matrix_chain_multiplication.cpp

#include <climits>
#include <iostream>
using namespace std;

#define MAX 10

// dp table to store the solution for already computed sub problems
int dp[MAX][MAX];

// Function to find the most efficient way to multiply the given sequence of
// matrices
int MatrixChainMultiplication(int dim[], int i, int j) {
    // base case: one matrix
    if (j <= i + 1)
        return 0;

    // stores minimum number of scalar multiplications (i.e., cost)
    // needed to compute the matrix M[i+1]...M[j] = M[i..j]
    int min = INT_MAX;

    // if dp[i][j] is not calculated (calculate it!!)

    if (dp[i][j] == 0) {
        // take the minimum over each possible position at which the
        // sequence of matrices can be split

        for (int k = i + 1; k <= j - 1; k++) {
            // recur for M[i+1]..M[k] to get a i x k matrix
            int cost = MatrixChainMultiplication(dim, i, k);

            // recur for M[k+1]..M[j] to get a k x j matrix
            cost += MatrixChainMultiplication(dim, k, j);

            // cost to multiply two (i x k) and (k x j) matrix
            cost += dim[i] * dim[k] * dim[j];

            if (cost < min)
                min = cost;  // store the minimum cost
        }
        dp[i][j] = min;
    }

    // return min cost to multiply M[j+1]..M[j]
    return dp[i][j];
}

// main function
int main() {
    // Matrix i has Dimensions dim[i-1] & dim[i] for i=1..n
    // input is 10 x 30 matrix, 30 x 5 matrix, 5 x 60 matrix
    int dim[] = {10, 30, 5, 60};
    int n = sizeof(dim) / sizeof(dim[0]);

    // Function Calling: MatrixChainMultiplications(dimensions_array, starting,
    // ending);

    cout << "Minimum cost is " << MatrixChainMultiplication(dim, 0, n - 1)
         << "\n";

    return 0;
}