Problem
Find positive integers a < b < c with a² + b² = c² and a + b + c = perimeter. Return the largest product a × b × c among qualifying triangles, or −1 if there are none. This generalizes the fixed-perimeter source task and explicitly handles multiple answers.
Implement pythagorean_product(perimeter).
Input
perimeter: The required sum of the three sides.
Output
Return the largest product, or −1 when no triangle qualifies.
Constraints
3 ≤ perimeter ≤ 100,000. Products fit signed 64-bit integers.
Examples
Input:
perimeter = 30
Expected output:
expected = 780Input:
long long perimeter = 30;
Expected output:
long long expected = 780;Input:
long perimeter = 30;
Expected output:
long expected = 780;Explanation
The triangle is (5, 12, 13): 25 + 144 = 169 and 5 + 12 + 13 = 30. Its product is 780.
Input:
perimeter = 11
Expected output:
expected = -1Input:
long long perimeter = 11;
Expected output:
long long expected = -1;Input:
long perimeter = 11;
Expected output:
long expected = -1;Explanation
No increasing positive integer right-triangle sides sum to 11.
How to approach it
Try on your own first, then open one hint at a time.
Hint 1
Only certain perimeters can form a right triangle, so first narrow the search using the side-sum constraint.
Hint 2
For each possible shortest side, derive the other two sides from the perimeter and check the right-triangle condition.
Hint 3
More than one triangle may fit; keep the largest product and return no-solution when nothing valid appears.
Expected complexity
O(perimeter^2) time, O(1) extra space
References
This challenge is adapted for CodeUtility. Follow the statement and constraints above.