号称世界最难的数独
程序源码
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";
solve(input);
}
}
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运行结果
... ...
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:343
8 │ 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
进程已结束,退出代码0
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答案
