feat : new dp algo added UniqueSubsequenceCount.java (#5586)

* feat : new algo uniquesubseqcount

* Update UniqueSubsequencesCount.java

* Update UniqueSubsequencesCountTest.java

* Update UniqueSubsequencesCount.java

* Update UniqueSubsequencesCount.java

* Update UniqueSubsequencesCount.java

* Update UniqueSubsequencesCount.java

* Update UniqueSubsequencesCount.java

* Update UniqueSubsequencesCount.java

* Update UniqueSubsequencesCountTest.java

* Update UniqueSubsequencesCount.java

* Update UniqueSubsequencesCountTest.java

* Update UniqueSubsequencesCount.java

* Update UniqueSubsequencesCountTest.java

* Update UniqueSubsequencesCountTest.java

* Update UniqueSubsequencesCountTest.java

* Update UniqueSubsequencesCount.java

---------

Co-authored-by: Alex Klymenko <alexanderklmn@gmail.com>

src/main/java/com/thealgorithms/dynamicprogramming/UniqueSubsequencesCount.java

@@ -0,0 +1,98 @@
+package com.thealgorithms.dynamicprogramming;
+
+import java.util.Arrays;
+import java.util.HashSet;
+import java.util.Set;
+
+/**
+ * Utility class to find the number of unique subsequences that can be
+ * produced from a given string.
+ *
+ * <p> This class contains static methods to compute the unique subsequence count
+ * using dynamic programming and recursion. It ensures that duplicate characters
+ * are not counted multiple times in the subsequences.</p>
+ *
+ * <p> Author: https://github.com/Tuhinm2002 </p>
+ */
+public final class UniqueSubsequencesCount {
+
+    /**
+     * Private constructor to prevent instantiation of this utility class.
+     * This class should only be used in a static context.
+     *
+     * @throws UnsupportedOperationException if attempted to instantiate.
+     */
+    private UniqueSubsequencesCount() {
+        throw new UnsupportedOperationException("Utility class");
+    }
+
+    /**
+     * Finds the number of unique subsequences that can be generated from
+     * the given string.
+     *
+     * <p> This method initializes a dynamic programming (DP) array and invokes
+     * the recursive helper function to compute the subsequence count.</p>
+     *
+     * @param str the input string from which subsequences are generated
+     * @return the total count of unique subsequences
+     */
+    public static int countSubseq(String str) {
+
+        // DP array initialized to store intermediate results
+        int[] dp = new int[str.length() + 1];
+        Arrays.fill(dp, -1);
+
+        // Calls the recursive function to compute the result
+        return countSubsequences(str, 0, dp);
+    }
+
+    /**
+     * Recursive helper function to count the number of unique subsequences
+     * starting from the given index.
+     *
+     * <p> Uses a HashSet to avoid counting duplicate characters within
+     * a single subsequence.</p>
+     *
+     * @param st the input string
+     * @param idx the current index from which to calculate subsequences
+     * @param dp dynamic programming array used to memoize results
+     * @return the total number of unique subsequences starting from the
+     *         current index
+     */
+    public static int countSubsequences(String st, int idx, int[] dp) {
+
+        // Base case: when index exceeds the string length
+        if (idx >= st.length()) {
+            return 0;
+        }
+
+        // If result is already calculated, return the memoized value
+        if (dp[idx] != -1) {
+            return dp[idx];
+        }
+
+        // Set to store characters to avoid duplicates
+        Set<Character> set = new HashSet<>();
+
+        int res = 0;
+
+        // Iterate over the string starting from current index
+        for (int j = idx; j < st.length(); j++) {
+
+            // If character is already in the set, skip it
+            if (set.contains(st.charAt(j))) {
+                continue;
+            }
+
+            // Add character to set and recursively calculate subsequences
+            set.add(st.charAt(j));
+
+            // 1 for the current subsequence + recursive call for the rest of the string
+            res = 1 + countSubsequences(st, j + 1, dp) + res;
+        }
+
+        // Memoize the result
+        dp[idx] = res;
+        return dp[idx];
+    }
+}

src/test/java/com/thealgorithms/dynamicprogramming/UniqueSubsequencesCountTest.java

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+package com.thealgorithms.dynamicprogramming;
+
+import static org.junit.jupiter.api.Assertions.assertEquals;
+
+import org.junit.jupiter.params.ParameterizedTest;
+import org.junit.jupiter.params.provider.CsvSource;
+
+public class UniqueSubsequencesCountTest {
+
+    @ParameterizedTest
+    @CsvSource({"abc, 7", "abcdashgdhas, 3592", "a, 1", "'a b', 7", "a1b2, 15", "AaBb, 15", "abab, 11"})
+    void subseqCountParameterizedTest(String input, int expected) {
+        assertEquals(expected, UniqueSubsequencesCount.countSubseq(input));
+    }
+}