Law of cosines - triples: Difference between revisions

=={{header|Java}}==

<lang java>

public class LawOfCosines {

public static void main(String[] args) {

generateTriples(13);

generateTriples60(10000);

}

private static void generateTriples(int max) {

for ( int coeff : new int[] {0, -1, 1} ) {

int count = 0;

System.out.printf("Max side length %d, formula: a*a + b*b %s= c*c%n", max, coeff == 0 ? "" : (coeff>0 ? "-" : "+") + " a*b ");

for ( int a = 1 ; a <= max ; a++ ) {

for ( int b = 1 ; b <= a ; b++ ) {

int val = a*a + b*b + coeff*a*b;

int c = (int) (Math.sqrt(val) + .5d);

if ( c > max ) {

break;

}

if ( c*c == val ) {

System.out.printf(" (%d, %d, %d)%n", a, b ,c);

count++;

}

}

}

System.out.printf("%d triangles%n", count);

}

}

private static void generateTriples60(int max) {

int count = 0;

System.out.printf("%nExtra Credit.%nMax side length %d, sides different length, formula: a*a + b*b - a*b = c*c%n", max);

for ( int a = 1 ; a <= max ; a++ ) {

for ( int b = 1 ; b < a ; b++ ) {

int val = a*a + b*b - a*b;

int c = (int) (Math.sqrt(val) + .5d);

if ( c > max ) {

break;

}

if ( c*c == val ) {

count++;

}

}

}

System.out.printf("%d triangles%n", count);

}

}

</lang>

{{out}}

<pre>

Max side length 13, formula: a*a + b*b = c*c

(4, 3, 5)

(8, 6, 10)

(12, 5, 13)

3 triangles

Max side length 13, formula: a*a + b*b + a*b = c*c

(1, 1, 1)

(2, 2, 2)

(3, 3, 3)

(4, 4, 4)

(5, 5, 5)

(6, 6, 6)

(7, 7, 7)

(8, 3, 7)

(8, 5, 7)

(8, 8, 8)

(9, 9, 9)

(10, 10, 10)

(11, 11, 11)

(12, 12, 12)

(13, 13, 13)

15 triangles

Max side length 13, formula: a*a + b*b - a*b = c*c

(5, 3, 7)

(8, 7, 13)

2 triangles

Extra Credit.

Max side length 10000, sides different length, formula: a*a + b*b - a*b = c*c

18394 triangles

</pre>