Solution to Project Euler Problem 39: Integer right triangles - If p is the perimeter of a right angle triangle with integral length sides, {a,b,c}, there are exactly three solutions for p = 120. {20,48,52}, {24,45,51}, {30,40,50} For which value of p ≤ 1000, is the number of solutions maximised?

• Java Code

package sikademy;
/**
 *
 * @author Archangel Macsika
 * Copyright (c) Sikademy. All rights reserved
 */

public class SikademyEulerSolution {
	
	public String run() {
		int maxPerimeter = 0;
		int maxTriangles = 0;
		for (int p = 1; p <= 1000; p++) {
			int triangles = countSolutions(p);
			if (triangles > maxTriangles) {
				maxTriangles = triangles;
				maxPerimeter = p;
			}
		}
		return Integer.toString(maxPerimeter);
	}
	
	
	private static int countSolutions(int p) {
		int count = 0;
		for (int a = 1; a <= p; a++) {
			for (int b = a; b <= p; b++) {
				int c = p - a - b;
				if (b <= c && a * a + b * b == c * c)
					count++;
			}
		}
		return count;
	}

	public static void main(String[] args) {
                SikademyEulerSolution solution = new SikademyEulerSolution();
		System.out.println(solution.run());
	}	
}

• Python Code

# 
# @author Archangel Macsika
# Copyright (c) Sikademy. All rights reserved.
# 

def compute():
	ans = max(range(1, 1001), key=count_solutions)
	return str(ans)


def count_solutions(p):
	result = 0
	for a in range(1, p + 1):
		for b in range(a, (p - a) // 2 + 1):
			c = p - a - b  # c >= b
			if a * a + b * b == c * c:
				result += 1
	return result


if __name__ == "__main__":
	print(compute())