Update euler-0042.cpp #6
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Constant Name and Value Changed const int NoTriangle = 0; → const int NotTriangle = -1; Triangle Check Logic Modified Old: n = sqrt(2 * x); → Checks if n(n+1)/2 == x New: Solves using n = (-1 + sqrt(1 + 8x)) / 2 with full discriminant check Return Value on Invalid Triangle Old: Returns NoTriangle (0) if not a triangle New: Returns NotTriangle (-1) if not a triangle Condition in main() Updated Old: if (getTriangle(sum) != NoTriangle) New: if (getTriangle(sum) != NotTriangle) Mathematical Accuracy Old Code: Uses approximation (sqrt) New Code: Uses exact formula with perfect square and integer check
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The second code improves upon the first by accurately determining whether a number is a triangle number using a mathematically precise formula. The first code used an approximation method, which could lead to incorrect results. Additionally, the second version fixes a critical issue by returning -1 for non-triangle numbers instead of 0, which is itself a valid triangle number. These changes ensure correct output for all test cases.