目錄

• 號稱世界最難的數獨
• 程序源碼
• 運行結果
• 答案

號稱世界最難的數獨

程序源碼

import java.util.ArrayList; import java.util.HashSet;public class Main {private static final int MAX_GUESS_COUNT = 4096;private static int guessCount = 0;private static long startTime;private static void guessOneUnit(Sudoku sudoku) {if (++guessCount > MAX_GUESS_COUNT) {System.err.println("sudoku can't find the answer after " + guessCount + " times' guess so have to exit");sudoku.printEx(true);long endTime = System.currentTimeMillis();System.out.println("sudoku costs " + (endTime - startTime) + "ms to analyze this problem");System.exit(-1);}Sudoku.UnitToGuess unitToGuess = sudoku.fetchOneUnitToGuess();if (unitToGuess == null) {sudoku.printEx(true);System.err.println("sudoku enter a impossible situation and has to exit");return;}for (Integer e : unitToGuess.getOnes()) {Sudoku sudokuNew = sudoku.clone();sudokuNew.setOneUnit(unitToGuess.getRowIndex(), unitToGuess.getColIndex(), e);sudokuNew.printEx(true);if (sudokuNew.setUnitLoop()) {guessOneUnit(sudokuNew);}}}public static void solve(String input) {String[] lines = input.split("\\n");int[][] matrix = new int[Sudoku.LINE_UNIT_COUNT][Sudoku.LINE_UNIT_COUNT];for (int i = 0; i < Sudoku.LINE_UNIT_COUNT; ++i) {String[] units = lines[i].split(",");for (int j = 0; j < Sudoku.LINE_UNIT_COUNT; ++j) {matrix[i][j] = Integer.parseInt(units[j]);}}Sudoku sudoku = new Sudoku(matrix);sudoku.print("----------------original sudo matrix----------------");sudoku.initArray();sudoku.printEx(true);sudoku.setUnitLoop();guessOneUnit(sudoku);}public static class Sudoku implements Cloneable {public static final int LINE_MATRIX_UNIT_COUNT = 3;public static final int MATRIX_LINT_UNIT_COUNT = LINE_MATRIX_UNIT_COUNT;public static final int LINE_MATRIX_COUNT = LINE_MATRIX_UNIT_COUNT;public static final int MATRIX_UNIT_COUNT = LINE_MATRIX_UNIT_COUNT * LINE_MATRIX_UNIT_COUNT;public static final int LINE_UNIT_COUNT = MATRIX_UNIT_COUNT;public static final int PRINT_STEP_COUNT = 2000;private int[][] matrix;private ArrayList<Integer>[][] matrixEx;private HashSet<Integer>[] matrixRow;private HashSet<Integer>[] matrixCol;private HashSet<Integer>[][] matrixBlocks;private int finish;private int effective;private int empty;private static int index = 0;public Sudoku() {this(new int[LINE_UNIT_COUNT][LINE_UNIT_COUNT]);}public Sudoku(int[][] matrix) {this.finish = 0;this.effective = 0;this.empty = LINE_UNIT_COUNT * LINE_UNIT_COUNT;this.matrix = new int[LINE_UNIT_COUNT][LINE_UNIT_COUNT];this.matrixEx = new ArrayList[LINE_UNIT_COUNT][LINE_UNIT_COUNT];this.matrixRow = new HashSet[LINE_UNIT_COUNT];this.matrixCol = new HashSet[LINE_UNIT_COUNT];this.matrixBlocks = new HashSet[LINE_MATRIX_COUNT][LINE_MATRIX_COUNT];for (int i = 0; i < LINE_UNIT_COUNT; ++i) {for (int j = 0; j < LINE_UNIT_COUNT; ++j) {this.matrix[i][j] = matrix[i][j];this.matrixEx[i][j] = new ArrayList<>();if (matrix[i][j] != 0) {--this.empty;++this.finish;}}}for (int k = 0; k < LINE_UNIT_COUNT; ++k) {matrixRow[k] = new HashSet<>();matrixCol[k] = new HashSet<>();}for (int i = 0; i < LINE_MATRIX_COUNT; ++i) {for (int j = 0; j < LINE_MATRIX_COUNT; ++j) {matrixBlocks[i][j] = new HashSet<>();}}}public Sudoku clone() {Sudoku sudoku = new Sudoku();sudoku.empty = empty;sudoku.effective = effective;sudoku.finish = finish;for (int i = 0; i < LINE_UNIT_COUNT; ++i) {for (int j = 0; j < LINE_UNIT_COUNT; ++j) {sudoku.matrix[i][j] = matrix[i][j];for (Integer e : matrixEx[i][j]) {sudoku.matrixEx[i][j].add(e);}}}for (int k = 0; k < LINE_UNIT_COUNT; ++k) {for (Integer e : matrixRow[k]) {sudoku.matrixRow[k].add(e);}for (Integer e : matrixRow[k]) {sudoku.matrixRow[k].add(e);}}for (int i = 0; i < LINE_MATRIX_COUNT; ++i) {for (int j = 0; j < LINE_MATRIX_COUNT; ++j) {for (Integer e : matrixBlocks[i][j]) {sudoku.matrixBlocks[i][j].add(e);}}}return sudoku;}private ArrayList<Integer> getInitUnit() {ArrayList<Integer> unit = new ArrayList<>();for (int i = 1; i <= LINE_UNIT_COUNT; ++i) {unit.add(i);}return unit;}private ArrayList<Integer> getInitUnitWithValue(int i) {ArrayList<Integer> unit = new ArrayList<>();unit.add(i);return unit;}private void initArray() {for (int i = 0; i < LINE_UNIT_COUNT; ++i) {for (int j = 0; j < LINE_UNIT_COUNT; ++j) {if (matrix[i][j] != 0) {matrixEx[i][j] = getInitUnitWithValue(matrix[i][j]);matrixRow[i].add(matrix[i][j]);matrixCol[j].add(matrix[i][j]);matrixBlocks[i / LINE_MATRIX_UNIT_COUNT][j / LINE_MATRIX_UNIT_COUNT].add(matrix[i][j]);}}}for (int i = 0; i < LINE_UNIT_COUNT; ++i) {for (int j = 0; j < LINE_UNIT_COUNT; ++j) {if (matrix[i][j] == 0) {matrixEx[i][j] = getInitUnit();}}}}private void print(String title) {System.out.println(title);System.out.println("empty:" + empty + ",finish:" + finish + ",effective:" + effective);StringBuilder stringBuilder = new StringBuilder();for (int i = 0; i < LINE_UNIT_COUNT; ++i) {for (int j = 0; j < LINE_UNIT_COUNT; ++j) {if (matrix[i][j] != 0) {stringBuilder.append(" ").append(matrix[i][j]).append(" ");} else {stringBuilder.append(" ");}if (j != LINE_UNIT_COUNT - 1) {if (j % 3 == 2) {stringBuilder.append('║');} else {stringBuilder.append('│');}}}stringBuilder.append(System.lineSeparator());if (i != LINE_UNIT_COUNT - 1) {boolean isDouble = i % 3 == 2;printRowLine(isDouble, stringBuilder);}}stringBuilder.append(System.lineSeparator());System.out.println(stringBuilder);}private void printRowLine(boolean isDouble, StringBuilder stringBuilder) {String edge;char cross1;char cross2;if (isDouble) {edge = "═══";cross1 = '╪';cross2 = '╬';} else {edge = "───";cross1 = '┼';cross2 = '╫';}for (int i = 0; i < LINE_UNIT_COUNT; ++i) {stringBuilder.append(edge);if (i != LINE_UNIT_COUNT - 1) {if (i % LINE_MATRIX_UNIT_COUNT == 2) {stringBuilder.append(cross2);} else {stringBuilder.append(cross1);}}}stringBuilder.append(System.lineSeparator());}private void printEx(boolean force) {if (!force && ++index % PRINT_STEP_COUNT != 0) {return;}System.out.println("this is the " + index + "'th loop result");System.out.println("empty:" + empty + ",finish:" + finish + ",effective:" + effective);StringBuilder stringBuilder = new StringBuilder();for (int i = 0; i < LINE_UNIT_COUNT; ++i) {for (int l = 0; l < MATRIX_LINT_UNIT_COUNT; ++l) {for (int j = 0; j < LINE_UNIT_COUNT; ++j) {for (int k = 0; k < MATRIX_LINT_UNIT_COUNT; ++k) {int n = l * MATRIX_LINT_UNIT_COUNT + k + 1;if (matrixEx[i][j].contains(n)) {stringBuilder.append(" ").append(n).append(" ");} else {stringBuilder.append(" ");}}if (j != LINE_UNIT_COUNT - 1) {if (j % 3 == 2) {stringBuilder.append('║');} else {stringBuilder.append('│');}}}stringBuilder.append(System.lineSeparator());}if (i != LINE_UNIT_COUNT - 1) {boolean isDouble = i % 3 == 2;printRowLineEx(isDouble, stringBuilder);}}stringBuilder.append(System.lineSeparator());System.out.println(stringBuilder);}private void printRowLineEx(boolean isDouble, StringBuilder stringBuilder) {String edge;char cross1;char cross2;if (isDouble) {edge = "═══";cross1 = '╪';cross2 = '╬';} else {edge = "───";cross1 = '┼';cross2 = '╫';}for (int j = 0; j < LINE_UNIT_COUNT; ++j) {for (int k = 0; k < LINE_MATRIX_UNIT_COUNT; ++k) {stringBuilder.append(edge);}if (j != LINE_UNIT_COUNT - 1) {if (j % LINE_MATRIX_UNIT_COUNT == 2) {stringBuilder.append(cross2);} else {stringBuilder.append(cross1);}}}stringBuilder.append(System.lineSeparator());}private void finish() {print("sudoku has find one answer showed followed so will exit normally");long endTime = System.currentTimeMillis();System.out.println("sudoku costs " + (endTime - startTime) + "ms to analyze this problem");System.exit(0);}public static class UnitToGuess {private int rowIndex;private int colIndex;private ArrayList<Integer> ones = new ArrayList<>();public int getRowIndex() {return rowIndex;}public int getColIndex() {return colIndex;}public ArrayList<Integer> getOnes() {return ones;}public UnitToGuess(int rowIndex, int colIndex, ArrayList<Integer> ones) {this.rowIndex = rowIndex;this.colIndex = colIndex;for (Integer e : ones) {this.ones.add(e);}}}private boolean setOneUnit(int rowIndex, int colIndex, int element) {System.out.println("try to set unit[" + rowIndex + "," + colIndex + "]=" + element + " for next loop");return setUnit(false, rowIndex, colIndex, element);}public UnitToGuess fetchOneUnitToGuess() {int miniSize = MATRIX_UNIT_COUNT;int rowIndex = -1;int colIndex = -1;for (int i = 0; i < LINE_UNIT_COUNT; ++i) {for (int j = 0; j < LINE_UNIT_COUNT; ++j) {if (matrixEx[i][j].size() > 1 && matrixEx[i][j].size() < miniSize) {rowIndex = i;colIndex = j;miniSize = matrixEx[i][j].size();}}}if (rowIndex != -1 && colIndex != -1) {return new UnitToGuess(rowIndex, colIndex, matrixEx[rowIndex][colIndex]);}return null;}public boolean setUnitLoop() {while (true) {int lastEffective = effective;if (!setUnitOfOneSize() || !setUnitInBlock() || !setUnitInLine(true) || !setUnitInLine(false)) {printEx(true);return false;}if (empty == 0) {finish();}if (effective == lastEffective) {System.out.println("this removeLoop can't remove any more");break;}}return true;}private ArrayList<Integer> getUnit(boolean revert, int rowIndex, int colIndex) {return revert ? matrixEx[colIndex][rowIndex] : matrixEx[rowIndex][colIndex];}private boolean checkRight() {boolean flag = true;for (int i = 0; i < LINE_UNIT_COUNT; ++i) {for (int j = 0; j < LINE_UNIT_COUNT; ++j) {if (matrix[i][j] != 0) {for (int ii = i / LINE_MATRIX_UNIT_COUNT * LINE_MATRIX_UNIT_COUNT;ii < i / LINE_MATRIX_UNIT_COUNT * LINE_MATRIX_UNIT_COUNT + LINE_MATRIX_UNIT_COUNT; ++ii) {for (int jj = j / LINE_MATRIX_UNIT_COUNT * LINE_MATRIX_UNIT_COUNT;jj < j / LINE_MATRIX_UNIT_COUNT * LINE_MATRIX_UNIT_COUNT + LINE_MATRIX_UNIT_COUNT; ++jj) {if ((i != ii || j != jj) && matrix[i][j] == matrix[ii][jj]) {System.out.println("[" + i + ',' + j + "]=[" + ii + ',' + jj + "]=" + matrix[i][j]);flag = false;}}}for (int k = 0; k < LINE_UNIT_COUNT; ++k) {if (i != k && matrix[i][j] == matrix[k][j]) {System.out.println("[" + i + ',' + j + "]=[" + k + ',' + j + "]=" + matrix[i][j]);flag = false;}if (j != k && matrix[i][j] == matrix[i][k]) {System.out.println("[" + i + ',' + j + "]=[" + i + ',' + k + "]=" + matrix[i][j]);flag = false;}}}}}if (!flag) {System.out.println("sudoku's first guess is error and will try the other guess again");printEx(true);}return flag;}private boolean setUnit(boolean revert, int rowIndex, int colIndex, Integer e) {int i;int j;if (revert) {i = colIndex;j = rowIndex;} else {i = rowIndex;j = colIndex;}if (matrix[i][j] == 0 && matrixEx[i][j].contains(e)) {matrixEx[i][j].clear();matrixEx[i][j].add(e);matrix[i][j] = e;matrixRow[i].add(e);matrixCol[j].add(e);matrixBlocks[i / LINE_MATRIX_UNIT_COUNT][j / LINE_MATRIX_UNIT_COUNT].add(e);--empty;++finish;++effective;printEx(false);return checkRight();}return true;}private boolean setUnitInLine(boolean isRow) {boolean revert = !isRow;for (int j = 0; j < LINE_UNIT_COUNT; ++j) {int[] count = new int[LINE_UNIT_COUNT + 1];for (int i = 0; i < LINE_UNIT_COUNT; ++i) {for (int e : getUnit(revert, i, j)) {count[e]++;}}ArrayList<Integer> ones = new ArrayList<>();for (int k = 1; k <= MATRIX_UNIT_COUNT; ++k) {if (count[k] == 1) {ones.add(k);}}for (int e : ones) {for (int i = 0; i < LINE_UNIT_COUNT; ++i) {boolean flag = setUnit(revert, i, j, e);if (!flag) {return false;}}}}return true;}private boolean setUnitInBlock() {for (int i = 0; i < LINE_MATRIX_COUNT; ++i) {for (int j = 0; j < LINE_MATRIX_COUNT; ++j) {int[] count = new int[MATRIX_UNIT_COUNT + 1];for (int ii = 0; ii < LINE_MATRIX_UNIT_COUNT; ++ii) {for (int jj = 0; jj < LINE_MATRIX_UNIT_COUNT; ++jj) {int indexI = i * LINE_MATRIX_UNIT_COUNT + ii;int indexJ = j * LINE_MATRIX_UNIT_COUNT + jj;for (int e : matrixEx[indexI][indexJ]) {count[e]++;}}}ArrayList<Integer> ones = new ArrayList<>();for (int k = 1; k <= MATRIX_UNIT_COUNT; ++k) {if (count[k] == 1) {ones.add(k);}}for (int e : ones) {for (int ii = 0; ii < LINE_MATRIX_UNIT_COUNT; ++ii) {for (int jj = 0; jj < LINE_MATRIX_UNIT_COUNT; ++jj) {int indexI = i * LINE_MATRIX_UNIT_COUNT + ii;int indexJ = j * LINE_MATRIX_UNIT_COUNT + jj;boolean flag = setUnit(false, indexI, indexJ, e);if (!flag) {return false;}}}}}}return true;}private boolean setUnitOfOneSize() {for (int i = 0; i < LINE_UNIT_COUNT; ++i) {for (int j = 0; j < LINE_UNIT_COUNT; ++j) {if (matrix[i][j] == 0) {if (matrixEx[i][j].removeAll(matrixRow[i]) || matrixEx[i][j].removeAll(matrixCol[j])|| matrixEx[i][j].removeAll(matrixBlocks[i / LINE_MATRIX_UNIT_COUNT][j / LINE_MATRIX_UNIT_COUNT])) {if (effective > 1000) {System.out.println("may error occur");}++effective;}if (matrixEx[i][j].size() == 0) {return false;} else if (matrixEx[i][j].size() == 1) {boolean flag = setUnit(false, i, j, matrixEx[i][j].get(0));if (!flag) {return false;}}}}}return true;}}public static void main(String[] args) {startTime = System.currentTimeMillis();String input = "8,0,0,0,0,0,0,0,0\n" +"0,0,3,6,0,0,0,0,0\n" +"0,7,0,0,9,0,2,0,0\n" +"0,5,0,0,0,7,0,0,0\n" +"0,0,0,0,4,5,7,0,0\n" +"0,0,0,1,0,0,0,3,0\n" +"0,0,1,0,0,0,0,6,8\n" +"0,0,8,5,0,0,0,1,0\n" +"0,9,0,0,0,0,4,0,0"; // "0,0,0,1,0,2,0,0,0\n" + // "0,0,8,0,6,0,7,0,5\n" + // "0,9,0,0,0,0,0,8,0\n" + // "4,0,0,0,1,0,0,0,0\n" + // "0,8,0,3,0,4,0,6,0\n" + // "3,0,0,0,2,0,8,0,0\n" + // "0,6,0,0,0,5,4,7,0\n" + // "0,0,5,0,7,0,6,0,9\n" + // "0,7,0,0,0,0,0,5,0"; // "0,0,0,0,0,2,0,5,0\n" + // "0,7,8,0,0,0,3,0,0\n" + // "0,0,0,0,0,4,0,0,0\n" + // "5,0,0,0,0,0,0,0,0\n" + // "0,0,0,0,0,0,1,0,0\n" + // "0,0,0,0,3,0,7,0,8\n" + // "2,0,0,0,0,0,0,4,0\n" + // "0,0,0,0,0,5,0,9,0\n" + // "0,1,0,0,7,0,0,0,0"; // "0,0,0,0,0,0,7,0,0\n" + // "0,4,0,0,3,0,0,6,5\n" + // "0,0,1,0,0,8,0,0,0\n" + // "0,6,0,0,5,0,0,3,9\n" + // "4,0,0,6,0,0,0,0,0\n" + // "0,0,0,0,0,0,0,2,0\n" + // "8,0,0,0,0,3,0,9,7\n" + // "0,0,0,0,7,0,4,0,0\n" + // "0,9,0,0,0,0,2,0,0";solve(input);} }

運行結果

... ...this is the 2068'th loop result empty:21,finish:60,effective:309│ 1 │ 2 ║ │ │ 3 ║ │ │ │ │ ║ │ 5 │ ║ 6 │ 4 │ 8 │ │ ║ 7 │ │ ║ │ │ 9 ─────────┼─────────┼─────────╫─────────┼─────────┼─────────╫─────────┼─────────┼─────────│ │ 3 ║ │ 2 │ ║ 1 │ │ 1 │ 4 │ ║ 6 │ │ ║ 5 │ │ 5 9 │ │ ║ │ │ 8 ║ │ 7 │ ─────────┼─────────┼─────────╫─────────┼─────────┼─────────╫─────────┼─────────┼─────────│ │ ║ │ │ 1 ║ 2 │ │ 3 6 │ │ 5 ║ 4 │ │ ║ │ │ │ 7 │ ║ │ 9 │ ║ │ 8 │ ═════════╪═════════╪═════════╬═════════╪═════════╪═════════╬═════════╪═════════╪═════════1 │ │ ║ 2 3 │ 3 │ ║ │ 2 │ │ 5 │ 4 6 ║ │ 6 │ ║ │ │ 4 6 │ │ 9 ║ │ 8 │ 7 ║ 8 │ 9 │ ─────────┼─────────┼─────────╫─────────┼─────────┼─────────╫─────────┼─────────┼─────────│ 3 │ ║ 2 3 │ │ ║ │ 2 │ 1 │ 6 │ 6 ║ │ 4 │ 5 ║ │ │ 6 │ 8 │ 9 ║ 8 │ │ ║ 7 │ 9 │ ─────────┼─────────┼─────────╫─────────┼─────────┼─────────╫─────────┼─────────┼─────────2 │ │ ║ 1 │ │ ║ │ 3 │ │ 6 │ 4 6 ║ │ 6 │ ║ 5 │ │ 4 5 6 │ 8 │ 7 ║ │ 8 │ 9 ║ 8 │ │ ═════════╪═════════╪═════════╬═════════╪═════════╪═════════╬═════════╪═════════╪═════════│ 2 │ 1 ║ │ │ ║ 3 │ │ 5 │ │ ║ │ │ 4 ║ │ 6 │ │ │ ║ 9 │ 7 │ ║ │ │ 8 ─────────┼─────────┼─────────╫─────────┼─────────┼─────────╫─────────┼─────────┼─────────│ 3 │ ║ │ 3 │ 2 ║ │ 1 │ 4 │ 6 │ ║ 5 │ 6 │ ║ │ │ │ │ 8 ║ │ │ ║ 9 │ │ 7 ─────────┼─────────┼─────────╫─────────┼─────────┼─────────╫─────────┼─────────┼─────────3 │ │ ║ │ 1 │ ║ │ │ 2 │ │ 6 ║ │ │ 6 ║ 4 │ 5 │ │ 9 │ 7 ║ 8 │ │ ║ │ │ try to set unit[1,4]=8 for next loop this is the 2069'th loop result empty:29,finish:52,effective:291│ 1 │ 2 ║ │ │ 3 ║ │ │ │ │ ║ │ 5 │ ║ 6 │ 4 │ 8 │ │ ║ 7 │ │ ║ │ │ 9 ─────────┼─────────┼─────────╫─────────┼─────────┼─────────╫─────────┼─────────┼─────────│ │ 3 ║ │ │ 2 ║ 1 │ │ 1 │ 4 │ ║ 6 │ │ ║ 5 │ │ 5 9 │ │ ║ │ 8 │ 8 ║ │ 7 │ ─────────┼─────────┼─────────╫─────────┼─────────┼─────────╫─────────┼─────────┼─────────│ │ ║ │ │ 1 ║ 2 │ │ 3 6 │ │ 5 ║ 4 │ │ ║ │ │ │ 7 │ ║ │ 9 │ ║ │ 8 │ ═════════╪═════════╪═════════╬═════════╪═════════╪═════════╬═════════╪═════════╪═════════1 2 3 │ │ ║ 2 3 │ 2 3 │ ║ 1 │ 2 │ 1 │ 5 │ 4 6 ║ │ 6 │ ║ │ │ 4 6 │ │ 9 ║ 8 │ 8 │ 7 ║ 8 │ 9 │ ─────────┼─────────┼─────────╫─────────┼─────────┼─────────╫─────────┼─────────┼─────────1 2 3 │ 3 │ ║ 2 3 │ │ ║ │ 2 │ 1 │ 6 │ 6 ║ │ 4 │ 5 ║ │ │ 6 │ 8 │ 9 ║ 8 │ │ ║ 7 │ 9 │ ─────────┼─────────┼─────────╫─────────┼─────────┼─────────╫─────────┼─────────┼─────────2 │ │ ║ 1 │ 2 │ ║ │ 3 │ │ 6 │ 4 6 ║ │ 6 │ ║ 5 │ │ 4 5 6 7 │ 8 │ 7 ║ │ 8 │ 9 ║ 8 │ │ ═════════╪═════════╪═════════╬═════════╪═════════╪═════════╬═════════╪═════════╪═════════│ 2 │ 1 ║ │ │ ║ 3 │ │ 5 │ │ ║ │ │ 4 ║ │ 6 │ │ │ ║ 9 │ 7 │ ║ │ │ 8 ─────────┼─────────┼─────────╫─────────┼─────────┼─────────╫─────────┼─────────┼─────────│ 3 │ ║ │ 2 3 │ 2 ║ │ 1 │ 4 │ 6 │ ║ 5 │ 6 │ 6 ║ │ │ │ │ 8 ║ │ │ ║ 9 │ │ 7 ─────────┼─────────┼─────────╫─────────┼─────────┼─────────╫─────────┼─────────┼─────────3 │ │ ║ 3 │ 1 │ ║ │ │ 2 │ │ 6 ║ │ │ 6 ║ 4 │ 5 │ 7 │ 9 │ 7 ║ 8 │ │ 8 ║ │ │ sudoku has find one answer showed followed so will exit normally empty:0,finish:81,effective:3438 │ 1 │ 2 ║ 7 │ 5 │ 3 ║ 6 │ 4 │ 9 ───┼───┼───╫───┼───┼───╫───┼───┼───9 │ 4 │ 3 ║ 6 │ 8 │ 2 ║ 1 │ 7 │ 5 ───┼───┼───╫───┼───┼───╫───┼───┼───6 │ 7 │ 5 ║ 4 │ 9 │ 1 ║ 2 │ 8 │ 3 ═══╪═══╪═══╬═══╪═══╪═══╬═══╪═══╪═══1 │ 5 │ 4 ║ 2 │ 3 │ 7 ║ 8 │ 9 │ 6 ───┼───┼───╫───┼───┼───╫───┼───┼───3 │ 6 │ 9 ║ 8 │ 4 │ 5 ║ 7 │ 2 │ 1 ───┼───┼───╫───┼───┼───╫───┼───┼───2 │ 8 │ 7 ║ 1 │ 6 │ 9 ║ 5 │ 3 │ 4 ═══╪═══╪═══╬═══╪═══╪═══╬═══╪═══╪═══5 │ 2 │ 1 ║ 9 │ 7 │ 4 ║ 3 │ 6 │ 8 ───┼───┼───╫───┼───┼───╫───┼───┼───4 │ 3 │ 8 ║ 5 │ 2 │ 6 ║ 9 │ 1 │ 7 ───┼───┼───╫───┼───┼───╫───┼───┼───7 │ 9 │ 6 ║ 3 │ 1 │ 8 ║ 4 │ 5 │ 2 sudoku costs 128ms to analyze this problem進程已結束,退出代碼0

答案

總結

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