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| 1 | +// https://leetcode.com/problems/sudoku-solver |
| 2 | +// T: O(n^2 * k) but n = 9 and k = 9 so just O(1) |
| 3 | +// S: O(n^2) but n = 9 so just O(1) |
| 4 | + |
| 5 | +import java.util.HashMap; |
| 6 | +import java.util.HashSet; |
| 7 | +import java.util.Map; |
| 8 | +import java.util.Set; |
| 9 | + |
| 10 | +public class SudokuSolver { |
| 11 | + private record Position(int row, int column) { |
| 12 | + private static final Position start = new Position(0, 0); |
| 13 | + |
| 14 | + private boolean isValid() { |
| 15 | + return row >= 0 |
| 16 | + && row < 9 |
| 17 | + && column >= 0 |
| 18 | + && column < 9; |
| 19 | + } |
| 20 | + |
| 21 | + private Position next() { |
| 22 | + if (column == 8) return new Position(row + 1, 0); |
| 23 | + return new Position(row, column + 1); |
| 24 | + } |
| 25 | + } |
| 26 | + |
| 27 | + private static final Map<Integer, Set<Integer>> rows = new HashMap<>(); |
| 28 | + private static final Map<Integer, Set<Integer>> columns = new HashMap<>(); |
| 29 | + private static final Map<Integer, Set<Integer>> subGrids = new HashMap<>(); |
| 30 | + |
| 31 | + public static void solveSudoku(char[][] board) { |
| 32 | + computeDigitsInRows(board); |
| 33 | + computeDigitsInColumns(board); |
| 34 | + computeDigitsInSubGrids(board); |
| 35 | + solveSudoku(board, Position.start); |
| 36 | + } |
| 37 | + |
| 38 | + private static boolean solveSudoku(char[][] board, Position position) { |
| 39 | + if (!position.isValid()) return true; |
| 40 | + if (isAlreadyFilled(board, position)) return solveSudoku(board, position.next()); |
| 41 | + |
| 42 | + for (int i = 1 ; i <= 9 ; i++) { |
| 43 | + if (isInRow(i, position) || isInColumn(i, position) || isInSubGrid(i, position)) continue; |
| 44 | + insertInGrid(i, position, board); |
| 45 | + boolean solved = solveSudoku(board, position.next()); |
| 46 | + if (solved) return true; |
| 47 | + removeFromGrid(i, position, board); |
| 48 | + } |
| 49 | + return false; |
| 50 | + } |
| 51 | + |
| 52 | + private static boolean isAlreadyFilled(char[][] board, Position position) { |
| 53 | + return board[position.row][position.column] != '.'; |
| 54 | + } |
| 55 | + |
| 56 | + private static boolean isInRow(int digit, Position position) { |
| 57 | + return rows.get(position.row).contains(digit); |
| 58 | + } |
| 59 | + |
| 60 | + private static boolean isInColumn(int digit, Position position) { |
| 61 | + return columns.get(position.column).contains(digit); |
| 62 | + } |
| 63 | + |
| 64 | + private static boolean isInSubGrid(int digit, Position position) { |
| 65 | + return subGrids.get(getSubGridId(position)).contains(digit); |
| 66 | + } |
| 67 | + |
| 68 | + private static void insertInGrid(int digit, Position position, char[][] board) { |
| 69 | + rows.get(position.row).add(digit); |
| 70 | + columns.get(position.column).add(digit); |
| 71 | + subGrids.get(getSubGridId(position)).add(digit); |
| 72 | + board[position.row][position.column] = toChar(digit); |
| 73 | + } |
| 74 | + |
| 75 | + private static void removeFromGrid(int digit, Position position, char[][] board) { |
| 76 | + rows.get(position.row).remove(digit); |
| 77 | + columns.get(position.column).remove(digit); |
| 78 | + subGrids.get(getSubGridId(position)).remove(digit); |
| 79 | + board[position.row][position.column] = '.'; |
| 80 | + } |
| 81 | + |
| 82 | + private static void computeDigitsInRows(char[][] board) { |
| 83 | + for (int row = 0 ; row < 9 ; row++) { |
| 84 | + final Set<Integer> digits = new HashSet<>(); |
| 85 | + for (char element : board[row]) { |
| 86 | + if (Character.isDigit(element)) { |
| 87 | + digits.add(toInt(element)); |
| 88 | + } |
| 89 | + } |
| 90 | + rows.put(row, digits); |
| 91 | + } |
| 92 | + } |
| 93 | + |
| 94 | + private static void computeDigitsInColumns(char[][] board) { |
| 95 | + for (int column = 0 ; column < 9 ; column++) { |
| 96 | + final Set<Integer> digits = new HashSet<>(); |
| 97 | + for (int row = 0 ; row < 9 ; row++) { |
| 98 | + if (Character.isDigit(board[row][column])) { |
| 99 | + digits.add(toInt(board[row][column])); |
| 100 | + } |
| 101 | + } |
| 102 | + columns.put(column, digits); |
| 103 | + } |
| 104 | + } |
| 105 | + |
| 106 | + private static void computeDigitsInSubGrids(char[][] board) { |
| 107 | + for (int i = 0 ; i < 3 ; i++) { |
| 108 | + for (int j = 0 ; j < 3 ; j++) { |
| 109 | + final int subGridId = getSubGridId(i, j); |
| 110 | + final Set<Integer> digits = new HashSet<>(); |
| 111 | + for (int row = 3 * i ; row < 3 * i + 3 ; row++) { |
| 112 | + for (int column = 3 * j ; column < 3 * j + 3 ; column++) { |
| 113 | + if (Character.isDigit(board[row][column])) { |
| 114 | + digits.add(toInt(board[row][column])); |
| 115 | + } |
| 116 | + } |
| 117 | + } |
| 118 | + subGrids.put(subGridId, digits); |
| 119 | + } |
| 120 | + } |
| 121 | + } |
| 122 | + |
| 123 | + private static int toInt(char c) { |
| 124 | + return c - '0'; |
| 125 | + } |
| 126 | + |
| 127 | + private static char toChar(int digit) { |
| 128 | + return (char) ('0' + digit); |
| 129 | + } |
| 130 | + |
| 131 | + private static int getSubGridId(int i, int j) { |
| 132 | + return 10 * i + j; |
| 133 | + } |
| 134 | + |
| 135 | + private static int getSubGridId(Position position) { |
| 136 | + int i = position.row / 3; |
| 137 | + int j = position.column / 3; |
| 138 | + return getSubGridId(i, j); |
| 139 | + } |
| 140 | +} |
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