{"id":"isqrt-over-sqrt-for-large-inputs","text":"Solutions needing integer square roots use `math.isqrt` instead of `int(math.sqrt(...))` to avoid floating-point precision errors, especially for inputs near 2^31-1.","truth_value":"IN","source":"entries/2026/06/06/arranging-coins-solution.md","source_url":"","source_hash":"","justifications":[],"dependents":["integer-arithmetic-avoids-float-precision"],"metadata":{},"created_at":"","updated_at":"","reviewed_at":"","verified_at":"","retracted_at":"","explanation":{"steps":[{"node":"isqrt-over-sqrt-for-large-inputs","truth_value":"IN","reason":"premise"}]}}