Problème
Find every triple of positive integers a < b < c for which a² + b² = c² and a + b + c = perimeter. Return each triple as [a, b, c], ordered by increasing a and then b. Do not include permutations of the same sides.
Implement pythagorean_triplets(perimeter).
Input
perimeter: The required sum of all three sides.
Output
Return a list of triples in the specified order.
Contraintes
3 ≤ perimeter ≤ 100,000. Return an empty list if no triangle qualifies.
Exemples
Entrée :
perimeter = 30
Sortie attendue :
expected = [
[5, 12, 13]
]Entrée :
long long perimeter = 30;
Sortie attendue :
std::vector<std::vector<long long>> expected = {
{5, 12, 13}
};Entrée :
long perimeter = 30;
Sortie attendue :
long[][] expected = new long[][] {
new long[] {5, 12, 13}
};Explication
5 + 12 + 13 = 30 and 5² + 12² = 13². This is the only qualifying triple.
Entrée :
perimeter = 11
Sortie attendue :
expected = []Entrée :
long long perimeter = 11;
Sortie attendue :
std::vector<std::vector<long long>> expected = {};Entrée :
long perimeter = 11;
Sortie attendue :
long[][] expected = new long[][] {};Explication
No increasing positive integer right-triangle triple sums to 11.
Comment l'aborder
Essayez d'abord seul, puis ouvrez les indices un par un.
Indice 1
A valid triple must satisfy both the Pythagorean equation and the perimeter sum.
Indice 2
Use the perimeter to limit the search instead of trying every ordering of sides.
Indice 3
Remember to keep only a < b < c, and skip duplicates from symmetric side choices.
Complexité attendue
O(n^2) time, O(1) extra space
Références
Ce défi a été adapté pour CodeUtility. Suivez l'énoncé et les contraintes ci-dessus.