MatrixChainMultiplication.cpp

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

using namespace std;

/*———————————————————————————————————————————————————————————————————————————*/
// Matrix Ai has dimension p[i-1] x p[i] for i = 1..n
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; //number of multiplications are 0(zero) when there is only one matrix
        
    //Here L is chain length. It varies from length 2 to length n.
    for (L = 2; L < n; L++){
        for (i = 1; i < (n - L + 1); i++){
            j =  i + L - 1; 
            m[i][j] = INT_MAX; //assigning to maximum value
            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; //if number of multiplications found less that number will be updated.
                }
            }
        }
    }
    return m[1][n-1]; //returning the final answer which is M[1][n-1]
}

/*———————————————————————————————————————————————————————————————————————————*/
int main(){
    int n, i;
    cout << "Enter number of matrices : ";
   
    cin >> n;
    n++;
    
    int arr[n];
    cout<<"Enter dimensions \n";
    
    for(i = 0; i < n; i++){
        cout << "Enter d" << i << " :: ";
        cin >> arr[i];
    }
    
    int size = sizeof(arr) / sizeof(arr[0]);
    cout << "\nMinimum number of multiplications is : " << MatrixChainMultiplication(arr, size);
    return 0;
}