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Create package prime, matrix and games (#6139)
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varada610
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package com.thealgorithms.others;
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/**
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* A class that provides methods to solve Sudoku puzzles of any n x n size
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* using a backtracking approach, where n must be a perfect square.
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* The algorithm checks for safe number placements in rows, columns,
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* and subgrids (which are sqrt(n) x sqrt(n) in size) and recursively solves the puzzle.
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* Though commonly used for 9x9 grids, it is adaptable to other valid Sudoku dimensions.
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*/
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final class Sudoku {
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private Sudoku() {
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}
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/**
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* Checks if placing a number in a specific position on the Sudoku board is safe.
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* The number is considered safe if it does not violate any of the Sudoku rules:
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* - It should not be present in the same row.
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* - It should not be present in the same column.
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* - It should not be present in the corresponding 3x3 subgrid.
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* - It should not be present in the corresponding subgrid, which is sqrt(n) x sqrt(n) in size (e.g., for a 9x9 grid, the subgrid will be 3x3).
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*
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* @param board The current state of the Sudoku board.
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* @param row The row index where the number is to be placed.
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* @param col The column index where the number is to be placed.
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* @param num The number to be placed on the board.
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* @return True if the placement is safe, otherwise false.
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*/
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public static boolean isSafe(int[][] board, int row, int col, int num) {
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// Check the row for duplicates
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for (int d = 0; d < board.length; d++) {
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if (board[row][d] == num) {
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return false;
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}
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}
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// Check the column for duplicates
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for (int r = 0; r < board.length; r++) {
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if (board[r][col] == num) {
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return false;
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}
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}
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// Check the corresponding 3x3 subgrid for duplicates
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int sqrt = (int) Math.sqrt(board.length);
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int boxRowStart = row - row % sqrt;
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int boxColStart = col - col % sqrt;
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for (int r = boxRowStart; r < boxRowStart + sqrt; r++) {
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for (int d = boxColStart; d < boxColStart + sqrt; d++) {
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if (board[r][d] == num) {
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return false;
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}
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}
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}
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return true;
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}
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/**
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* Solves the Sudoku puzzle using backtracking.
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* The algorithm finds an empty cell and tries placing numbers
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* from 1 to n, where n is the size of the board
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* (for example, from 1 to 9 in a standard 9x9 Sudoku).
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* The algorithm finds an empty cell and tries placing numbers from 1 to 9.
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* The standard version of Sudoku uses numbers from 1 to 9, so the algorithm can be
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* easily modified for other variations of the game.
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* If a number placement is valid (checked via `isSafe`), the number is
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* placed and the function recursively attempts to solve the rest of the puzzle.
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* If no solution is possible, the number is removed (backtracked),
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* and the process is repeated.
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*
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* @param board The current state of the Sudoku board.
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* @param n The size of the Sudoku board (typically 9 for a standard puzzle).
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* @return True if the Sudoku puzzle is solvable, false otherwise.
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*/
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public static boolean solveSudoku(int[][] board, int n) {
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int row = -1;
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int col = -1;
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boolean isEmpty = true;
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// Find the next empty cell
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for (int i = 0; i < n; i++) {
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for (int j = 0; j < n; j++) {
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if (board[i][j] == 0) {
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row = i;
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col = j;
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isEmpty = false;
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break;
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}
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}
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if (!isEmpty) {
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break;
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}
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}
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// No empty space left
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if (isEmpty) {
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return true;
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}
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// Try placing numbers 1 to n in the empty cell (n should be a perfect square)
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// Eg: n=9 for a standard 9x9 Sudoku puzzle, n=16 for a 16x16 puzzle, etc.
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for (int num = 1; num <= n; num++) {
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if (isSafe(board, row, col, num)) {
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board[row][col] = num;
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if (solveSudoku(board, n)) {
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return true;
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} else {
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// replace it
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board[row][col] = 0;
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}
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}
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}
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return false;
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}
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/**
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* Prints the current state of the Sudoku board in a readable format.
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* Each row is printed on a new line, with numbers separated by spaces.
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*
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* @param board The current state of the Sudoku board.
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* @param n The size of the Sudoku board (typically 9 for a standard puzzle).
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*/
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public static void print(int[][] board, int n) {
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// Print the board in a nxn grid format
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// if n=9, print the board in a 9x9 grid format
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// if n=16, print the board in a 16x16 grid format
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for (int r = 0; r < n; r++) {
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for (int d = 0; d < n; d++) {
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System.out.print(board[r][d]);
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System.out.print(" ");
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}
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System.out.print("\n");
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if ((r + 1) % (int) Math.sqrt(n) == 0) {
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System.out.print("");
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}
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}
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}
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/**
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* The driver method to demonstrate solving a Sudoku puzzle.
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* A sample 9x9 Sudoku puzzle is provided, and the program attempts to solve it
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* using the `solveSudoku` method. If a solution is found, it is printed to the console.
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*
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* @param args Command-line arguments (not used in this program).
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*/
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public static void main(String[] args) {
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int[][] board = new int[][] {
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{3, 0, 6, 5, 0, 8, 4, 0, 0},
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{5, 2, 0, 0, 0, 0, 0, 0, 0},
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{0, 8, 7, 0, 0, 0, 0, 3, 1},
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{0, 0, 3, 0, 1, 0, 0, 8, 0},
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{9, 0, 0, 8, 6, 3, 0, 0, 5},
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{0, 5, 0, 0, 9, 0, 6, 0, 0},
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{1, 3, 0, 0, 0, 0, 2, 5, 0},
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{0, 0, 0, 0, 0, 0, 0, 7, 4},
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{0, 0, 5, 2, 0, 6, 3, 0, 0},
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};
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int n = board.length;
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if (solveSudoku(board, n)) {
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print(board, n);
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} else {
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System.out.println("No solution");
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}
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}
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}
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@@ -1,65 +0,0 @@
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package com.thealgorithms.others;
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import java.util.List;
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/**
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* The {@code TowerOfHanoi} class provides a recursive solution to the Tower of Hanoi puzzle.
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* This puzzle involves moving a set of discs from one pole to another, following specific rules:
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* 1. Only one disc can be moved at a time.
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* 2. A disc can only be placed on top of a larger disc.
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* 3. All discs must start on one pole and end on another.
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*
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* This implementation recursively calculates the steps required to solve the puzzle and stores them
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* in a provided list.
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*
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* <p>
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* For more information about the Tower of Hanoi, see
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* <a href="https://en.wikipedia.org/wiki/Tower_of_Hanoi">Tower of Hanoi on Wikipedia</a>.
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* </p>
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*
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* The {@code shift} method takes the number of discs and the names of the poles,
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* and appends the steps required to solve the puzzle to the provided list.
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* Time Complexity: O(2^n) - Exponential time complexity due to the recursive nature of the problem.
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* Space Complexity: O(n) - Linear space complexity due to the recursion stack.
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* Wikipedia: https://en.wikipedia.org/wiki/Tower_of_Hanoi
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*/
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final class TowerOfHanoi {
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private TowerOfHanoi() {
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}
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/**
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* Recursively solve the Tower of Hanoi puzzle by moving discs between poles.
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*
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* @param n The number of discs to move.
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* @param startPole The name of the start pole from which discs are moved.
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* @param intermediatePole The name of the intermediate pole used as a temporary holding area.
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* @param endPole The name of the end pole to which discs are moved.
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* @param result A list to store the steps required to solve the puzzle.
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*
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* <p>
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* This method is called recursively to move n-1 discs
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* to the intermediate pole,
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* then moves the nth disc to the end pole, and finally
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* moves the n-1 discs from the
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* intermediate pole to the end pole.
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* </p>
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*
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* <p>
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* Time Complexity: O(2^n) - Exponential time complexity due to the recursive nature of the problem.
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* Space Complexity: O(n) - Linear space complexity due to the recursion stack.
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* </p>
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*/
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public static void shift(int n, String startPole, String intermediatePole, String endPole, List<String> result) {
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if (n != 0) {
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// Move n-1 discs from startPole to intermediatePole
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shift(n - 1, startPole, endPole, intermediatePole, result);
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// Add the move of the nth disc from startPole to endPole
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result.add(String.format("Move %d from %s to %s", n, startPole, endPole));
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// Move the n-1 discs from intermediatePole to endPole
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shift(n - 1, intermediatePole, startPole, endPole, result);
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}
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}
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}
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