package dickson_test
import (
	"pythagorean"
	"pythagorean/dickson"
	"reflect"
	"testing"
)
var rangeTests = []struct {
	min, max int
	ts       []pythagorean.Triplet
}{
	{1, 10, []pythagorean.Triplet{{3, 4, 5}, {6, 8, 10}}},
	{11, 20, []pythagorean.Triplet{{12, 16, 20}}},
}
func TestRange(t *testing.T) {
	for _, test := range rangeTests {
		ts := dickson.Range(test.min, test.max)
		if !reflect.DeepEqual(ts, test.ts) {
			t.Fatalf("Range(%d, %d) = %v, want %v",
				test.min, test.max, ts, test.ts)
		}
	}
}
var sumTests = []struct {
	sum int
	ts  []pythagorean.Triplet
}{
	{180, []pythagorean.Triplet{{18, 80, 82}, {30, 72, 78}, {45, 60, 75}}},
	{1000, []pythagorean.Triplet{{200, 375, 425}}},
}
func TestSum(t *testing.T) {
	for _, test := range sumTests {
		ts := dickson.Sum(test.sum)
		if !reflect.DeepEqual(ts, test.ts) {
			t.Fatalf("Sum(%d) = %v, want %v",
				test.sum, ts, test.ts)
		}
	}
}
func BenchmarkRange(b *testing.B) {
	for i := 0; i < b.N; i++ {
		dickson.Range(1, 100)
	}
}
func BenchmarkSum(b *testing.B) {
	for i := 0; i < b.N; i++ {
		dickson.Sum(1000)
	}
}

// Package dickson calculates pythagorean triplets using Dickson's method.
// https://en.wikipedia.org/wiki/Formulas_for_generating_Pythagorean_triples#Dickson's_method
package dickson
import (
	"pythagorean"
)
// Range return a list of all Pythagorean triplets with sides int he range min to max inclusive.
func Range(min, max int) []pythagorean.Triplet {
	ret := []pythagorean.Triplet{}
	var a, b, c int
	for c < max {
		for r := 2; r < max/2; r = r + 2 {
			fact := factors((r * r) / 2)
			for i := 0; i < len(fact)/2; i++ {
				s := fact[i]
				t := (r * r) / 2 / fact[i]
				a = r + s
				b = r + t
				c = r + s + t
				if a >= min && c <= max {
					ret = append(ret, pythagorean.Triplet{a, b, c})
				}
			}
		}
	}
	return ret
}
func factors(input int) []int {
	var factor []int
	for i := 1; i < input/2+1; i++ {
		if input%i == 0 {
			factor = append(factor, i)
		}
	}
	factor = append(factor, input)
	return factor
}
// Sum returns a list of all Pythagorean triplets where the sum a+b+c is equal to p.
func Sum(p int) []pythagorean.Triplet {
	var ret []pythagorean.Triplet
	candidates := Range(1, p/2)
	for i, tr := range candidates {
		if tr[0]+tr[1]+tr[2] == p {
			ret = append(ret, candidates[i])
		}
	}
	return ret
}