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

Java Numbers: Exercise-21 with Solution

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

//http://introcs.cs.princeton.edu/java/13flow/Ramanujan.java.html
Here are some examples of Ramanujan numbers :
1729 = 1^3 + 12^3 = 9^3 + 10^3
* 10000
1729 = 1^3 + 12^3 = 9^3 + 10^3
4104 = 2^3 + 16^3 = 9^3 + 15^3
* 100000
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

Sample Solution:

Java Code:

import java.util.Scanner;
public class Example21  {

   public static void main(String[] args) { 

         int n = 100000;
        // for each a, b, c, d, check whether a^3 + b^3 = c^3 + d^3
        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) {
                            System.out.print((a3+b3) + " = ");
                            System.out.print(a + "^3 + " + b + "^3 = "); 
                            System.out.print(c + "^3 + " + d + "^3"); 
                            System.out.println();
                        }
                    }
                }
            }
        }
    }
}

Sample Output:

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

Java Code Editor:

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Java: Tips of the Day

Array vs ArrayLists:

The main difference between these two is that an Array is of fixed size so once you have created an Array you cannot change it but the ArrayList is not of fixed size. You can create instances of ArrayLists without specifying its size. So if you create such instances of an ArrayList without specifying its size Java will create an instance of an ArrayList of default size.

Once an ArrayList is full it re-sizes itself. In fact, an ArrayList is internally supported by an array. So when an ArrayList is resized it will slow down its performance a bit as the contents of the old Array must be copied to a new Array.

At the same time, it's compulsory to specify the size of an Array directly or indirectly while creating it. And also Arrays can store both primitives and objects while ArrayLists only can store objects.

Ref: https://bit.ly/3o8L2KH