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 that:
- They should be distinct from (nested) for loops 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.
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.
There is no equivalent construct in C++. The code below uses two nested loops and an if statement:
#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 ) ) ; } } } } }
This produces the following output:
3 4 5 5 12 13 6 8 10 8 15 17 9 12 15 12 16 20
#include <functional> #include <iostream> void PythagoreanTriples(int limit, std::function<void(int,int,int)> yield) { for (int a = 1; a < limit; ++a) { for (int b = a+1; b < limit; ++b) { for (int c = b+1; c <= limit; ++c) { if (a*a + b*b == c*c) { yield(a, b, c); } } } } } int main() { PythagoreanTriples(20, [](int x, int y, int z) { std::cout << x << "," << y << "," << z << "\n"; }); return 0; }
Output:
3,4,5 5,12,13 6,8,10 8,15,17 9,12,15 12,16,20
Content is available under GNU Free Documentation License 1.2.
