====== MPI Ring Algorithm ======

In this algorithm, processes form a logical ring. Each process sends a message to the next process in the ring (the last process sends the message back to the first process). This is a typical example used to demonstrate MPI communication patterns.

<code c mpi-ring-algorithm.c>
#include <mpi.h>
#include <stdio.h>

int main(int argc, char** argv) {
    // Initialize the MPI environment
    MPI_Init(&argc, &argv);

    // Get the rank of the process
    int world_rank;
    MPI_Comm_rank(MPI_COMM_WORLD, &world_rank);

    // Get the total number of processes
    int world_size;
    MPI_Comm_size(MPI_COMM_WORLD, &world_size);

    // Variable to hold the message
    int token;

    // Determine the rank of the next process in the ring
    int next_rank = (world_rank + 1) % world_size;

    // Determine the rank of the previous process in the ring
    int prev_rank = world_rank - 1;
    if (prev_rank < 0) {
        prev_rank = world_size - 1;
    }

    // The first process starts the ring
    if (world_rank == 0) {
        // Set the initial value of the token
        token = -1;
        MPI_Send(&token, 1, MPI_INT, next_rank, 0, MPI_COMM_WORLD);
        MPI_Recv(&token, 1, MPI_INT, prev_rank, 0, MPI_COMM_WORLD, MPI_STATUS_IGNORE);
        printf("Process %d received token %d from process %d\n", world_rank, token, prev_rank);
    } else {
        // All other processes
        MPI_Recv(&token, 1, MPI_INT, prev_rank, 0, MPI_COMM_WORLD, MPI_STATUS_IGNORE);
        printf("Process %d received token %d from process %d\n", world_rank, token, prev_rank);
        // Increment the token's value
        token += 1;
        MPI_Send(&token, 1, MPI_INT, next_rank, 0, MPI_COMM_WORLD);
    }

    // Finalize the MPI environment
    MPI_Finalize();
}
</code>

**Initialization**: The MPI environment is initialized.

**Determining Next and Previous Rank**: Each process calculates the rank of the next and previous process in the ring.

**Ring Communication**:
The first process (rank 0) initializes the token (here, with a value of -1) and sends it to the next process.
Each subsequent process receives the token from the previous process, increments its value, and sends it to the next process. \\ 
The first process completes the ring by receiving the token from the last process.

**Output**: Each process prints a message when it receives the token, showing its current value and the rank of the process that sent it.

**Finalization**: The MPI environment is finalized.

This program forms a simple ring where each process communicates with its immediate neighbor, and the token travels around the ring.