From 41e9b63f5dc5be8929716eb6d0b1ec68cfe569b3 Mon Sep 17 00:00:00 2001 From: Hardik Pawar Date: Sun, 13 Oct 2024 08:40:23 +0530 Subject: [PATCH 1/4] feat: Add `TilingProblem` new algorithm with Junit tests --- .../divideandconquer/TilingProblem.java | 100 ++++++++++++++++++ .../divideandconquer/TilingProblemTest.java | 18 ++++ 2 files changed, 118 insertions(+) create mode 100644 src/main/java/com/thealgorithms/divideandconquer/TilingProblem.java create mode 100644 src/test/java/com/thealgorithms/divideandconquer/TilingProblemTest.java diff --git a/src/main/java/com/thealgorithms/divideandconquer/TilingProblem.java b/src/main/java/com/thealgorithms/divideandconquer/TilingProblem.java new file mode 100644 index 000000000000..e30d4cd2782a --- /dev/null +++ b/src/main/java/com/thealgorithms/divideandconquer/TilingProblem.java @@ -0,0 +1,100 @@ +package com.thealgorithms.divideandconquer; + +/** + * This class provides a solution to the Tiling Problem using divide-and-conquer. + *

+ * 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. + * + *

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. + * + *

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); + } + } +} diff --git a/src/test/java/com/thealgorithms/divideandconquer/TilingProblemTest.java b/src/test/java/com/thealgorithms/divideandconquer/TilingProblemTest.java new file mode 100644 index 000000000000..faefa164ba42 --- /dev/null +++ b/src/test/java/com/thealgorithms/divideandconquer/TilingProblemTest.java @@ -0,0 +1,18 @@ +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); + } +} From 5e9e5f2e7756170eab6b39457ca87f375ea0570f Mon Sep 17 00:00:00 2001 From: Hardvan Date: Sun, 13 Oct 2024 03:10:40 +0000 Subject: [PATCH 2/4] Update directory --- DIRECTORY.md | 12 ++++++++++++ 1 file changed, 12 insertions(+) diff --git a/DIRECTORY.md b/DIRECTORY.md index 30fa2cbee199..1989fc797462 100644 --- a/DIRECTORY.md +++ b/DIRECTORY.md @@ -25,9 +25,11 @@ * bitmanipulation * [BinaryPalindromeCheck](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/bitmanipulation/BinaryPalindromeCheck.java) * [BitSwap](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/bitmanipulation/BitSwap.java) + * [BooleanAlgebraGates](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/bitmanipulation/BooleanAlgebraGates.java) * [ClearLeftmostSetBit](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/bitmanipulation/ClearLeftmostSetBit.java) * [CountLeadingZeros](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/bitmanipulation/CountLeadingZeros.java) * [CountSetBits](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/bitmanipulation/CountSetBits.java) + * [FindNthBit](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/bitmanipulation/FindNthBit.java) * [GrayCodeConversion](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/bitmanipulation/GrayCodeConversion.java) * [HammingDistance](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/bitmanipulation/HammingDistance.java) * [HigherLowerPowerOfTwo](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/bitmanipulation/HigherLowerPowerOfTwo.java) @@ -54,6 +56,7 @@ * [CompositeLFSR](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/ciphers/a5/CompositeLFSR.java) * [LFSR](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/ciphers/a5/LFSR.java) * [Utils](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/ciphers/a5/Utils.java) + * [ADFGVXCipher](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/ciphers/ADFGVXCipher.java) * [AES](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/ciphers/AES.java) * [AESEncryption](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/ciphers/AESEncryption.java) * [AffineCipher](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/ciphers/AffineCipher.java) @@ -133,6 +136,7 @@ * [FordFulkerson](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/datastructures/graphs/FordFulkerson.java) * [Graphs](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/datastructures/graphs/Graphs.java) * [HamiltonianCycle](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/datastructures/graphs/HamiltonianCycle.java) + * [JohnsonsAlgorithm](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/datastructures/graphs/JohnsonsAlgorithm.java) * [KahnsAlgorithm](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/datastructures/graphs/KahnsAlgorithm.java) * [Kosaraju](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/datastructures/graphs/Kosaraju.java) * [Kruskal](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/datastructures/graphs/Kruskal.java) @@ -247,6 +251,7 @@ * [MedianOfTwoSortedArrays](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/divideandconquer/MedianOfTwoSortedArrays.java) * [SkylineAlgorithm](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/divideandconquer/SkylineAlgorithm.java) * [StrassenMatrixMultiplication](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/divideandconquer/StrassenMatrixMultiplication.java) + * [TilingProblem](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/divideandconquer/TilingProblem.java) * dynamicprogramming * [BoardPath](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/dynamicprogramming/BoardPath.java) * [BoundaryFill](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/dynamicprogramming/BoundaryFill.java) @@ -340,6 +345,7 @@ * [EulersFunction](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/maths/EulersFunction.java) * [Factorial](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/maths/Factorial.java) * [FactorialRecursion](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/maths/FactorialRecursion.java) + * [FastExponentiation](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/maths/FastExponentiation.java) * [FastInverseSqrt](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/maths/FastInverseSqrt.java) * [FFT](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/maths/FFT.java) * [FFTBluestein](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/maths/FFTBluestein.java) @@ -656,9 +662,11 @@ * bitmanipulation * [BinaryPalindromeCheckTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/bitmanipulation/BinaryPalindromeCheckTest.java) * [BitSwapTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/bitmanipulation/BitSwapTest.java) + * [BooleanAlgebraGatesTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/bitmanipulation/BooleanAlgebraGatesTest.java) * [ClearLeftmostSetBitTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/bitmanipulation/ClearLeftmostSetBitTest.java) * [CountLeadingZerosTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/bitmanipulation/CountLeadingZerosTest.java) * [CountSetBitsTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/bitmanipulation/CountSetBitsTest.java) + * [FindNthBitTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/bitmanipulation/FindNthBitTest.java) * [GrayCodeConversionTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/bitmanipulation/GrayCodeConversionTest.java) * [HammingDistanceTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/bitmanipulation/HammingDistanceTest.java) * [HigherLowerPowerOfTwoTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/bitmanipulation/HigherLowerPowerOfTwoTest.java) @@ -682,6 +690,7 @@ * [A5CipherTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/ciphers/a5/A5CipherTest.java) * [A5KeyStreamGeneratorTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/ciphers/a5/A5KeyStreamGeneratorTest.java) * [LFSRTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/ciphers/a5/LFSRTest.java) + * [ADFGVXCipherTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/ciphers/ADFGVXCipherTest.java) * [AESEncryptionTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/ciphers/AESEncryptionTest.java) * [AffineCipherTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/ciphers/AffineCipherTest.java) * [AtbashTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/ciphers/AtbashTest.java) @@ -750,6 +759,7 @@ * [FloydWarshallTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/datastructures/graphs/FloydWarshallTest.java) * [FordFulkersonTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/datastructures/graphs/FordFulkersonTest.java) * [HamiltonianCycleTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/datastructures/graphs/HamiltonianCycleTest.java) + * [JohnsonsAlgorithmTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/datastructures/graphs/JohnsonsAlgorithmTest.java) * [KosarajuTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/datastructures/graphs/KosarajuTest.java) * [TarjansAlgorithmTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/datastructures/graphs/TarjansAlgorithmTest.java) * [WelshPowellTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/datastructures/graphs/WelshPowellTest.java) @@ -817,6 +827,7 @@ * [MedianOfTwoSortedArraysTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/divideandconquer/MedianOfTwoSortedArraysTest.java) * [SkylineAlgorithmTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/divideandconquer/SkylineAlgorithmTest.java) * [StrassenMatrixMultiplicationTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/divideandconquer/StrassenMatrixMultiplicationTest.java) + * [TilingProblemTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/divideandconquer/TilingProblemTest.java) * dynamicprogramming * [BoardPathTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/dynamicprogramming/BoardPathTest.java) * [BoundaryFillTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/dynamicprogramming/BoundaryFillTest.java) @@ -902,6 +913,7 @@ * [EulersFunctionTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/maths/EulersFunctionTest.java) * [FactorialRecursionTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/maths/FactorialRecursionTest.java) * [FactorialTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/maths/FactorialTest.java) + * [FastExponentiationTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/maths/FastExponentiationTest.java) * [FastInverseSqrtTests](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/maths/FastInverseSqrtTests.java) * [FFTTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/maths/FFTTest.java) * [FibonacciJavaStreamsTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/maths/FibonacciJavaStreamsTest.java) From ecfbcf53c6c36d73db5c5827591b22ac90305a71 Mon Sep 17 00:00:00 2001 From: Hardik Pawar Date: Sun, 13 Oct 2024 08:42:02 +0530 Subject: [PATCH 3/4] Fix --- .../thealgorithms/divideandconquer/TilingProblemTest.java | 5 +---- 1 file changed, 1 insertion(+), 4 deletions(-) diff --git a/src/test/java/com/thealgorithms/divideandconquer/TilingProblemTest.java b/src/test/java/com/thealgorithms/divideandconquer/TilingProblemTest.java index faefa164ba42..720e425f5ea3 100644 --- a/src/test/java/com/thealgorithms/divideandconquer/TilingProblemTest.java +++ b/src/test/java/com/thealgorithms/divideandconquer/TilingProblemTest.java @@ -8,10 +8,7 @@ public class TilingProblemTest { @Test public void testTilingSize2() { - int[][] expected = { - {1, 1}, - {1, 0} - }; + int[][] expected = {{1, 1}, {1, 0}}; int[][] result = TilingProblem.solveTiling(2, 1, 1); assertArrayEquals(expected, result); } From bc6dd02fbaabd08069bb9ea2eb0340bc3a97cf05 Mon Sep 17 00:00:00 2001 From: Hardik Pawar Date: Sun, 13 Oct 2024 08:44:24 +0530 Subject: [PATCH 4/4] Fix --- .../java/com/thealgorithms/divideandconquer/TilingProblem.java | 1 - 1 file changed, 1 deletion(-) diff --git a/src/main/java/com/thealgorithms/divideandconquer/TilingProblem.java b/src/main/java/com/thealgorithms/divideandconquer/TilingProblem.java index e30d4cd2782a..ff2e1678ab48 100644 --- a/src/main/java/com/thealgorithms/divideandconquer/TilingProblem.java +++ b/src/main/java/com/thealgorithms/divideandconquer/TilingProblem.java @@ -64,7 +64,6 @@ private static void fillBoard(int size, int row, int col, int missingRow, int mi int half = size / 2; int t = tile++; - // Top-left quadrant if (missingRow < row + half && missingCol < col + half) { fillBoard(half, row, col, missingRow, missingCol);