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

C++ Numbers: Exercise-34 with Solution

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>
# include <math.h>
using namespace std;
int main()
{
    int a,b,c,d,n;
	double result;
	cout << "\n\n Find the numbers between a range that can be expressed as the sum of two cubes:\n";
	cout << "------------------------------------------------------------------------------------\n";
	cout << " The numbers in the above range are: "<<endl;
         n = 100000;  
        for (int a = 1; a <= n; a++) 
		{  
            int a3 = a*a*a;  
            if (a3 > n) break;  
  
            for (int b = a; b <= n; b++) 
			{  
                int b3 = b*b*b;  
                if (a3 + b3 > n) break;  
  
                 for (int c = a + 1; c <= n; c++) 
				 {  
                    int c3 = c*c*c;  
                    if (c3 > a3 + b3) break;  
  
                    for (int d = c; d <= n; d++) 
					{  
                        int d3 = d*d*d;  
                        if (c3 + d3 > a3 + b3) break;  
  
                        if (c3 + d3 == a3 + b3) 
						{  
                            cout<<" "<<(a3+b3) << " = ";  
                            cout<<a << "^3 + " << b << "^3 = ";   
                            cout<<c << "^3 + " << d << "^3";   
                            cout<<endl; 
                        }  
                    }  
                }  
            }  
        }
}

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:

Flowchart: Find any number between 1 and n that can be expressed as the sum of two cubes in two (or more) different ways

C++ Code Editor:

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C++ Programming: Tips of the Day

How to use the PI constant in C++?

On some (especially older) platforms (see the comments below) you might need to

#define _USE_MATH_DEFINES and then include the necessary header file:
#include<math.h>

and the value of pi can be accessed via:

M_PI

In math.h (2014) it is defined as:

# define M_PI           3.14159265358979323846  /* pi */

but check your math.h for more. An extract from the "old" math.h (in 2009):

/* Define _USE_MATH_DEFINES before including math.h to expose these macro
 * definitions for common math constants.  These are placed under an #ifdef 
 * since these commonly-defined names are not part of the C/C++ standards.
 */

However:

  1. on newer platforms (at least on my 64 bit Ubuntu 14.04) I do not need to define the _USE_MATH_DEFINES
  2. On (recent) Linux platforms there are long double values too provided as a GNU Extension:
# define M_PIl          3.14159265358979323846

Ref: https://bit.ly/3G4BgzQ