Adding class for generating all subsequences from a given List (#5194)

* Adding class for generating all subsequences from a given List

* Fix test data format

* Fix braces wrong placement

* Fix "Utility classes should not have a public or default constructor."

* Fix checkstyle " Class Subsequence should be declared as final."

* Renaming class Subsequence to SubsequenceFinder. Refactored test to Parametrized test. Fixed input parameter as final.

* Fix formatting

* Fix formatting

* Fix formatting

* Fix import ordering

* Renaming method generate all.
Renaming test method.
Adding duplication test.
Renaming TestData to TestCase.

* Fix formatting

* style: add assertion to avoid potential infinite loop

---------

Co-authored-by: Piotr Idzik <65706193+vil02@users.noreply.github.com>

src/main/java/com/thealgorithms/backtracking/SubsequenceFinder.java

@@ -0,0 +1,54 @@
+package com.thealgorithms.backtracking;
+
+import java.util.ArrayList;
+import java.util.List;
+
+/**
+ * Class generates all subsequences for a given list of elements using backtracking
+ */
+public final class SubsequenceFinder {
+    private SubsequenceFinder() {
+    }
+
+    /**
+     * Find all subsequences of given list using backtracking
+     *
+     * @param sequence a list of items on the basis of which we need to generate all subsequences
+     * @param <T> the type of elements in the array
+     * @return a list of all subsequences
+     */
+    public static <T> List<List<T>> generateAll(List<T> sequence) {
+        List<List<T>> allSubSequences = new ArrayList<>();
+        if (sequence.isEmpty()) {
+            allSubSequences.add(new ArrayList<>());
+            return allSubSequences;
+        }
+        List<T> currentSubsequence = new ArrayList<>();
+        backtrack(sequence, currentSubsequence, 0, allSubSequences);
+        return allSubSequences;
+    }
+
+    /**
+     * Iterate through each branch of states
+     * We know that each state has exactly two branching
+     * It terminates when it reaches the end of the given sequence
+     *
+     * @param sequence all elements
+     * @param currentSubsequence current subsequence
+     * @param index current index
+     * @param allSubSequences contains all sequences
+     * @param <T> the type of elements which we generate
+     */
+    private static <T> void backtrack(List<T> sequence, List<T> currentSubsequence, final int index, List<List<T>> allSubSequences) {
+        assert index <= sequence.size();
+        if (index == sequence.size()) {
+            allSubSequences.add(new ArrayList<>(currentSubsequence));
+            return;
+        }
+
+        backtrack(sequence, currentSubsequence, index + 1, allSubSequences);
+        currentSubsequence.add(sequence.get(index));
+        backtrack(sequence, currentSubsequence, index + 1, allSubSequences);
+        currentSubsequence.removeLast();
+    }
+}

src/test/java/com/thealgorithms/backtracking/SubsequenceFinderTest.java

@@ -0,0 +1,28 @@
+package com.thealgorithms.backtracking;
+
+import static org.junit.jupiter.api.Assertions.assertIterableEquals;
+
+import java.util.ArrayList;
+import java.util.List;
+import java.util.stream.Stream;
+import org.junit.jupiter.params.ParameterizedTest;
+import org.junit.jupiter.params.provider.MethodSource;
+
+public class SubsequenceFinderTest {
+
+    @ParameterizedTest
+    @MethodSource("getTestCases")
+    void testGenerateAll(TestCase testData) {
+        final var actual = SubsequenceFinder.generateAll(testData.input());
+        assertIterableEquals(testData.expected(), actual);
+    }
+
+    static Stream<TestCase> getTestCases() {
+        return Stream.of(new TestCase(new ArrayList<>(), List.of(List.of())), new TestCase(List.of(1, 2), List.of(List.of(), List.of(2), List.of(1), List.of(1, 2))),
+            new TestCase(List.of("A", "B", "C"), List.of(List.of(), List.of("C"), List.of("B"), List.of("B", "C"), List.of("A"), List.of("A", "C"), List.of("A", "B"), List.of("A", "B", "C"))),
+            new TestCase(List.of(1, 2, 3), List.of(List.of(), List.of(3), List.of(2), List.of(2, 3), List.of(1), List.of(1, 3), List.of(1, 2), List.of(1, 2, 3))), new TestCase(List.of(2, 2), List.of(List.of(), List.of(2), List.of(2), List.of(2, 2))));
+    }
+
+    record TestCase(List<Object> input, List<List<Object>> expected) {
+    }
+}