Right Angle Triangle 2

Summary

Given a right angle triangle with legs of length a and b, we need to find whether it is possible to have an integer hypotenuse c such that the Pythagorean theorem holds true (i.e., a^2 + b^2 = c^2). The problem involves basic number theory and mathematical concepts.

Detailed Explanation

The problem can be solved by using the mathematical concept of finding the greatest common divisor (GCD) of two numbers. We know that if we find an integer hypotenuse c such that a^2 + b^2 = c^2, then it must be true that c is an integer and c > max(a, b). Therefore, we can start by checking for all possible values of c up to the maximum value of a and b. For each value of c, check if a^2 + b^2 = c^2. If we find such a value of c, return it as the result.

Here's a step-by-step breakdown of the solution:

Find the maximum value of a and b.
Initialize a variable result to null.
Iterate over all possible values of c from 1 to max(a, b).
For each value of c, check if a^2 + b^2 = c^2.
If we find such a value of c, return it as the result.

Time complexity: O(max(a, b)) Space complexity: O(1)

Optimized Solutions

Java

public class RightAngleTriangle { public static int rightAngleTriangle(int a, int b) { int max = Math.max(a, b); for (int c = 1; c <= max; c++) { if (a * a + b * b == c * c) { return c; } } return -1; // No solution found } }