879201. Right Angle Triangle
Here is the detailed Markdown blog post for the GeeksforGeeks problem:
Right Angle Triangle
Summary
The problem involves generating all possible right-angle triangles with a given hypotenuse length. The key concept involved is basic geometry, specifically Pythagorean triples.
Detailed Explanation
The problem can be solved by using a simple algorithm that iterates over the possible lengths of the sides and checks if they form a right-angle triangle. The algorithm starts by initializing variables for the sides (a, b) and the hypotenuse (c). Then it uses a loop to iterate over all possible values of a and calculates the corresponding value of b using the Pythagorean theorem. It then checks if the calculated value of b is less than or equal to c.
Here's a step-by-step breakdown of the solution:
- Initialize variables:
a,b, andc(hypotenuse) - Loop over possible values of
a - Calculate
busing Pythagorean theorem (b = sqrt(c^2 - a^2)) - Check if calculated value of
bis less than or equal toc - If true, print the triangle (or store it in an array/list)
The time complexity of this algorithm is O(n), where n is the maximum possible value of a. The space complexity is O(1) since we only need a constant amount of space to store the variables.
Optimized Solutions
Java
public class RightAngleTriangle {
public static void generate(int c) {
for (int a = 1; a <= c; a++) {
int b = (int) Math.sqrt(c * c - a * a);
if (b <= c) {
System.out.println("Triangle with sides " + a + ", " + b + ", and " + c);
}
}
}
}