Merge branch 'master' into median_sorted_arrays_new_algo

Author: siriak

DIRECTORY.md

@@ -63,7 +63,7 @@
         <plugins>
             <plugin>
                 <artifactId>maven-surefire-plugin</artifactId>
-                <version>3.5.0</version>
+                <version>3.5.1</version>
                 <configuration>
                     <forkNode implementation="org.apache.maven.plugin.surefire.extensions.SurefireForkNodeFactory"/>
                 </configuration>

pom.xml

@@ -58,7 +58,7 @@ public void setCoeffs(double[] aCoeffs, double[] bCoeffs) throws IllegalArgument
             throw new IllegalArgumentException("bCoeffs must be of size " + order + ", got " + bCoeffs.length);
         }
 
-        for (int i = 0; i <= order; i++) {
+        for (int i = 0; i < order; i++) {
             coeffsA[i] = aCoeffs[i];
             coeffsB[i] = bCoeffs[i];
         }

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

@@ -0,0 +1,124 @@
+package com.thealgorithms.backtracking;
+
+import java.util.ArrayList;
+import java.util.List;
+
+/**
+ * A class to solve a crossword puzzle using backtracking.
+ * Example:
+ * Input:
+ *  puzzle = {
+ *      {' ', ' ', ' '},
+ *      {' ', ' ', ' '},
+ *      {' ', ' ', ' '}
+ *  }
+ *  words = List.of("cat", "dog")
+ *
+ * Output:
+ *  {
+ *      {'c', 'a', 't'},
+ *      {' ', ' ', ' '},
+ *      {'d', 'o', 'g'}
+ *  }
+ */
+public final class CrosswordSolver {
+    private CrosswordSolver() {
+    }
+
+    /**
+     * Checks if a word can be placed at the specified position in the crossword.
+     *
+     * @param puzzle   The crossword puzzle represented as a 2D char array.
+     * @param word     The word to be placed.
+     * @param row      The row index where the word might be placed.
+     * @param col      The column index where the word might be placed.
+     * @param vertical If true, the word is placed vertically; otherwise, horizontally.
+     * @return true if the word can be placed, false otherwise.
+     */
+    public static boolean isValid(char[][] puzzle, String word, int row, int col, boolean vertical) {
+        for (int i = 0; i < word.length(); i++) {
+            if (vertical) {
+                if (row + i >= puzzle.length || puzzle[row + i][col] != ' ') {
+                    return false;
+                }
+            } else {
+                if (col + i >= puzzle[0].length || puzzle[row][col + i] != ' ') {
+                    return false;
+                }
+            }
+        }
+        return true;
+    }
+
+    /**
+     * Places a word at the specified position in the crossword.
+     *
+     * @param puzzle   The crossword puzzle represented as a 2D char array.
+     * @param word     The word to be placed.
+     * @param row      The row index where the word will be placed.
+     * @param col      The column index where the word will be placed.
+     * @param vertical If true, the word is placed vertically; otherwise, horizontally.
+     */
+    public static void placeWord(char[][] puzzle, String word, int row, int col, boolean vertical) {
+        for (int i = 0; i < word.length(); i++) {
+            if (vertical) {
+                puzzle[row + i][col] = word.charAt(i);
+            } else {
+                puzzle[row][col + i] = word.charAt(i);
+            }
+        }
+    }
+
+    /**
+     * Removes a word from the specified position in the crossword.
+     *
+     * @param puzzle   The crossword puzzle represented as a 2D char array.
+     * @param word     The word to be removed.
+     * @param row      The row index where the word is placed.
+     * @param col      The column index where the word is placed.
+     * @param vertical If true, the word was placed vertically; otherwise, horizontally.
+     */
+    public static void removeWord(char[][] puzzle, String word, int row, int col, boolean vertical) {
+        for (int i = 0; i < word.length(); i++) {
+            if (vertical) {
+                puzzle[row + i][col] = ' ';
+            } else {
+                puzzle[row][col + i] = ' ';
+            }
+        }
+    }
+
+    /**
+     * Solves the crossword puzzle using backtracking.
+     *
+     * @param puzzle The crossword puzzle represented as a 2D char array.
+     * @param words  The list of words to be placed.
+     * @return true if the crossword is solved, false otherwise.
+     */
+    public static boolean solveCrossword(char[][] puzzle, List<String> words) {
+        // Create a mutable copy of the words list
+        List<String> remainingWords = new ArrayList<>(words);
+
+        for (int row = 0; row < puzzle.length; row++) {
+            for (int col = 0; col < puzzle[0].length; col++) {
+                if (puzzle[row][col] == ' ') {
+                    for (String word : new ArrayList<>(remainingWords)) {
+                        for (boolean vertical : new boolean[] {true, false}) {
+                            if (isValid(puzzle, word, row, col, vertical)) {
+                                placeWord(puzzle, word, row, col, vertical);
+                                remainingWords.remove(word);
+                                if (solveCrossword(puzzle, remainingWords)) {
+                                    return true;
+                                }
+                                remainingWords.add(word);
+                                removeWord(puzzle, word, row, col, vertical);
+                            }
+                        }
+                    }
+                    return false;
+                }
+            }
+        }
+        return true;
+    }
+}

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

@@ -4,33 +4,26 @@
 import java.util.Comparator;
 import java.util.List;
 
-/*
-    * Problem Statement: -
-
-    Given a N*N board with the Knight placed on the first block of an empty board. Moving according
-   to the rules of chess knight must visit each square exactly once. Print the order of each cell in
-   which they are visited.
-
-    Example: -
-
-    Input : N = 8
-
-    Output:
-        0  59  38  33  30  17   8  63
-        37  34  31  60   9  62  29  16
-        58   1  36  39  32  27  18   7
-        35  48  41  26  61  10  15  28
-        42  57   2  49  40  23   6  19
-        47  50  45  54  25  20  11  14
-        56  43  52   3  22  13  24   5
-        51  46  55  44  53   4  21  12
-
+/**
+ * The KnightsTour class solves the Knight's Tour problem using backtracking.
+ *
+ * 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.
+ *
+ * Example:
+ * Input: N = 8 (8x8 chess board)
+ * Output: The sequence of numbers representing the order in which the knight visits each square.
  */
 public final class KnightsTour {
     private KnightsTour() {
     }
 
+    // The size of the chess board (12x12 grid, with 2 extra rows/columns as a buffer around a 8x8 area)
     private static final int BASE = 12;
+
+    // Possible moves for a knight in chess
     private static final int[][] MOVES = {
         {1, -2},
         {2, -1},
@@ -40,36 +33,40 @@ private KnightsTour() {
         {-2, 1},
         {-2, -1},
         {-1, -2},
-    }; // Possible moves by knight on chess
-    private static int[][] grid; // chess grid
-    private static int total; // total squares in chess
+    };
+
+    // Chess grid representing the board
+    static int[][] grid;
+
+    // Total number of cells the knight needs to visit
+    static int total;
 
-    public static void main(String[] args) {
+    /**
+     * Resets the chess board to its initial state.
+     * Initializes the grid with boundary cells marked as -1 and internal cells as 0.
+     * Sets the total number of cells the knight needs to visit.
+     */
+    public static void resetBoard() {
         grid = new int[BASE][BASE];
         total = (BASE - 4) * (BASE - 4);
-
         for (int r = 0; r < BASE; r++) {
             for (int c = 0; c < BASE; c++) {
                 if (r < 2 || r > BASE - 3 || c < 2 || c > BASE - 3) {
-                    grid[r][c] = -1;
+                    grid[r][c] = -1; // Mark boundary cells
                 }
             }
         }
-
-        int row = 2 + (int) (Math.random() * (BASE - 4));
-        int col = 2 + (int) (Math.random() * (BASE - 4));
-
-        grid[row][col] = 1;
-
-        if (solve(row, col, 2)) {
-            printResult();
-        } else {
-            System.out.println("no result");
-        }
     }
 
-    // Return True when solvable
-    private static boolean solve(int row, int column, int count) {
+    /**
+     * Recursive method to solve the Knight's Tour problem.
+     *
+     * @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
+     */
+    static boolean solve(int row, int column, int count) {
         if (count > total) {
             return true;
         }
@@ -80,49 +77,72 @@ private static boolean solve(int row, int column, int count) {
             return false;
         }
 
+        // Sort neighbors by Warnsdorff's rule (fewest onward moves)
         neighbor.sort(Comparator.comparingInt(a -> a[2]));
 
         for (int[] nb : neighbor) {
-            row = nb[0];
-            column = nb[1];
-            grid[row][column] = count;
-            if (!orphanDetected(count, row, column) && solve(row, column, count + 1)) {
+            int nextRow = nb[0];
+            int nextCol = nb[1];
+            grid[nextRow][nextCol] = count;
+            if (!orphanDetected(count, nextRow, nextCol) && solve(nextRow, nextCol, count + 1)) {
                 return true;
             }
-            grid[row][column] = 0;
+            grid[nextRow][nextCol] = 0; // Backtrack
         }
 
         return false;
     }
 
-    // Returns List of neighbours
-    private static List<int[]> neighbors(int row, int column) {
+    /**
+     * Returns a list of valid neighboring cells where the knight can move.
+     *
+     * @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}
+     */
+    static List<int[]> neighbors(int row, int column) {
         List<int[]> neighbour = new ArrayList<>();
 
         for (int[] m : MOVES) {
             int x = m[0];
             int y = m[1];
-            if (grid[row + y][column + x] == 0) {
+            if (row + y >= 0 && row + y < BASE && column + x >= 0 && column + x < BASE && grid[row + y][column + x] == 0) {
                 int num = countNeighbors(row + y, column + x);
                 neighbour.add(new int[] {row + y, column + x, num});
             }
         }
         return neighbour;
     }
 
-    // Returns the total count of neighbors
-    private static int countNeighbors(int row, int column) {
+    /**
+     * Counts the number of possible valid moves for a knight from a given position.
+     *
+     * @param row    The row of the current position
+     * @param column The column of the current position
+     * @return The number of valid neighboring moves
+     */
+    static int countNeighbors(int row, int column) {
         int num = 0;
         for (int[] m : MOVES) {
-            if (grid[row + m[1]][column + m[0]] == 0) {
+            int x = m[0];
+            int y = m[1];
+            if (row + y >= 0 && row + y < BASE && column + x >= 0 && column + x < BASE && grid[row + y][column + x] == 0) {
                 num++;
             }
         }
         return num;
     }
 
-    // Returns true if it is orphan
-    private static boolean orphanDetected(int count, 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
+     * @return True if an orphan is detected, False otherwise
+     */
+    static boolean orphanDetected(int count, int row, int column) {
         if (count < total - 1) {
             List<int[]> neighbor = neighbors(row, column);
             for (int[] nb : neighbor) {
@@ -133,17 +153,4 @@ private static boolean orphanDetected(int count, int row, int column) {
         }
         return false;
     }
-
-    // Prints the result grid
-    private static void printResult() {
-        for (int[] row : grid) {
-            for (int i : row) {
-                if (i == -1) {
-                    continue;
-                }
-                System.out.printf("%2d ", i);
-            }
-            System.out.println();
-        }
-    }
 }