The challenge
You have to give the number of different integer triangles with one angle of 120 degrees which perimeters are under or equal a certain value. Each side of an integer triangle is an integer value.
// number of integer triangles,
give_triang(max. perimeter)
with sides a, b, and c integers such that:
a + b + c <= max. perimeter
See some of the following cases
// No Integer triangles with perimeter under or equal five
give_triang(5) // 0
// One integer triangle of (120 degrees). It's (3, 5, 7)
give_triang(15) // 1
// Three triangles: (3, 5, 7), (6, 10, 14) and (7, 8, 13)
give_triang(30) // 3
// (3, 5, 7), (5, 16, 19), (6, 10, 14), (7, 8, 13) and (9, 15, 21) are the triangles with perim under or equal 50.
give_triang(50) // 5
The solution in Java code
Option 1:
public class IntTriangles {
public static int giveTriang(int per) {
int cnt = 0; int a = 3;
while (a < per) {
if (2*a > per) break;
int b = a;
while (b < per) {
if (a + 2*b > per) break;
double c = Math.sqrt(a*a + a*b + b*b);
if ((c % 1 == 0) && (a+b+c <= per))
cnt++;
b++;
}
a++;
}
return cnt;
}
}
Option 2:
public class IntTriangles {
public static int giveTriang(int per) {
int res = 0;
for(int i =1;i<per-1;i++)
for(int j = i;j<per-1;j++){
double k = Math.sqrt(i*i+i*j+j*j);
if(i+j+k<=per&&i+j>k&&j+k>i&&k+i>j&&k%1==0)
res++;
}
return res;
}
}
Option 3:
public class IntTriangles {
public static int giveTriang(int per) {
int count = 0;
for (int a = 1; a < per / 2; a++) {
for (int b = 1; b < a; b++) {
double cSquare = a * a + b * b + a * b;
int c = (int)Math.sqrt(cSquare);
if (c * c == cSquare && a + b + c <= per) {
count++;
}
}
}
return count;
}
}
Test cases to validate our solution
import static org.junit.Assert.*;
import java.util.Random;
import org.junit.Test;
public class IntTrianglesTest {
private static void testing(int i, int results) {
assertEquals(results, i);
}
public static void tests(int[] list1, int[] results) {
for (int i = 0; i < list1.length; i++)
testing(IntTriangles.giveTriang(list1[i]), results[i]);
return;
}
@Test
public void test1() {
System.out.println("Basic Tests");
int[] list1 = new int[] {5, 15, 30, 50, 80, 90, 100, 150, 180, 190};
int[] results = new int[] {0, 1, 3, 5, 11, 13, 14, 25, 32, 35};
tests(list1, results);
}
}
