====== MPI Scan ======

**MPI_Scan** is similar to **MPI_Reduce**, but instead of gathering the reduced result at a single root process, it performs a parallel prefix reduction, providing each process with a partial result of the reduction operation up to that point in the sequence of processes.

In this example, each process will generate a random number, and we'll use **MPI_Scan** to compute the cumulative sum of these numbers across all processes. Each process will receive the sum of random numbers from the first process up to itself.

<code c mpi-scan.c>
#include <mpi.h>
#include <stdio.h>
#include <stdlib.h>
#include <time.h>

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

    // Get the rank of the process and the total number of processes
    int world_rank, world_size;
    MPI_Comm_rank(MPI_COMM_WORLD, &world_rank);
    MPI_Comm_size(MPI_COMM_WORLD, &world_size);

    // Seed the random number generator to get different results each time
    srand(time(NULL) + world_rank);

    // Generate a random number at each process
    int rand_num = rand() % 100;

    printf("Process %d generated number %d\n", world_rank, rand_num);

    // Use MPI_Scan to compute the cumulative sum of all random numbers
    int cum_sum;
    MPI_Scan(&rand_num, &cum_sum, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD);

    // Each process prints its partial sum
    printf("Process %d has cumulative sum %d\n", world_rank, cum_sum);

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

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

**Random Number Generation**: Each process generates a random number.

**Scan Operation**: **MPI_Scan** is used to compute the cumulative sum of the random numbers. Each process receives the sum of random numbers from the start up to its rank.

**Output**: Each process prints its rank and its cumulative sum.

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

This program demonstrates the use of **MPI_Scan** for computing cumulative sums across processes in an MPI environment.