Solution Explanation for the Dining Philosophers Problem

The Dining Philosophers problem is a classic concurrency problem that illustrates the challenges of deadlock and starvation in concurrent systems. The solution presented uses C++ mutexes and scoped locks to prevent these issues.

Approach

The core idea is to prevent deadlock by ensuring that philosophers acquire forks in a specific order. Deadlock occurs when two or more philosophers simultaneously grab one fork each, preventing any of them from getting the second fork and proceeding to eat. Starvation occurs when a philosopher is perpetually unable to acquire the necessary resources to eat.

The provided C++ solution uses a vector of mutex objects, mutexes_, one for each fork. A philosopher, before attempting to eat, tries to acquire the mutexes for both its left and right forks. Crucially, the code employs std::scoped_lock to acquire these locks in a specific order. std::scoped_lock ensures that the locks are acquired atomically (all or none), preventing partial acquisition and thus avoiding deadlock.

The order of acquiring the locks is important. A philosopher will always try to acquire the mutex associated with the fork that's lower in index order. If philosopher 1 has forks 1 and 2, then he'll grab mutex 1 before mutex 2. This prevents circular dependencies.

After eating, the philosopher releases both forks by letting go of the mutexes. This allows other philosophers to acquire the forks.

C++ Code Explained

class DiningPhilosophers {
public:
    using Act = function<void()>;
 
    void wantsToEat(int philosopher, Act pickLeftFork, Act pickRightFork, Act eat, Act putLeftFork, Act putRightFork) {
        std::scoped_lock lock(mutexes_[philosopher], mutexes_[philosopher >= 4 ? 0 : philosopher + 1]);
        pickLeftFork();
        pickRightFork();
        eat();
        putLeftFork();
        putRightFork();
    }
 
private:
    vector<mutex> mutexes_ = vector<mutex>(5);
};

1. using Act = function<void()>;: This line defines a type alias Act for a function that takes no arguments and returns void. This is used to represent the actions of picking up/putting down forks and eating.

2. vector<mutex> mutexes_ = vector<mutex>(5);: This creates a vector of five mutexes. Each mutex represents a fork.

3. wantsToEat(...): This function is the core logic.

   • std::scoped_lock lock(mutexes_[philosopher], mutexes_[philosopher >= 4 ? 0 : philosopher + 1]);: This line is crucial. It uses std::scoped_lock to acquire two mutexes atomically:
     • mutexes_[philosopher]: The mutex representing the philosopher's left fork.
     • mutexes_[philosopher >= 4 ? 0 : philosopher + 1]: The mutex representing the philosopher's right fork. The ternary operator handles the case of philosopher 4 (the last philosopher), whose right fork is fork 0.
   • The pickLeftFork(), pickRightFork(), eat(), putLeftFork(), and putRightFork() calls are placeholders for the actual actions. These would be provided by the LeetCode environment.
   • The scoped_lock automatically releases the mutexes when the function exits, even if exceptions are thrown.

Time and Space Complexity

• Time Complexity: The time complexity is highly dependent on the concurrency and the specific implementation details of the mutexes and the eat function. In the best case (no contention), it's O(1) for each philosopher. However, in the worst case (high contention), the time complexity could be unbounded due to the potential for waiting on mutexes.

• Space Complexity: The space complexity is O(n), where n is the number of philosophers (5 in this case). This is due to the storage of the mutexes_ vector.

This solution effectively avoids deadlock and starvation by carefully managing the acquisition and release of resources (forks) using mutexes and a specific locking order. The use of scoped_lock ensures atomicity and simplifies the code, making it easier to reason about the correctness.