Improve docs, remove main, add tests for `MatrixChainRecursiveTopDo… (#5659)

Author: Hardvan

DIRECTORY.md

@@ -836,6 +836,7 @@
             * [LongestPalindromicSubstringTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/dynamicprogramming/LongestPalindromicSubstringTest.java)
             * [LongestValidParenthesesTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/dynamicprogramming/LongestValidParenthesesTest.java)
             * [MatrixChainMultiplicationTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/dynamicprogramming/MatrixChainMultiplicationTest.java)
+            * [MatrixChainRecursiveTopDownMemoisationTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/dynamicprogramming/MatrixChainRecursiveTopDownMemoisationTest.java)
             * [MaximumSumOfNonAdjacentElementsTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/dynamicprogramming/MaximumSumOfNonAdjacentElementsTest.java)
             * [MinimumPathSumTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/dynamicprogramming/MinimumPathSumTest.java)
             * [MinimumSumPartitionTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/dynamicprogramming/MinimumSumPartitionTest.java)

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

@@ -1,15 +1,31 @@
 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.
+/**
+ * The MatrixChainRecursiveTopDownMemoisation class implements the matrix-chain
+ * multiplication problem using a top-down recursive approach with memoization.
+ *
+ * <p>Given a chain of matrices A1, A2, ..., An, where matrix Ai has dimensions
+ * pi-1 × pi, this algorithm finds the optimal way to fully parenthesize the
+ * product A1A2...An in a way that minimizes the total number of scalar
+ * multiplications required.</p>
+ *
+ * <p>This implementation uses a memoization technique to store the results of
+ * subproblems, which significantly reduces the number of recursive calls and
+ * improves performance compared to a naive recursive approach.</p>
+ */
 public final class MatrixChainRecursiveTopDownMemoisation {
     private MatrixChainRecursiveTopDownMemoisation() {
     }
 
+    /**
+     * Calculates the minimum number of scalar multiplications needed to multiply
+     * a chain of matrices.
+     *
+     * @param p an array of integers representing the dimensions of the matrices.
+     *          The length of the array is n + 1, where n is the number of matrices.
+     * @return the minimum number of multiplications required to multiply the chain
+     *         of matrices.
+     */
     static int memoizedMatrixChain(int[] p) {
         int n = p.length;
         int[][] m = new int[n][n];
@@ -21,6 +37,17 @@ static int memoizedMatrixChain(int[] p) {
         return lookupChain(m, p, 1, n - 1);
     }
 
+    /**
+     * A recursive helper method to lookup the minimum number of multiplications
+     * for multiplying matrices from index i to index j.
+     *
+     * @param m the memoization table storing the results of subproblems.
+     * @param p an array of integers representing the dimensions of the matrices.
+     * @param i the starting index of the matrix chain.
+     * @param j the ending index of the matrix chain.
+     * @return the minimum number of multiplications needed to multiply matrices
+     *         from i to j.
+     */
     static int lookupChain(int[][] m, int[] p, int i, int j) {
         if (i == j) {
             m[i][j] = 0;
@@ -38,11 +65,4 @@ static int lookupChain(int[][] m, int[] p, int i, int j) {
         }
         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 " + memoizedMatrixChain(arr));
-    }
 }

src/test/java/com/thealgorithms/dynamicprogramming/MatrixChainRecursiveTopDownMemoisationTest.java

@@ -0,0 +1,68 @@
+package com.thealgorithms.dynamicprogramming;
+
+import static org.junit.jupiter.api.Assertions.assertEquals;
+
+import org.junit.jupiter.api.Test;
+
+class MatrixChainRecursiveTopDownMemoisationTest {
+
+    /**
+     * Test case for four matrices with dimensions 1x2, 2x3, 3x4, and 4x5.
+     * The expected minimum number of multiplications is 38.
+     */
+    @Test
+    void testFourMatrices() {
+        int[] dimensions = {1, 2, 3, 4, 5};
+        int expected = 38;
+        int actual = MatrixChainRecursiveTopDownMemoisation.memoizedMatrixChain(dimensions);
+        assertEquals(expected, actual, "The minimum number of multiplications should be 38.");
+    }
+
+    /**
+     * Test case for three matrices with dimensions 10x20, 20x30, and 30x40.
+     * The expected minimum number of multiplications is 6000.
+     */
+    @Test
+    void testThreeMatrices() {
+        int[] dimensions = {10, 20, 30, 40};
+        int expected = 18000;
+        int actual = MatrixChainRecursiveTopDownMemoisation.memoizedMatrixChain(dimensions);
+        assertEquals(expected, actual, "The minimum number of multiplications should be 18000.");
+    }
+
+    /**
+     * Test case for two matrices with dimensions 5x10 and 10x20.
+     * The expected minimum number of multiplications is 1000.
+     */
+    @Test
+    void testTwoMatrices() {
+        int[] dimensions = {5, 10, 20};
+        int expected = 1000;
+        int actual = MatrixChainRecursiveTopDownMemoisation.memoizedMatrixChain(dimensions);
+        assertEquals(expected, actual, "The minimum number of multiplications should be 1000.");
+    }
+
+    /**
+     * Test case for a single matrix.
+     * The expected minimum number of multiplications is 0, as there are no multiplications needed.
+     */
+    @Test
+    void testSingleMatrix() {
+        int[] dimensions = {10, 20}; // Single matrix dimensions
+        int expected = 0;
+        int actual = MatrixChainRecursiveTopDownMemoisation.memoizedMatrixChain(dimensions);
+        assertEquals(expected, actual, "The minimum number of multiplications should be 0.");
+    }
+
+    /**
+     * Test case for matrices with varying dimensions.
+     * The expected minimum number of multiplications is calculated based on the dimensions provided.
+     */
+    @Test
+    void testVaryingDimensions() {
+        int[] dimensions = {2, 3, 4, 5, 6}; // Dimensions for 4 matrices
+        int expected = 124; // Expected value needs to be calculated based on the problem
+        int actual = MatrixChainRecursiveTopDownMemoisation.memoizedMatrixChain(dimensions);
+        assertEquals(expected, actual, "The minimum number of multiplications should be 124.");
+    }
+}