matrixchain.cpp

#include <iostream>
#include <vector>
#include <climits>
using namespace std;
 
// Function to find the most efficient way to multiply
// a given sequence of matrices
int matrixChainMultiplication(vector<int> const &dims)
{
    int n = dims.size();
 
    // c[i, j] = Minimum number of scalar multiplications (i.e., cost)
    // needed to compute matrix `M[i] M[i+1] … M[j] = M[i…j]`
    // The cost is zero when multiplying one matrix
    int c[n + 1][n + 1];
 
    for (int i = 1; i <= n; i++) {
        c[i][i] = 0;
    }
 
    for (int len = 2; len <= n; len++)        // subsequence lengths
    {
        for (int i = 1; i <= n - len + 1; i++)
        {
            int j = i + len - 1;
            c[i][j] = INT_MAX;
 
            for (int k = i; j < n && k <= j - 1; k++)
            {
                int cost = c[i][k] + c[k + 1][j] + dims[i - 1] * dims[k] * dims[j];
                if (cost < c[i][j]) {
                    c[i][j] = cost;
                }
            }
        }
    }
    return c[1][n - 1];
}
 
// Matrix Chain Multiplication Problem
int main()
{
    // Matrix `M[i]` has dimension `dims[i-1] × dims[i]` for `i=1…n`
    // input is 10 × 30 matrix, 30 × 5 matrix, 5 × 60 matrix
    vector<int> dims = { 10, 30, 5, 60 };
 
    cout << "The minimum cost is " << matrixChainMultiplication(dims);
 
    return 0;
}