Matrix-Chain-Multiplication.cpp

#include <iostream>
#include <climits>
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;
}