matrix_chain_multiplication.cpp

#include<iostream>
#include<limits.h>

using namespace std;


int MatrixChainMultiplication(int p[], int n)
{
    int m[n][n];
    int i, j, k, L, q;

    for (i=1; i<n; i++)
        m[i][i] = 0;
    for (L=2; L<n; L++)
    {
        for (i=1; i<n-L+1; i++)
        {
            j = i+L-1;
            m[i][j] = INT_MAX;

            for (k=i; k<=j-1; k++)
            {
                q = m[i][k] + m[k+1][j] + p[i-1]*p[k]*p[j];
                if (q < m[i][j])
                {
                    m[i][j] = q;
                }
            }
        }
    }

    return m[1][n-1];

}

int main()
{
    int n,i;
    cout<<"Enter number of matrices\n";
    cin>>n;


    int arr[n];

    cout<<"Enter dimensions \n";

    for(i=0;i<n;i++)
    {
        cout<<"Enter d"<<i+1<<" :: ";
        cin>>arr[i];
    }

    int size = sizeof(arr)/sizeof(arr[0]);

    cout<<"Minimum number of multiplications is "<<MatrixChainMultiplication(arr, size);

    return 0;
}