feat: Add TilingProblem new algorithm with Junit tests

Author: Hardvan

src/main/java/com/thealgorithms/divideandconquer/TilingProblem.java

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+package com.thealgorithms.divideandconquer;
+
+/**
+ * This class provides a solution to the Tiling Problem using divide-and-conquer.
+ * <p>
+ * The Tiling Problem involves filling a 2^n x 2^n board with a single missing
+ * square using L-shaped tiles (each tile covers exactly three squares).
+ * The algorithm recursively divides the board into four quadrants, places an
+ * L-shaped tile in the appropriate quadrant, and fills the remaining areas.
+ *
+ * <p>Applications:
+ * - Used in graphics and image processing.
+ * - Helpful in solving puzzles and tiling problems in competitive programming.
+ *
+ * @author Hardvan
+ */
+public final class TilingProblem {
+    private TilingProblem() {
+    }
+
+    /**
+     * A counter used to label the L-shaped tiles placed on the board.
+     */
+    private static int tile = 1;
+
+    /**
+     * A 2D array representing the board to be tiled.
+     */
+    private static int[][] board;
+
+    /**
+     * Solves the tiling problem for a 2^n x 2^n board with one missing square.
+     *
+     * @param size The size of the board (must be a power of 2).
+     * @param missingRow The row index of the missing square.
+     * @param missingCol The column index of the missing square.
+     * @return A 2D array representing the tiled board with L-shaped tiles.
+     */
+    public static int[][] solveTiling(int size, int missingRow, int missingCol) {
+        board = new int[size][size];
+        fillBoard(size, 0, 0, missingRow, missingCol);
+        return board;
+    }
+
+    /**
+     * Recursively fills the board with L-shaped tiles.
+     *
+     * <p>The board is divided into four quadrants. Depending on the location of
+     * the missing square, an L-shaped tile is placed at the center of the board
+     * to cover three of the four quadrants. The process is then repeated for
+     * each quadrant until the entire board is filled.
+     *
+     * @param size The current size of the sub-board.
+     * @param row The starting row index of the current sub-board.
+     * @param col The starting column index of the current sub-board.
+     * @param missingRow The row index of the missing square within the board.
+     * @param missingCol The column index of the missing square within the board.
+     */
+    private static void fillBoard(int size, int row, int col, int missingRow, int missingCol) {
+        if (size == 1) {
+            return;
+        }
+
+        int half = size / 2;
+        int t = tile++;
+
+
+        // Top-left quadrant
+        if (missingRow < row + half && missingCol < col + half) {
+            fillBoard(half, row, col, missingRow, missingCol);
+        } else {
+            board[row + half - 1][col + half - 1] = t;
+            fillBoard(half, row, col, row + half - 1, col + half - 1);
+        }
+
+        // Top-right quadrant
+        if (missingRow < row + half && missingCol >= col + half) {
+            fillBoard(half, row, col + half, missingRow, missingCol);
+        } else {
+            board[row + half - 1][col + half] = t;
+            fillBoard(half, row, col + half, row + half - 1, col + half);
+        }
+
+        // Bottom-left quadrant
+        if (missingRow >= row + half && missingCol < col + half) {
+            fillBoard(half, row + half, col, missingRow, missingCol);
+        } else {
+            board[row + half][col + half - 1] = t;
+            fillBoard(half, row + half, col, row + half, col + half - 1);
+        }
+
+        // Bottom-right quadrant
+        if (missingRow >= row + half && missingCol >= col + half) {
+            fillBoard(half, row + half, col + half, missingRow, missingCol);
+        } else {
+            board[row + half][col + half] = t;
+            fillBoard(half, row + half, col + half, row + half, col + half);
+        }
+    }
+}

src/test/java/com/thealgorithms/divideandconquer/TilingProblemTest.java

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+package com.thealgorithms.divideandconquer;
+
+import static org.junit.jupiter.api.Assertions.assertArrayEquals;
+
+import org.junit.jupiter.api.Test;
+
+public class TilingProblemTest {
+
+    @Test
+    public void testTilingSize2() {
+        int[][] expected = {
+                {1, 1},
+                {1, 0}
+        };
+        int[][] result = TilingProblem.solveTiling(2, 1, 1);
+        assertArrayEquals(expected, result);
+    }
+}