backtracking: add unique permutation algorithm with test cases (#7078)

* Add unique permutation algorithm and test cases

* Fix: add braces for checkstyle

* Apply clang-format

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

@@ -0,0 +1,31 @@
+package com.thealgorithms.backtracking;
+
+import static org.junit.jupiter.api.Assertions.assertEquals;
+
+import java.util.Arrays;
+import java.util.List;
+import org.junit.jupiter.api.Test;
+
+public class UniquePermutationTest {
+
+    @Test
+    void testUniquePermutationsAab() {
+        List<String> expected = Arrays.asList("AAB", "ABA", "BAA");
+        List<String> result = UniquePermutation.generateUniquePermutations("AAB");
+        assertEquals(expected, result);
+    }
+
+    @Test
+    void testUniquePermutationsAbc() {
+        List<String> expected = Arrays.asList("ABC", "ACB", "BAC", "BCA", "CAB", "CBA");
+        List<String> result = UniquePermutation.generateUniquePermutations("ABC");
+        assertEquals(expected, result);
+    }
+
+    @Test
+    void testEmptyString() {
+        List<String> expected = Arrays.asList("");
+        List<String> result = UniquePermutation.generateUniquePermutations("");
+        assertEquals(expected, result);
+    }
+}