A list comprehension is a special syntax in some programming languages to describe lists. It is similar to the way mathematicians describe sets, with a set comprehension, hence the name.

Some attributes of a list comprehension are:

 They should be distinct from (nested) for loops and the use of map and filter functions within the syntax of the language.
 They should return either a list or an iterator (something that returns successive members of a collection, in order).
 The syntax has parts corresponding to that of set-builder notation. 


Task

Write a list comprehension that builds the list of all Pythagorean triples with elements between   1   and   n.

If the language has multiple ways for expressing such a construct (for example, direct list comprehensions and generators), write one example for each.




#include <vector>
#include <cmath>
#include <iostream>
#include <algorithm>
#include <iterator>
 
void list_comprehension( std::vector<int> & , int ) ;
 
int main( ) {
   std::vector<int> triangles ;
   list_comprehension( triangles , 20 ) ;
   std::copy( triangles.begin( ) , triangles.end( ) ,
	 std::ostream_iterator<int>( std::cout , " " ) ) ;
   std::cout << std::endl ;
   return 0 ;
}
 
void list_comprehension( std::vector<int> & numbers , int upper_border ) {
   for ( int a = 1 ; a < upper_border ; a++ ) {
      for ( int b = a + 1 ; b < upper_border ; b++ ) {
	 double c = pow( a * a + b * b , 0.5 ) ; //remembering Mr. Pythagoras
	 if ( ( c * c ) < pow( upper_border , 2 ) + 1 ) {
	    if ( c == floor( c ) ) {
	       numbers.push_back( a ) ;
	       numbers.push_back( b ) ;	      
	       numbers.push_back( static_cast<int>( c ) ) ;
	    }
	 }
      }
   }
}
 