added shuffle algorithm, it's implementation and problems related to it

src/main/java/com/thealgorithms/audiofilters/IIRFilter.java

@@ -2,7 +2,7 @@
 
 /**
  * N-Order IIR Filter Assumes inputs are normalized to [-1, 1]
- *
+ * <p>
  * Based on the difference equation from
  * <a href="https://en.wikipedia.org/wiki/Infinite_impulse_response">Wikipedia link</a>
  */
@@ -43,7 +43,7 @@ public IIRFilter(int order) throws IllegalArgumentException {
      * @param aCoeffs Denominator coefficients
      * @param bCoeffs Numerator coefficients
      * @throws IllegalArgumentException if {@code aCoeffs} or {@code bCoeffs} is
-     * not of size {@code order}, or if {@code aCoeffs[0]} is 0.0
+     *                                  not of size {@code order}, or if {@code aCoeffs[0]} is 0.0
      */
     public void setCoeffs(double[] aCoeffs, double[] bCoeffs) throws IllegalArgumentException {
         if (aCoeffs.length != order) {

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

@@ -33,10 +33,10 @@ public static List<List<Integer>> combination(int n, int k) {
      * A helper method that uses backtracking to find combinations.
      *
      * @param combinations The list to store all valid combinations found.
-     * @param current The current combination being built.
-     * @param start The starting index for the current recursion.
-     * @param n The total number of elements (0 to n-1).
-     * @param k The desired length of each combination.
+     * @param current      The current combination being built.
+     * @param start        The starting index for the current recursion.
+     * @param n            The total number of elements (0 to n-1).
+     * @param k            The desired length of each combination.
      */
     private static void combine(List<List<Integer>> combinations, List<Integer> current, int start, int n, int k) {
         // Base case: combination found

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

@@ -8,6 +8,7 @@
 
 /**
  * Finds all permutations of given array
+ *
  * @author Alan Piao (<a href="https://github.com/cpiao3">git-Alan Piao</a>)
  */
 public final class Combination {
@@ -16,8 +17,9 @@ private Combination() {
 
     /**
      * Find all combinations of given array using backtracking
+     *
      * @param arr the array.
-     * @param n length of combination
+     * @param n   length of combination
      * @param <T> the type of elements in the array.
      * @return a list of all combinations of length n. If n == 0, return null.
      */
@@ -39,12 +41,13 @@ public static <T> List<TreeSet<T>> combination(T[] arr, int n) {
 
     /**
      * Backtrack all possible combinations of a given array
-     * @param arr the array.
-     * @param n length of the combination
-     * @param index the starting index.
+     *
+     * @param arr     the array.
+     * @param n       length of the combination
+     * @param index   the starting index.
      * @param currSet set that tracks current combination
-     * @param result the list contains all combination.
-     * @param <T> the type of elements in the array.
+     * @param result  the list contains all combination.
+     * @param <T>     the type of elements in the array.
      */
     private static <T> void backtracking(T[] arr, int n, int index, TreeSet<T> currSet, List<TreeSet<T>> result) {
         if (index + n - currSet.size() > arr.length) {

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

@@ -8,19 +8,19 @@
  * A class to solve a crossword puzzle using backtracking.
  * Example:
  * Input:
- *  puzzle = {
- *      {' ', ' ', ' '},
- *      {' ', ' ', ' '},
- *      {' ', ' ', ' '}
- *  }
- *  words = List.of("cat", "dog")
- *
+ * puzzle = {
+ * {' ', ' ', ' '},
+ * {' ', ' ', ' '},
+ * {' ', ' ', ' '}
+ * }
+ * words = List.of("cat", "dog")
+ * <p>
  * Output:
- *  {
- *      {'c', 'a', 't'},
- *      {' ', ' ', ' '},
- *      {'d', 'o', 'g'}
- *  }
+ * {
+ * {'c', 'a', 't'},
+ * {' ', ' ', ' '},
+ * {'d', 'o', 'g'}
+ * }
  */
 public final class CrosswordSolver {
     private CrosswordSolver() {

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

@@ -2,6 +2,7 @@
 
 /**
  * Java program for Flood fill algorithm.
+ *
  * @author Akshay Dubey (<a href="https://github.com/itsAkshayDubey">Git-Akshay Dubey</a>)
  */
 public final class FloodFill {
@@ -12,8 +13,8 @@ private FloodFill() {
      * Get the color at the given coordinates of a 2D image
      *
      * @param image The image to be filled
-     * @param x The x co-ordinate of which color is to be obtained
-     * @param y The y co-ordinate of which color is to be obtained
+     * @param x     The x co-ordinate of which color is to be obtained
+     * @param y     The y co-ordinate of which color is to be obtained
      */
 
     public static int getPixel(final int[][] image, final int x, final int y) {
@@ -24,8 +25,8 @@ public static int getPixel(final int[][] image, final int x, final int y) {
      * Put the color at the given coordinates of a 2D image
      *
      * @param image The image to be filled
-     * @param x The x co-ordinate at which color is to be filled
-     * @param y The y co-ordinate at which color is to be filled
+     * @param x     The x co-ordinate at which color is to be filled
+     * @param y     The y co-ordinate at which color is to be filled
      */
     public static void putPixel(final int[][] image, final int x, final int y, final int newColor) {
         image[x][y] = newColor;
@@ -34,9 +35,9 @@ public static void putPixel(final int[][] image, final int x, final int y, final
     /**
      * Fill the 2D image with new color
      *
-     * @param image The image to be filled
-     * @param x The x co-ordinate at which color is to be filled
-     * @param y The y co-ordinate at which color is to be filled
+     * @param image    The image to be filled
+     * @param x        The x co-ordinate at which color is to be filled
+     * @param y        The y co-ordinate at which color is to be filled
      * @param newColor The new color which to be filled in the image
      * @param oldColor The old color which is to be replaced in the image
      */

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

@@ -6,12 +6,12 @@
 
 /**
  * The KnightsTour class solves the Knight's Tour problem using backtracking.
- *
+ * <p>
  * Problem Statement:
  * Given an N*N board with a knight placed on the first block, the knight must
  * move according to chess rules and visit each square on the board exactly once.
  * The class outputs the sequence of moves for the knight.
- *
+ * <p>
  * Example:
  * Input: N = 8 (8x8 chess board)
  * Output: The sequence of numbers representing the order in which the knight visits each square.
@@ -61,7 +61,7 @@ public static void resetBoard() {
     /**
      * Recursive method to solve the Knight's Tour problem.
      *
-     * @param row   The current row of the knight
+     * @param row    The current row of the knight
      * @param column The current column of the knight
      * @param count  The current move number
      * @return True if a solution is found, False otherwise
@@ -96,10 +96,10 @@ static boolean solve(int row, int column, int count) {
     /**
      * Returns a list of valid neighboring cells where the knight can move.
      *
-     * @param row   The current row of the knight
+     * @param row    The current row of the knight
      * @param column The current column of the knight
      * @return A list of arrays representing valid moves, where each array contains:
-     *         {nextRow, nextCol, numberOfPossibleNextMoves}
+     * {nextRow, nextCol, numberOfPossibleNextMoves}
      */
     static List<int[]> neighbors(int row, int column) {
         List<int[]> neighbour = new ArrayList<>();
@@ -137,9 +137,9 @@ static int countNeighbors(int row, int column) {
     /**
      * Detects if moving to a given position will create an orphan (a position with no further valid moves).
      *
-     * @param count   The current move number
-     * @param row     The row of the current position
-     * @param column  The column of the current position
+     * @param count  The current move number
+     * @param row    The row of the current position
+     * @param column The column of the current position
      * @return True if an orphan is detected, False otherwise
      */
     static boolean orphanDetected(int count, int row, int column) {

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

@@ -4,7 +4,7 @@
  * This class contains methods to solve a maze using recursive backtracking.
  * The maze is represented as a 2D array where walls, paths, and visited/dead
  * ends are marked with different integers.
- *
+ * <p>
  * The goal is to find a path from a starting position to the target position
  * (map[6][5]) while navigating through the maze.
  */

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

@@ -8,21 +8,21 @@
  * which N queens can be placed on the board such no two queens attack each
  * other. Ex. N = 6 Solution= There are 4 possible ways Arrangement: 1 ".Q....",
  * "...Q..", ".....Q", "Q.....", "..Q...", "....Q."
- *
+ * <p>
  * Arrangement: 2 "..Q...", ".....Q", ".Q....", "....Q.", "Q.....", "...Q.."
- *
+ * <p>
  * Arrangement: 3 "...Q..", "Q.....", "....Q.", ".Q....", ".....Q", "..Q..."
- *
+ * <p>
  * Arrangement: 4 "....Q.", "..Q...", "Q.....", ".....Q", "...Q..", ".Q...."
- *
+ * <p>
  * Solution: Brute Force approach:
- *
+ * <p>
  * Generate all possible arrangement to place N queens on N*N board. Check each
  * board if queens are placed safely. If it is safe, include arrangement in
  * solution set. Otherwise, ignore it
- *
+ * <p>
  * Optimized solution: This can be solved using backtracking in below steps
- *
+ * <p>
  * Start with first column and place queen on first row Try placing queen in a
  * row on second column If placing second queen in second column attacks any of
  * the previous queens, change the row in second column otherwise move to next
@@ -59,9 +59,9 @@ public static void placeQueens(final int queens) {
     /**
      * This is backtracking function which tries to place queen recursively
      *
-     * @param boardSize: size of chess board
-     * @param solutions: this holds all possible arrangements
-     * @param columns: columns[i] = rowId where queen is placed in ith column.
+     * @param boardSize:   size of chess board
+     * @param solutions:   this holds all possible arrangements
+     * @param columns:     columns[i] = rowId where queen is placed in ith column.
      * @param columnIndex: This is the column in which queen is being placed
      */
     private static void getSolution(int boardSize, List<List<String>> solutions, int[] columns, int columnIndex) {
@@ -94,8 +94,8 @@ private static void getSolution(int boardSize, List<List<String>> solutions, int
      * This function checks if queen can be placed at row = rowIndex in column =
      * columnIndex safely
      *
-     * @param columns: columns[i] = rowId where queen is placed in ith column.
-     * @param rowIndex: row in which queen has to be placed
+     * @param columns:     columns[i] = rowId where queen is placed in ith column.
+     * @param rowIndex:    row in which queen has to be placed
      * @param columnIndex: column in which queen is being placed
      * @return true: if queen can be placed safely false: otherwise
      */

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

@@ -5,6 +5,7 @@
 
 /**
  * Finds all permutations of given array
+ *
  * @author Alan Piao (<a href="https://github.com/cpiao3">Git-Alan Piao</a>)
  */
 public final class Permutation {
@@ -13,6 +14,7 @@ private Permutation() {
 
     /**
      * Find all permutations of given array using backtracking
+     *
      * @param arr the array.
      * @param <T> the type of elements in the array.
      * @return a list of all permutations.
@@ -26,10 +28,11 @@ public static <T> List<T[]> permutation(T[] arr) {
 
     /**
      * Backtrack all possible orders of a given array
-     * @param arr the array.
-     * @param index the starting index.
+     *
+     * @param arr    the array.
+     * @param index  the starting index.
      * @param result the list contains all permutations.
-     * @param <T> the type of elements in the array.
+     * @param <T>    the type of elements in the array.
      */
     private static <T> void backtracking(T[] arr, int index, List<T[]> result) {
         if (index == arr.length) {
@@ -44,8 +47,9 @@ private static <T> void backtracking(T[] arr, int index, List<T[]> result) {
 
     /**
      * Swap two element for a given array
-     * @param a first index
-     * @param b second index
+     *
+     * @param a   first index
+     * @param b   second index
      * @param arr the array.
      * @param <T> the type of elements in the array.
      */

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

@@ -6,7 +6,7 @@
  * of unique, natural numbers.
  * For example, if N=100 and X=3, we have to find all combinations of unique cubes adding up to 100.
  * The only solution is 1^3 + 2^3 + 3^3 + 4^3. Therefore, the output will be 1.
- *
+ * <p>
  * N is represented by the parameter 'targetSum' in the code.
  * X is represented by the parameter 'power' in the code.
  */
@@ -16,7 +16,7 @@ public class PowerSum {
      * Calculates the number of ways to express the target sum as a sum of Xth powers of unique natural numbers.
      *
      * @param targetSum The target sum to achieve (N in the problem statement)
-     * @param power The power to raise natural numbers to (X in the problem statement)
+     * @param power     The power to raise natural numbers to (X in the problem statement)
      * @return The number of ways to express the target sum
      */
     public int powSum(int targetSum, int power) {
@@ -30,10 +30,10 @@ public int powSum(int targetSum, int power) {
     /**
      * Recursively calculates the number of ways to express the remaining sum as a sum of Xth powers.
      *
-     * @param remainingSum The remaining sum to achieve
-     * @param power The power to raise natural numbers to (X in the problem statement)
+     * @param remainingSum  The remaining sum to achieve
+     * @param power         The power to raise natural numbers to (X in the problem statement)
      * @param currentNumber The current natural number being considered
-     * @param currentSum The current sum of powered numbers
+     * @param currentSum    The current sum of powered numbers
      * @return The number of valid combinations
      */
     private int sumRecursive(int remainingSum, int power, int currentNumber, int currentSum) {

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

@@ -14,7 +14,7 @@ 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
+     * @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) {
@@ -33,11 +33,11 @@ public static <T> List<List<T>> generateAll(List<T> sequence) {
      * 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 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
+     * @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();