diff --git a/DIRECTORY.md b/DIRECTORY.md index 46affca47109..1407ba199756 100644 --- a/DIRECTORY.md +++ b/DIRECTORY.md @@ -814,6 +814,7 @@ * [LongestIncreasingSubsequenceTests](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/dynamicprogramming/LongestIncreasingSubsequenceTests.java) * [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) * [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) * [OptimalJobSchedulingTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/dynamicprogramming/OptimalJobSchedulingTest.java) diff --git a/src/main/java/com/thealgorithms/dynamicprogramming/MatrixChainMultiplication.java b/src/main/java/com/thealgorithms/dynamicprogramming/MatrixChainMultiplication.java index 45568d21f295..1edb7207dee2 100644 --- a/src/main/java/com/thealgorithms/dynamicprogramming/MatrixChainMultiplication.java +++ b/src/main/java/com/thealgorithms/dynamicprogramming/MatrixChainMultiplication.java @@ -2,38 +2,32 @@ import java.util.ArrayList; import java.util.Arrays; -import java.util.Scanner; +/** + * The MatrixChainMultiplication class provides functionality to compute the + * optimal way to multiply a sequence of matrices. The optimal multiplication + * order is determined using dynamic programming, which minimizes the total + * number of scalar multiplications required. + */ public final class MatrixChainMultiplication { private MatrixChainMultiplication() { } - private static final Scanner SCANNER = new Scanner(System.in); - private static final ArrayList MATRICES = new ArrayList<>(); - private static int size; + // Matrices to store minimum multiplication costs and split points private static int[][] m; private static int[][] s; private static int[] p; - public static void main(String[] args) { - int count = 1; - while (true) { - String[] mSize = input("input size of matrix A(" + count + ") ( ex. 10 20 ) : "); - int col = Integer.parseInt(mSize[0]); - if (col == 0) { - break; - } - int row = Integer.parseInt(mSize[1]); - - Matrix matrix = new Matrix(count, col, row); - MATRICES.add(matrix); - count++; - } - for (Matrix m : MATRICES) { - System.out.format("A(%d) = %2d x %2d%n", m.count(), m.col(), m.row()); - } - - size = MATRICES.size(); + /** + * Calculates the optimal order for multiplying a given list of matrices. + * + * @param matrices an ArrayList of Matrix objects representing the matrices + * to be multiplied. + * @return a Result object containing the matrices of minimum costs and + * optimal splits. + */ + public static Result calculateMatrixChainOrder(ArrayList matrices) { + int size = matrices.size(); m = new int[size + 1][size + 1]; s = new int[size + 1][size + 1]; p = new int[size + 1]; @@ -44,51 +38,20 @@ public static void main(String[] args) { } for (int i = 0; i < p.length; i++) { - p[i] = i == 0 ? MATRICES.get(i).col() : MATRICES.get(i - 1).row(); + p[i] = i == 0 ? matrices.get(i).col() : matrices.get(i - 1).row(); } - matrixChainOrder(); - for (int i = 0; i < size; i++) { - System.out.print("-------"); - } - System.out.println(); - printArray(m); - for (int i = 0; i < size; i++) { - System.out.print("-------"); - } - System.out.println(); - printArray(s); - for (int i = 0; i < size; i++) { - System.out.print("-------"); - } - System.out.println(); - - System.out.println("Optimal solution : " + m[1][size]); - System.out.print("Optimal parens : "); - printOptimalParens(1, size); - } - - private static void printOptimalParens(int i, int j) { - if (i == j) { - System.out.print("A" + i); - } else { - System.out.print("("); - printOptimalParens(i, s[i][j]); - printOptimalParens(s[i][j] + 1, j); - System.out.print(")"); - } - } - - private static void printArray(int[][] array) { - for (int i = 1; i < size + 1; i++) { - for (int j = 1; j < size + 1; j++) { - System.out.printf("%7d", array[i][j]); - } - System.out.println(); - } + matrixChainOrder(size); + return new Result(m, s); } - private static void matrixChainOrder() { + /** + * A helper method that computes the minimum cost of multiplying + * the matrices using dynamic programming. + * + * @param size the number of matrices in the multiplication sequence. + */ + private static void matrixChainOrder(int size) { for (int i = 1; i < size + 1; i++) { m[i][i] = 0; } @@ -109,33 +72,92 @@ private static void matrixChainOrder() { } } - private static String[] input(String string) { - System.out.print(string); - return (SCANNER.nextLine().split(" ")); - } -} - -class Matrix { + /** + * The Result class holds the results of the matrix chain multiplication + * calculation, including the matrix of minimum costs and split points. + */ + public static class Result { + private final int[][] m; + private final int[][] s; + + /** + * Constructs a Result object with the specified matrices of minimum + * costs and split points. + * + * @param m the matrix of minimum multiplication costs. + * @param s the matrix of optimal split points. + */ + public Result(int[][] m, int[][] s) { + this.m = m; + this.s = s; + } - private final int count; - private final int col; - private final int row; + /** + * Returns the matrix of minimum multiplication costs. + * + * @return the matrix of minimum multiplication costs. + */ + public int[][] getM() { + return m; + } - Matrix(int count, int col, int row) { - this.count = count; - this.col = col; - this.row = row; + /** + * Returns the matrix of optimal split points. + * + * @return the matrix of optimal split points. + */ + public int[][] getS() { + return s; + } } - int count() { - return count; - } + /** + * The Matrix class represents a matrix with its dimensions and count. + */ + public static class Matrix { + private final int count; + private final int col; + private final int row; + + /** + * Constructs a Matrix object with the specified count, number of columns, + * and number of rows. + * + * @param count the identifier for the matrix. + * @param col the number of columns in the matrix. + * @param row the number of rows in the matrix. + */ + public Matrix(int count, int col, int row) { + this.count = count; + this.col = col; + this.row = row; + } - int col() { - return col; - } + /** + * Returns the identifier of the matrix. + * + * @return the identifier of the matrix. + */ + public int count() { + return count; + } - int row() { - return row; + /** + * Returns the number of columns in the matrix. + * + * @return the number of columns in the matrix. + */ + public int col() { + return col; + } + + /** + * Returns the number of rows in the matrix. + * + * @return the number of rows in the matrix. + */ + public int row() { + return row; + } } } diff --git a/src/test/java/com/thealgorithms/dynamicprogramming/MatrixChainMultiplicationTest.java b/src/test/java/com/thealgorithms/dynamicprogramming/MatrixChainMultiplicationTest.java new file mode 100644 index 000000000000..2bee0ca52918 --- /dev/null +++ b/src/test/java/com/thealgorithms/dynamicprogramming/MatrixChainMultiplicationTest.java @@ -0,0 +1,54 @@ +package com.thealgorithms.dynamicprogramming; + +import static org.junit.jupiter.api.Assertions.assertEquals; + +import java.util.ArrayList; +import org.junit.jupiter.api.Test; + +class MatrixChainMultiplicationTest { + + @Test + void testMatrixCreation() { + MatrixChainMultiplication.Matrix matrix1 = new MatrixChainMultiplication.Matrix(1, 10, 20); + MatrixChainMultiplication.Matrix matrix2 = new MatrixChainMultiplication.Matrix(2, 20, 30); + + assertEquals(1, matrix1.count()); + assertEquals(10, matrix1.col()); + assertEquals(20, matrix1.row()); + + assertEquals(2, matrix2.count()); + assertEquals(20, matrix2.col()); + assertEquals(30, matrix2.row()); + } + + @Test + void testMatrixChainOrder() { + // Create a list of matrices to be multiplied + ArrayList matrices = new ArrayList<>(); + matrices.add(new MatrixChainMultiplication.Matrix(1, 10, 20)); // A(1) = 10 x 20 + matrices.add(new MatrixChainMultiplication.Matrix(2, 20, 30)); // A(2) = 20 x 30 + + // Calculate matrix chain order + MatrixChainMultiplication.Result result = MatrixChainMultiplication.calculateMatrixChainOrder(matrices); + + // Expected cost of multiplying A(1) and A(2) + int expectedCost = 6000; // The expected optimal cost of multiplying A(1)(10x20) and A(2)(20x30) + int actualCost = result.getM()[1][2]; + + assertEquals(expectedCost, actualCost); + } + + @Test + void testOptimalParentheses() { + // Create a list of matrices to be multiplied + ArrayList matrices = new ArrayList<>(); + matrices.add(new MatrixChainMultiplication.Matrix(1, 10, 20)); // A(1) = 10 x 20 + matrices.add(new MatrixChainMultiplication.Matrix(2, 20, 30)); // A(2) = 20 x 30 + + // Calculate matrix chain order + MatrixChainMultiplication.Result result = MatrixChainMultiplication.calculateMatrixChainOrder(matrices); + + // Check the optimal split for parentheses + assertEquals(1, result.getS()[1][2]); // s[1][2] should point to the optimal split + } +}