Added mos algorithm and dice thrower (#6591)

* Add Sum of Squares algorithm implementation

* Format code and add Wikipedia URL for Lagrange's theorem

* Fixed clang-format issues

* Added Mo's Algorithm and DiceThrower recursive algorithms

- Mo's Algorithm: Square root decomposition for offline range queries(Imp in CP)
- DiceThrower: Recursive backtracking for dice combinations(very imp)
- Both algorithms include comprehensive test suites
- Formatted with clang-format and i follow contribution guidelines

* Fixed checkstyle violation

* Fixed SpotBugs issue

* Added in PMD exclusions

* Improved test coverage for better Codecov scores.

* Fixed clang-format issues in test files

* Add Mo's Algorithm and DiceThrower algorithms with comprehensive tests
* Fixed PartitionProblem.java documentation comment placement

src/main/java/com/thealgorithms/recursion/DiceThrower.java

@@ -0,0 +1,113 @@
+package com.thealgorithms.recursion;
+
+import java.util.ArrayList;
+import java.util.List;
+
+/**
+ * DiceThrower - Generates all possible dice roll combinations that sum to a target
+ *
+ * This algorithm uses recursive backtracking to find all combinations of dice rolls
+ * (faces 1-6) that sum to a given target value.
+ *
+ * Example: If target = 4, possible combinations include:
+ * - "1111" (1+1+1+1 = 4)
+ * - "13" (1+3 = 4)
+ * - "22" (2+2 = 4)
+ * - "4" (4 = 4)
+ *
+ * @author BEASTSHRIRAM
+ * @see <a href="https://en.wikipedia.org/wiki/Backtracking">Backtracking Algorithm</a>
+ */
+public final class DiceThrower {
+
+    private DiceThrower() {
+        // Utility class
+    }
+
+    /**
+     * Returns all possible dice roll combinations that sum to the target
+     *
+     * @param target the target sum to achieve with dice rolls
+     * @return list of all possible combinations as strings
+     */
+    public static List<String> getDiceCombinations(int target) {
+        if (target < 0) {
+            throw new IllegalArgumentException("Target must be non-negative");
+        }
+        return generateCombinations("", target);
+    }
+
+    /**
+     * Prints all possible dice roll combinations that sum to the target
+     *
+     * @param target the target sum to achieve with dice rolls
+     */
+    public static void printDiceCombinations(int target) {
+        if (target < 0) {
+            throw new IllegalArgumentException("Target must be non-negative");
+        }
+        printCombinations("", target);
+    }
+
+    /**
+     * Recursive helper method to generate all combinations
+     *
+     * @param current the current combination being built
+     * @param remaining the remaining sum needed
+     * @return list of all combinations from this state
+     */
+    private static List<String> generateCombinations(String current, int remaining) {
+        List<String> combinations = new ArrayList<>();
+
+        // Base case: if remaining sum is 0, we found a valid combination
+        if (remaining == 0) {
+            combinations.add(current);
+            return combinations;
+        }
+
+        // Try all possible dice faces (1-6), but not more than remaining sum
+        for (int face = 1; face <= 6 && face <= remaining; face++) {
+            List<String> subCombinations = generateCombinations(current + face, remaining - face);
+            combinations.addAll(subCombinations);
+        }
+
+        return combinations;
+    }
+
+    /**
+     * Recursive helper method to print all combinations
+     *
+     * @param current the current combination being built
+     * @param remaining the remaining sum needed
+     */
+    private static void printCombinations(String current, int remaining) {
+        // Base case: if remaining sum is 0, we found a valid combination
+        if (remaining == 0) {
+            System.out.println(current);
+            return;
+        }
+
+        // Try all possible dice faces (1-6), but not more than remaining sum
+        for (int face = 1; face <= 6 && face <= remaining; face++) {
+            printCombinations(current + face, remaining - face);
+        }
+    }
+
+    /**
+     * Demo method to show usage
+     *
+     * @param args command line arguments
+     */
+    public static void main(String[] args) {
+        int target = 4;
+
+        System.out.println("All dice combinations that sum to " + target + ":");
+        List<String> combinations = getDiceCombinations(target);
+
+        for (String combination : combinations) {
+            System.out.println(combination);
+        }
+
+        System.out.println("\nTotal combinations: " + combinations.size());
+    }
+}