Change project structure to a Maven Java project + Refactor (#2816)

src/main/java/com/thealgorithms/dynamicprogramming/MatrixChainRecursiveTopDownMemoisation.java

@@ -0,0 +1,47 @@
+package com.thealgorithms.dynamicprogramming;
+
+// Matrix-chain Multiplication
+// Problem Statement
+// we have given a chain A1,A2,...,Ani of n matrices, where for i = 1,2,...,n, 
+// matrix Ai has dimension pi−1 ×pi
+// , fully parenthesize the product A1A2 ···An in a way that
+// minimizes the number of scalar multiplications.
+public class MatrixChainRecursiveTopDownMemoisation {
+
+    static int Memoized_Matrix_Chain(int p[]) {
+        int n = p.length;
+        int m[][] = new int[n][n];
+        for (int i = 0; i < n; i++) {
+            for (int j = 0; j < n; j++) {
+                m[i][j] = Integer.MAX_VALUE;
+            }
+        }
+        return Lookup_Chain(m, p, 1, n - 1);
+    }
+
+    static int Lookup_Chain(int m[][], int p[], int i, int j) {
+        if (i == j) {
+            m[i][j] = 0;
+            return m[i][j];
+        }
+        if (m[i][j] < Integer.MAX_VALUE) {
+            return m[i][j];
+        } else {
+            for (int k = i; k < j; k++) {
+                int q = Lookup_Chain(m, p, i, k) + Lookup_Chain(m, p, k + 1, j) + (p[i - 1] * p[k] * p[j]);
+                if (q < m[i][j]) {
+                    m[i][j] = q;
+                }
+            }
+        }
+        return m[i][j];
+    }
+
+    // in this code we are taking the example of 4 matrixes whose orders are 1x2,2x3,3x4,4x5 respectively
+    // output should be  Minimum number of multiplications is 38
+    public static void main(String[] args) {
+
+        int arr[] = {1, 2, 3, 4, 5};
+        System.out.println("Minimum number of multiplications is " + Memoized_Matrix_Chain(arr));
+    }
+}