878892. Right Angle Triangle
Right Angle Triangle
Summary
The problem involves generating all possible right angle triangles with a given set of integer values. The input consists of two integers, and we need to find all possible combinations of two integers from 1 to that can form a right angle triangle.
Detailed Explanation
To solve this problem, we'll use the concept of Pythagorean triples. A right-angled triangle has legs of length a and b, and hypotenuse c. The condition for a right-angled triangle is that a^2 + b^2 = c^2.
We can generate all possible combinations of two integers from 1 to n, calculate their sum as the hypotenuse (c), and check if they satisfy the Pythagorean condition. If they do, we've found another right angle triangle.
Here's the step-by-step solution:
- Initialize an empty list to store the right angle triangles.
- Iterate through all possible combinations of two integers from 1 to n.
- Calculate the sum of the two integers as the hypotenuse (c).
- Check if the Pythagorean condition is satisfied: a^2 + b^2 = c^2.
- If it is, add the triangle to the list.
Time complexity: O(n^2), where n is the input integer. Space complexity: O(n), as we need to store all possible right angle triangles in the list.
Optimized Solutions
Java
import java.util.ArrayList;
import java.util.List;
public class RightAngleTriangle {
public static List<String> generateTriangles(int n) {
List<String> triangles = new ArrayList<>();
for (int i = 1; i <= n; i++) {
for (int j = i; j <= n; j++) {
int c = i * i + j * j;
if (Math.sqrt(c) % 1 == 0) { // Check Pythagorean condition
triangles.add(String.format("(%d, %d, %d)", i, j, (int) Math.sqrt(c)));
}
}
}
return triangles;
}
public static void main(String[] args) {
int n = 5; // Example input
List<String> triangles = generateTriangles(n);
System.out.println(triangles);
}
}