test: LongestAlternatingSubsequenceTest
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package com.thealgorithms.dynamicprogramming;
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package com.thealgorithms.dynamicprogramming;
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/*
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/**
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* Class for finding the length of the longest alternating subsequence in an array.
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* Problem Statement: -
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*
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* Find Longest Alternating Subsequence
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* <p>An alternating sequence is a sequence of numbers where the elements alternate
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* between increasing and decreasing. Specifically, a sequence is alternating if its elements
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* A sequence {x1, x2, .. xn} is alternating sequence if its elements satisfy one of the following
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* satisfy one of the following relations:
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relations :
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*
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* <ul>
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x1 < x2 > x3 < x4 > x5 < …. xn or
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* <li>{@code x1 < x2 > x3 < x4 > x5 < ... < xn}</li>
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x1 > x2 < x3 > x4 < x5 > …. xn
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* <li>{@code x1 > x2 < x3 > x4 < x5 > ... > xn}</li>
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* </ul>
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*
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* <p>This class provides a method to compute the length of the longest such subsequence
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* from a given array of integers.
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*/
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*/
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public final class LongestAlternatingSubsequence {
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public final class LongestAlternatingSubsequence {
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private LongestAlternatingSubsequence() {
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private LongestAlternatingSubsequence() {
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}
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}
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/* Function to return longest alternating subsequence length*/
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/**
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* Finds the length of the longest alternating subsequence in the given array.
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*
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* @param arr an array of integers where the longest alternating subsequence is to be found
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* @param n the length of the array {@code arr}
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* @return the length of the longest alternating subsequence
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*
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* <p>The method uses dynamic programming to solve the problem. It maintains a 2D array
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* {@code las} where:
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* <ul>
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* <li>{@code las[i][0]} represents the length of the longest alternating subsequence
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* ending at index {@code i} with the last element being greater than the previous element.</li>
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* <li>{@code las[i][1]} represents the length of the longest alternating subsequence
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* ending at index {@code i} with the last element being smaller than the previous element.</li>
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* </ul>
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*
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* <p>The method iterates through the array and updates the {@code las} array based on
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* whether the current element is greater or smaller than the previous elements.
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* The result is the maximum value found in the {@code las} array.
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*/
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static int alternatingLength(int[] arr, int n) {
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static int alternatingLength(int[] arr, int n) {
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/*
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las[i][0] = Length of the longest
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alternating subsequence ending at
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index i and last element is
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greater than its previous element
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las[i][1] = Length of the longest
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alternating subsequence ending at
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index i and last element is
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smaller than its previous
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element
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*/
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int[][] las = new int[n][2]; // las = LongestAlternatingSubsequence
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int[][] las = new int[n][2]; // las = LongestAlternatingSubsequence
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// Initialize the dp array
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for (int i = 0; i < n; i++) {
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for (int i = 0; i < n; i++) {
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las[i][0] = 1;
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las[i][0] = 1;
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las[i][1] = 1;
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las[i][1] = 1;
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@ -40,34 +50,24 @@ public final class LongestAlternatingSubsequence {
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int result = 1; // Initialize result
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int result = 1; // Initialize result
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/* Compute values in bottom up manner */
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// Compute values in a bottom-up manner
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for (int i = 1; i < n; i++) {
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for (int i = 1; i < n; i++) {
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/* Consider all elements as previous of arr[i]*/
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for (int j = 0; j < i; j++) {
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for (int j = 0; j < i; j++) {
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/* If arr[i] is greater, then check with las[j][1] */
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// If arr[i] is greater than arr[j], update las[i][0]
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if (arr[j] < arr[i] && las[i][0] < las[j][1] + 1) {
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if (arr[j] < arr[i] && las[i][0] < las[j][1] + 1) {
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las[i][0] = las[j][1] + 1;
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las[i][0] = las[j][1] + 1;
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}
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}
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/* If arr[i] is smaller, then check with las[j][0]*/
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// If arr[i] is smaller than arr[j], update las[i][1]
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if (arr[j] > arr[i] && las[i][1] < las[j][0] + 1) {
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if (arr[j] > arr[i] && las[i][1] < las[j][0] + 1) {
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las[i][1] = las[j][0] + 1;
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las[i][1] = las[j][0] + 1;
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}
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}
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}
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}
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/* Pick maximum of both values at index i */
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// Pick the maximum of both values at index i
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if (result < Math.max(las[i][0], las[i][1])) {
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result = Math.max(result, Math.max(las[i][0], las[i][1]));
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result = Math.max(las[i][0], las[i][1]);
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}
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}
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}
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return result;
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return result;
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}
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}
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public static void main(String[] args) {
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int[] arr = {10, 22, 9, 33, 49, 50, 31, 60};
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int n = arr.length;
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System.out.println("Length of Longest "
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+ "alternating subsequence is " + alternatingLength(arr, n));
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}
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}
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}
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@ -0,0 +1,22 @@
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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 java.util.stream.Stream;
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import org.junit.jupiter.params.ParameterizedTest;
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import org.junit.jupiter.params.provider.Arguments;
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import org.junit.jupiter.params.provider.MethodSource;
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public class LongestAlternatingSubsequenceTest {
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@ParameterizedTest
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@MethodSource("provideTestCases")
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void testAlternatingLength(int[] arr, int expected) {
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assertEquals(expected, LongestAlternatingSubsequence.alternatingLength(arr, arr.length));
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}
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private static Stream<Arguments> provideTestCases() {
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return Stream.of(Arguments.of(new int[] {1}, 1), Arguments.of(new int[] {1, 2}, 2), Arguments.of(new int[] {2, 1}, 2), Arguments.of(new int[] {1, 3, 2, 4, 3, 5}, 6), Arguments.of(new int[] {1, 2, 3, 4, 5}, 2), Arguments.of(new int[] {5, 4, 3, 2, 1}, 2),
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Arguments.of(new int[] {10, 22, 9, 33, 49, 50, 31, 60}, 6), Arguments.of(new int[] {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, 2));
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}
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}
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