matrixChainMultiply.java

/* A naive recursive implementation that simply follows
the above optimal substructure property */
class MatrixChainMultiplication {
	// Matrix Ai has dimension p[i-1] x p[i] for i = 1..n
	static int MatrixChainOrder(int p[], int i, int j)
	{
		if (i == j)
			return 0;

		int min = Integer.MAX_VALUE;

		// place parenthesis at different places between
		// first and last matrix, recursively calculate
		// count of multiplications for each parenthesis
		// placement and return the minimum count
		for (int k = i; k < j; k++)
		{
			int count = MatrixChainOrder(p, i, k)
						+ MatrixChainOrder(p, k + 1, j)
						+ p[i - 1] * p[k] * p[j];

			if (count < min)
				min = count;
		}

		// Return minimum count
		return min;
	}

	// Driver code
	public static void main(String args[])
	{
		int arr[] = new int[] { 1, 2, 3, 4, 3 };
		int n = arr.length;

		System.out.println(
			"Minimum number of multiplications is "
			+ MatrixChainOrder(arr, 1, n - 1));
	}
}
/* This code is contributed by Rajat Mishra*/