Dining Philosophers

**Concurrency design problem (paper-only).** Threading is not available in the sandbox; the auto-grader validates a simulation of a deadlock-free fork-acquisition order. Five silent philosophers sit at a round table with bowls of spaghetti. Forks are placed between each pair of adjacent philosophers. Each philosopher must alternately think and eat. However, a philosopher can only eat when they have both the left and right forks. Each fork can be held by only one philosopher at a time. After eating, they need to put down both forks so they become available to others. Naïve "pick up left then pick up right" deadlocks if every philosopher grabs a left fork simultaneously. You must produce a deadlock-free schedule. **For the auto-grader:** given an integer array `order` of length `5 * meals` representing the order in which philosophers `0..4` would *like* to eat (each value 0..4, each value appears exactly `meals` times), return an array of the same length giving the order in which they actually eat under the **odd-even** strategy: philosopher `i` is allowed to eat next iff neither of their forks is currently held. The simulation processes the wish-list from left to right; if the current wisher's neighbours are eating they are skipped to the back of a waiting queue, and you re-check the queue first on each step. The output array must be a valid deadlock-free permutation in which no two adjacent philosophers (mod 5) ever appear in adjacent positions of the output.