C++ Exercises: Find any number between 1 and n that can be expressed as the sum of two cubes in two different ways

Last update on December 20 2024 12:30:53 (UTC/GMT +8 hours)

Write a program in C++ to find any number between 1 and n that can be expressed as the sum of two cubes in two (or more) different ways.

Sample Solution:

C++ Code :

# include <iostream> // Including input-output stream library
# include <math.h> // Including math library for mathematical functions
using namespace std; // Using the standard namespace

int main() // Start of the main function
{
    int a, b, c, d, n; // Declaring variables for looping and storage
    double result; // Declaring a variable for storing the sum of cubes

    cout << "\n\n Find the numbers between a range that can be expressed as the sum of two cubes:\n"; // Display purpose
    cout << "------------------------------------------------------------------------------------\n"; // Display purpose
    cout << " The numbers in the above range are: " << endl; // Display purpose

    n = 100000; // Assigning the upper limit for the range

    for (int a = 1; a <= n; a++) // Loop through potential values of 'a'
    {  
        int a3 = a * a * a; // Calculate the cube of 'a' 

        if (a3 > n) break; // If the cube of 'a' exceeds the limit, exit loop

        for (int b = a; b <= n; b++) // Loop through potential values of 'b'
        {  
            int b3 = b * b * b; // Calculate the cube of 'b'

            if (a3 + b3 > n) break; // If the sum of cubes of 'a' and 'b' exceeds the limit, exit loop

            for (int c = a + 1; c <= n; c++) // Loop through potential values of 'c'
            {  
                int c3 = c * c * c; // Calculate the cube of 'c'

                if (c3 > a3 + b3) break; // If the cube of 'c' exceeds the sum of cubes of 'a' and 'b', exit loop

                for (int d = c; d <= n; d++) // Loop through potential values of 'd'
                {  
                    int d3 = d * d * d; // Calculate the cube of 'd'

                    if (c3 + d3 > a3 + b3) break; // If the sum of cubes of 'c' and 'd' exceeds the sum of cubes of 'a' and 'b', exit loop

                    if (c3 + d3 == a3 + b3) // If the sum of cubes of 'c' and 'd' equals the sum of cubes of 'a' and 'b'
                    {  
                        cout << " " << (a3 + b3) << " = "; // Output the sum of cubes
                        cout << a << "^3 + " << b << "^3 = "; // Output the equation for 'a' and 'b'
                        cout << c << "^3 + " << d << "^3"; // Output the equation for 'c' and 'd'
                        cout << endl; // Move to the next line for the next output
                    }  
                }  
            }  
        }  
    }
}

Sample Output:

Find the numbers between a range that can be expressed as the sum of two cubes:                                                              
------------------------------------------------------------------------------------                                                          
 The numbers in the above range are:                                   
 1729 = 1^3 + 12^3 = 9^3 + 10^3                                        
 4104 = 2^3 + 16^3 = 9^3 + 15^3                                        
 13832 = 2^3 + 24^3 = 18^3 + 20^3                                      
 39312 = 2^3 + 34^3 = 15^3 + 33^3                                      
 46683 = 3^3 + 36^3 = 27^3 + 30^3                                      
 32832 = 4^3 + 32^3 = 18^3 + 30^3                                      
 40033 = 9^3 + 34^3 = 16^3 + 33^3                                      
 20683 = 10^3 + 27^3 = 19^3 + 24^3                                     
 65728 = 12^3 + 40^3 = 31^3 + 33^3                                     
 64232 = 17^3 + 39^3 = 26^3 + 36^3

Flowchart:

C++ Code Editor:

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