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.
+ * + *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.
+ */ 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 @@ public final class MatrixChainRecursiveTopDownMemoisation { 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 @@ public final class MatrixChainRecursiveTopDownMemoisation { } 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)); - } } diff --git a/src/test/java/com/thealgorithms/dynamicprogramming/MatrixChainRecursiveTopDownMemoisationTest.java b/src/test/java/com/thealgorithms/dynamicprogramming/MatrixChainRecursiveTopDownMemoisationTest.java new file mode 100644 index 000000000..f8270f6d5 --- /dev/null +++ b/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."); + } +}