Add CrosswordSolver algorithm (#5626)

src/main/java/com/thealgorithms/backtracking/CrosswordSolver.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;
+    }
+}