initial

Author: shivu2806

matrixChainMultiply.java

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+/* 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*/