i = 0; i < INT_MAX; i++)
    {
        // check number is
        // Trimorphic or not
        if(checkTrimorphic(i))
            count++;
             
        // if counter is equal to
        // the n then return nth number
        if(count == n)
            return i;
    }
    return -1;
}
 
// Driver code
public static void main(String[] args)
{
    int n = 9;
    System.out.println(nthTrimorphic(n));
}
}
 
// This code is contributed by mits.
Python3



# Python3 program to find
# nth Trimorphic number
import sys
# Functions to find nth
# Trimorphic number
def checkTrimorphic(num):
 
    cube = num * num * num
     
    # Comparing the digits
    while(num > 0):
        # Return false, if any digit
        # of num doesn't match with
        # its cube's digits from last
        if (num % 10 != cube % 10):
            return False
 
        # Reduce num and cube
        num = int(num / 10)
        cube = int(cube / 10)
    return True
 
 
def nthTrimorphic(n):
    count = 0
     
    # Check in max int size
    for i in range(sys.maxsize):
        # check number is
        # Trimorphic or not
        if(checkTrimorphic(i)):
            count+=1
             
        # if counter is equal to
        # the n then return nth
        # number
        if(count == n):
            return i
 
 
 
# Driver code
if __name__=='__main__':
    n = 9
    print(nthTrimorphic(n))
 
# This code is contributed
# by mits.
C#



// C# program to find nth
// Trimorphic number
using System;
 
class GFG
{
static int INT_MAX = 2147483647;
 
// Functions to find nth
// Trimorphic number
static bool checkTrimorphic(int num)
{
    int cube = num * num * num;
     
    // Comparing the digits
    while(num > 0)
    {
        // Return false, if any
        // digit of num doesn't
        // match with its cube's
        // digits from last
        if (num % 10 != cube % 10)
            return false;
 
        // Reduce num and cube
        num /= 10;
        cube /= 10;
    }
    return true;
}
 
static int nthTrimorphic(int n)
{
     
    int count = 0;
     
    // Check in max int size
    for(int i = 0; i < INT_MAX; i++)
    {
        // check number is
        // Trimorphic or not
        if(checkTrimorphic(i))
            count++;
             
        // if counter is equal to
        // the n then return nth number
        if(count == n)
            return i;
    }
    return -1;
}
 
// Driver code
static int Main()
{
    int n = 9;
    Console.Write(nthTrimorphic(n));
    return 0;
}
}
 
// This code is contributed by mits.
PHP



<?php
// PHP program to find
// nth Trimorphic number
 
// Functions to find nth
// Trimorphic number
function checkTrimorphic($num)
{
    $cube = $num * $num * $num;
     
    // Comparing the digits
    while($num > 0)
    {
        // Return false, if any digit
        // of num doesn't match with
        // its cube's digits from last
        if ($num % 10 != $cube % 10)
            return false;
 
        // Reduce num and cube
        $num = (int)($num / 10);
        $cube = (int)($cube / 10);
    }
    return true;
}
 
function nthTrimorphic($n)
{
    $count = 0;
     
    // Check in max int size
    for($i = 0;
        $i < PHP_INT_MAX; $i++)
    {
        // check number is
        // Trimorphic or not
        if(checkTrimorphic($i))
            $count++;
             
        // if counter is equal to
        // the n then return nth
        // number
        if($count == $n)
            return $i;
    }
}
 
// Driver code
$n = 9;
echo nthTrimorphic($n);
 
// This code is contributed
// by mits.
?>
Javascript



<script>
   
// JavaScript program for the above approach
 
let LET_MAX = 2147483647;
 
// Functions to find nth
// Trimorphic number
function checkTrimorphic(num)
{
    let cube = num * num * num;
     
    // Comparing the digits
    while(num > 0)
    {
        // Return false, if any
        // digit of num doesn't
        // match with its cube's
        // digits from last
        if (num % 10 != cube % 10)
            return false;
 
        // Reduce num and cube
        num = Math.floor(num / 10);
        cube = Math.floor(cube / 10);
    }
    return true;
}
 
function nthTrimorphic(n)
{
     
    let count = 0;
     
    // Check in max let size
    for(let i = 0; i < LET_MAX; i++)
    {
        // check number is
        // Trimorphic or not
        if(checkTrimorphic(i))
            count++;
             
        // if counter is equal to
        // the n then return nth number
        if(count == n)
            return i;
    }
    return -1;
}
 
// Driver Code
 
    let n = 9;
    document.write(nthTrimorphic(n));
         
</script>
Output: 
49
 Time complexity: O(INT_MAX*logN)
space complexity: O(1)

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