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Improve docs, remove main
, add tests for `MatrixChainRecursiveTopDo… (#5659)
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@ -836,6 +836,7 @@
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* [LongestPalindromicSubstringTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/dynamicprogramming/LongestPalindromicSubstringTest.java)
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* [LongestPalindromicSubstringTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/dynamicprogramming/LongestPalindromicSubstringTest.java)
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* [LongestValidParenthesesTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/dynamicprogramming/LongestValidParenthesesTest.java)
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* [LongestValidParenthesesTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/dynamicprogramming/LongestValidParenthesesTest.java)
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* [MatrixChainMultiplicationTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/dynamicprogramming/MatrixChainMultiplicationTest.java)
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* [MatrixChainMultiplicationTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/dynamicprogramming/MatrixChainMultiplicationTest.java)
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* [MatrixChainRecursiveTopDownMemoisationTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/dynamicprogramming/MatrixChainRecursiveTopDownMemoisationTest.java)
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* [MaximumSumOfNonAdjacentElementsTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/dynamicprogramming/MaximumSumOfNonAdjacentElementsTest.java)
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* [MaximumSumOfNonAdjacentElementsTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/dynamicprogramming/MaximumSumOfNonAdjacentElementsTest.java)
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* [MinimumPathSumTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/dynamicprogramming/MinimumPathSumTest.java)
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* [MinimumPathSumTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/dynamicprogramming/MinimumPathSumTest.java)
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* [MinimumSumPartitionTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/dynamicprogramming/MinimumSumPartitionTest.java)
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* [MinimumSumPartitionTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/dynamicprogramming/MinimumSumPartitionTest.java)
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@ -1,15 +1,31 @@
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package com.thealgorithms.dynamicprogramming;
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package com.thealgorithms.dynamicprogramming;
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// Matrix-chain Multiplication
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/**
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// Problem Statement
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* The MatrixChainRecursiveTopDownMemoisation class implements the matrix-chain
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// we have given a chain A1,A2,...,Ani of n matrices, where for i = 1,2,...,n,
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* multiplication problem using a top-down recursive approach with memoization.
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// matrix Ai has dimension pi−1 ×pi
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*
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// , fully parenthesize the product A1A2 ···An in a way that
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* <p>Given a chain of matrices A1, A2, ..., An, where matrix Ai has dimensions
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// minimizes the number of scalar multiplications.
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* pi-1 × pi, this algorithm finds the optimal way to fully parenthesize the
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* product A1A2...An in a way that minimizes the total number of scalar
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* multiplications required.</p>
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*
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* <p>This implementation uses a memoization technique to store the results of
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* subproblems, which significantly reduces the number of recursive calls and
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* improves performance compared to a naive recursive approach.</p>
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*/
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public final class MatrixChainRecursiveTopDownMemoisation {
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public final class MatrixChainRecursiveTopDownMemoisation {
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private MatrixChainRecursiveTopDownMemoisation() {
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private MatrixChainRecursiveTopDownMemoisation() {
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}
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}
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/**
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* Calculates the minimum number of scalar multiplications needed to multiply
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* a chain of matrices.
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*
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* @param p an array of integers representing the dimensions of the matrices.
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* The length of the array is n + 1, where n is the number of matrices.
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* @return the minimum number of multiplications required to multiply the chain
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* of matrices.
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*/
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static int memoizedMatrixChain(int[] p) {
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static int memoizedMatrixChain(int[] p) {
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int n = p.length;
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int n = p.length;
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int[][] m = new int[n][n];
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int[][] m = new int[n][n];
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@ -21,6 +37,17 @@ public final class MatrixChainRecursiveTopDownMemoisation {
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return lookupChain(m, p, 1, n - 1);
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return lookupChain(m, p, 1, n - 1);
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}
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}
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/**
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* A recursive helper method to lookup the minimum number of multiplications
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* for multiplying matrices from index i to index j.
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*
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* @param m the memoization table storing the results of subproblems.
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* @param p an array of integers representing the dimensions of the matrices.
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* @param i the starting index of the matrix chain.
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* @param j the ending index of the matrix chain.
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* @return the minimum number of multiplications needed to multiply matrices
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* from i to j.
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*/
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static int lookupChain(int[][] m, int[] p, int i, int j) {
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static int lookupChain(int[][] m, int[] p, int i, int j) {
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if (i == j) {
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if (i == j) {
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m[i][j] = 0;
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m[i][j] = 0;
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@ -38,11 +65,4 @@ public final class MatrixChainRecursiveTopDownMemoisation {
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}
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}
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return m[i][j];
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return m[i][j];
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}
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}
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// in this code we are taking the example of 4 matrixes whose orders are 1x2,2x3,3x4,4x5
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// respectively output should be Minimum number of multiplications is 38
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public static void main(String[] args) {
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int[] arr = {1, 2, 3, 4, 5};
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System.out.println("Minimum number of multiplications is " + memoizedMatrixChain(arr));
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}
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}
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}
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@ -0,0 +1,68 @@
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package com.thealgorithms.dynamicprogramming;
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import static org.junit.jupiter.api.Assertions.assertEquals;
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import org.junit.jupiter.api.Test;
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class MatrixChainRecursiveTopDownMemoisationTest {
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/**
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* Test case for four matrices with dimensions 1x2, 2x3, 3x4, and 4x5.
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* The expected minimum number of multiplications is 38.
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*/
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@Test
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void testFourMatrices() {
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int[] dimensions = {1, 2, 3, 4, 5};
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int expected = 38;
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int actual = MatrixChainRecursiveTopDownMemoisation.memoizedMatrixChain(dimensions);
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assertEquals(expected, actual, "The minimum number of multiplications should be 38.");
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}
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/**
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* Test case for three matrices with dimensions 10x20, 20x30, and 30x40.
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* The expected minimum number of multiplications is 6000.
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*/
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@Test
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void testThreeMatrices() {
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int[] dimensions = {10, 20, 30, 40};
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int expected = 18000;
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int actual = MatrixChainRecursiveTopDownMemoisation.memoizedMatrixChain(dimensions);
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assertEquals(expected, actual, "The minimum number of multiplications should be 18000.");
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}
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/**
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* Test case for two matrices with dimensions 5x10 and 10x20.
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* The expected minimum number of multiplications is 1000.
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*/
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@Test
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void testTwoMatrices() {
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int[] dimensions = {5, 10, 20};
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int expected = 1000;
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int actual = MatrixChainRecursiveTopDownMemoisation.memoizedMatrixChain(dimensions);
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assertEquals(expected, actual, "The minimum number of multiplications should be 1000.");
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}
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/**
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* Test case for a single matrix.
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* The expected minimum number of multiplications is 0, as there are no multiplications needed.
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*/
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@Test
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void testSingleMatrix() {
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int[] dimensions = {10, 20}; // Single matrix dimensions
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int expected = 0;
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int actual = MatrixChainRecursiveTopDownMemoisation.memoizedMatrixChain(dimensions);
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assertEquals(expected, actual, "The minimum number of multiplications should be 0.");
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}
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/**
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* Test case for matrices with varying dimensions.
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* The expected minimum number of multiplications is calculated based on the dimensions provided.
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*/
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@Test
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void testVaryingDimensions() {
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int[] dimensions = {2, 3, 4, 5, 6}; // Dimensions for 4 matrices
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int expected = 124; // Expected value needs to be calculated based on the problem
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int actual = MatrixChainRecursiveTopDownMemoisation.memoizedMatrixChain(dimensions);
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assertEquals(expected, actual, "The minimum number of multiplications should be 124.");
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}
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}
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