Status: IN
Solutions for problems with circular, periodic, or wrap-around structure uniformly reduce to O(1) closed-form expressions via modular arithmetic (min-of-diff-and-complement for shortest arc, mod-then-truncate for cyclic shifts, division-and-modulo for periodic bouncing), eliminating iterative simulation entirely.
Three independent solutions use modular arithmetic to achieve O(1) on structurally similar circular/periodic problems — the shared technique constitutes a coherent reduction strategy complementary to algebraic closed-form reductions.
Depends on (SL): circular-distance-idiom-min-diff-n-minus-diff, shift-grid-k-mod-optimization, pillow-holder-o1-time