如何确定马在 java 中到达棋盘上的任何位置需要多少步
How to determine how many moves it takes a knight to get anywhere on the board in java
我正在尝试创建一个程序，当给定国际象棋的位置 knight and the destination, all marked in chess notation 时，return 骑士从该位置到达目的地所需的移动次数。在使用该算法计算列表中的 每个 单一可能性之前，我曾尝试过，但它非常慢并且有点问题。这是我的代码：
private static int translateChessNotation(String chess) {
int returned = 8 * (Integer.valueOf(String.valueOf(chess.charAt(1)))- 1);
return returned + (convertAlphabet(chess.charAt(0))); // File
}
public static int knight(String start, String finish) {
int knightPosition = translateChessNotation(start), end = translateChessNotation(finish), i = 0;
ArrayList<Integer> currentPossibleKnightPositions = new ArrayList<>();
currentPossibleKnightPositions.add(knightPosition);
for (; i < 8; i++) {
ArrayList<Integer> newList = new ArrayList<>();
for (int position : currentPossibleKnightPositions) {
newList.add(position + 17);
newList.add(position + 15);
newList.add(position + 10);
newList.add(position + 6);
newList.add(position - 6);
newList.add(position - 10);
newList.add(position - 15);
newList.add(position - 17);
}
ArrayList<Integer> removed = new ArrayList<>();
for (int j : newList) {if (j < 1 || j > 64) {removed.add(j);}}
newList.removeAll(removed);
currentPossibleKnightPositions.clear();
currentPossibleKnightPositions.addAll(newList);
for (int n : currentPossibleKnightPositions) {
if (n == end) {return i + 1;}
}
}
return -1;
}
如有帮助，万分感谢！
这里有一些 Proggy 可以解决所谓的 Knights-Tour 问题，从特定位置开始访问棋盘上的所有方块，因此您可以对其进行调整以将特定的 to-position 设置为结束条件。
这只是蛮力，尝试所有可能的组合，大约需要 50 分钟才能找到每个完整的 Knights-Tour 解决方案。
如果有帮助，我很荣幸收到您的投票。
import java.util.concurrent.atomic.AtomicInteger;
import java.util.stream.IntStream;
public class KnightMove {
@SuppressWarnings("serial")
private static final class KnightMoveSolvedException extends RuntimeException {
private final byte[][] solution;
private KnightMoveSolvedException(final byte[][] solution) {
this.solution = solution;
}
}
private static final int SIZE_X = 8;
private static final int SIZE_Y = 8;
private static final int SIZE_X_Y = SIZE_X * SIZE_Y; // Max 127! (=0x7F)
private static final int [][] KNIGHT_MOVES = new int[8][];
/**/ static {
final AtomicInteger moveIndex = new AtomicInteger();
IntStream.of(2, -2).forEach(deltaX ->
IntStream.of(1, -1).forEach(deltaY -> {
/*
* Mirror the 4 combinations above to get all 8 possible Knight moves...
*/
KNIGHT_MOVES[moveIndex.getAndIncrement()] = new int[] {deltaX, deltaY};
KNIGHT_MOVES[moveIndex.getAndIncrement()] = new int[] {deltaY, deltaX};
}));
}
private static void nextMoveToXY(int moveCount, final int x, final int y, final byte[][] board) {
moveCount++;
board[x][y] = (byte) moveCount;
if (moveCount >= SIZE_X_Y) {
System.out.println("Solved!.....: count=" + moveCount);
for ( final byte[] column : board ) {
for (final byte square : column) {
System.out.print(square + "\t");
}
System.out.println();
}
return; // (Back up & keep looking for next solution)
/*
* If 1 solution is enough, just throw the Exception...
*/
// throw new KnightMoveSolvedException(board);
}
for (final int[] knightMove : KNIGHT_MOVES) {
final int newX = x + knightMove[0]; if (newX < 0 || newX >= SIZE_X) {continue;}
final int newY = y + knightMove[1]; if (newY < 0 || newY >= SIZE_Y) {continue;}
if (board[newX][newY] == 0) {
/*
* Target Square is vacant, so try this move recursively...
*/
nextMoveToXY(moveCount, newX, newY, deepPrimitive2DArrayClone(board));
}
}
}
/**
* {@link Object#clone()} can create a Deep Clone of a 1D array of Primitives
* but will <b>not</b> deliver the desired result with 2D,
* so we have to wrap the rest by hand...
*/
private static byte[][] deepPrimitive2DArrayClone(final byte[][] source) {
final byte[][] clone = new byte[source.length][];
/**/ int cix = 0;
for (final byte[] col : source) {
clone[cix++] = col.clone();
}
return clone;
}
public static void main(final String[] args) throws Exception {
IntStream.range(0, SIZE_X).forEach(x ->
IntStream.range(0, SIZE_Y).forEach(y -> {
try {
System.out.println("Solve starting at X/Y.: " + x +"/" + y);
nextMoveToXY(0, x, y, new byte[SIZE_X][SIZE_Y]);
}
catch (final KnightMoveSolvedException e) {
System.out.println(e.solution);
}
}));
}
}
我已经把上一篇博文中的棋盘数组换成long了。
（64 位，刚好可以代表电路板）
新版本 显着 更快。
根据起始坐标，解决方案需要 1 分钟到 12 小时...
（我先放了几个更快的）
此示例旨在展示基础知识。有多种数学方法（参见维基百科）对其进行优化，但它们会使解决方案更加复杂。
一些要点：
- 如果可以的话，使用基元（byte、short、int、long，...）：它们非常快
- 使用蛮力时避免像 ArrayList 这样的对象：它们非常慢
- 使用递归：它为您保存和恢复状态。它可能会花费一些钱，但它会让生活变得更轻松
- 尽可能使用 final ：它不会更快，但有助于理解
希望你喜欢。 :-)
我现在已经磨练了这个东西。它 大大 比原来的速度更快（一点也不逊色！），使用 Warnsdorff 算法 & 可以解决多个起始位置，运行 同时在所有可用线程上。
大部分工作是正确设置数据结构和初始化。
递归 nextMoveToXY 求解器方法本身非常简单。
Warnsdorff 版本：
import java.time.Instant;
import java.util.Arrays;
import java.util.Collections;
import java.util.Map;
import java.util.TreeMap;
import java.util.concurrent.ExecutorService;
import java.util.concurrent.Executors;
import java.util.concurrent.TimeUnit;
import java.util.function.IntConsumer;
import java.util.stream.IntStream;
public class KnightsTourWarnsdorff {
private interface IntIntConsumer {
void accept(int t, int u);
}
private static final int MAX_INSTANT_TO_STRING_LENGTH = "2020-12-31T23:59:59.123456Z".length();
private static final int SIZE_X = 8;
private static final int SIZE_Y = 8;
private static final int SIZE_X_Y = SIZE_X * SIZE_Y;
/**/ static { check_SIZE_X_Y_withinCapacity();}
/**
* Do this in a Method (we don't want to mark the Class with SuppressWarnings)
*/
@SuppressWarnings("unused")
private static void check_SIZE_X_Y_withinCapacity() {
if (SIZE_X_Y > Long.SIZE) {
throw new UnsupportedOperationException("Number of squares on board exceeds capacity of long Solution");
}
}
/**
* Returns the unique offset corresponding to a Move or our position on the Board.
*/
private static int getDeltaXY(final int deltaX, final int deltaY) {
return deltaX + deltaY * SIZE_X; /* Yes, SIZE_X ! */
}
/**
* Returns a long with a single bit set, corresponding to our position on the Board.
*/
private static long getXYmaskBit(final int x, final int y) {
return 1L << (63 - getDeltaXY(x, y));
}
private static void walkBoard(final IntIntConsumer doXY) {
walkBoard(null, doXY, null);
}
private static void walkBoard(final IntConsumer doRowStart, final IntIntConsumer doXY, final Runnable doRowEnd) {
IntStream .range(0, SIZE_Y).forEach(y -> {if (doRowStart != null) {doRowStart.accept( y);}
IntStream.range(0, SIZE_X).forEach(x -> {if (doXY != null) {doXY .accept(x,y);}
}); if (doRowEnd != null) {doRowEnd .run ( );}
});
}
private static String toBinary(final long value) {
return leftPad(Long.SIZE, Long.toBinaryString(value)).replace('0', '_');
}
private static String leftPad (final int paddedLength, final String value) {
final int padCount = Math.max(0, paddedLength - value.length());
final char[] pad = new char[padCount];
Arrays.fill (pad, '0');
return String.valueOf(pad).concat(value);
}
private static String rightPad (final int paddedLength, final String value) {
final int padCount = Math.max(0, paddedLength - value.length());
final char[] pad = new char[padCount];
Arrays.fill (pad, '0');
return value.concat(String.valueOf(pad));
}
private static String header () {
return rightPad (MAX_INSTANT_TO_STRING_LENGTH, Instant.now().toString()) + " " + Thread.currentThread().getName() + " ";
}
/**
* Square on Board not only knows its x/y location, but also its position as an xyMask<br>
* (for checking whether a square is occupied & marking as occupied).<br>
* <br>
* It knows all possible Moves from this Square within the Board<br>
* (thus obviating the need to check whether we're still on the Board).<br>
* <br>
* Each Specific Move contains a reference to the Target Square, which in turn...<br>
* (these 2 measures speed up Navigation massively)
*/
private static final class Square {
private final int x;
private final int y;
/**
* Used to mark the Square as occupied on the Board
*/
private final long xyMask;
/**
* All possible Moves from this Square.<br>
* (initially all null: filled after all Squares have been instantiated)
*/
private final Move[] targetMove;
private Square(final int x, final int y) {
this.x = x;
this. y = y;
this.xyMask = getXYmaskBit(x, y);
this.targetMove = KNIGHT_MOVE_MAP.values().stream().filter(move -> {
final int newX = x + move.deltaX;
final int newY = y + move.deltaY;
return newX >= 0 && newX < SIZE_X
&& newY >= 0 && newY < SIZE_Y;
}).toArray(Move[]::new);
}
}
/**
* Either a Generic or a Specific Move
*/
private static final class Move {
private final int deltaX;
private final int deltaY;
private final int deltaXY;
private final Square target;
/**
* Create a Generic Move
*/
private Move(final int deltaX, final int deltaY) {
this.deltaX = deltaX;
this.deltaY = deltaY;
this.deltaXY = getDeltaXY(deltaX, deltaY);
this.target = null;
}
/**
* Create a Move to a specific Target Square
*/
private Move(final Move genericMove, final Square target) {
this.deltaX = genericMove.deltaX;
this.deltaY = genericMove.deltaY;
this.deltaXY = genericMove.deltaXY;
this.target = target;
}
}
@SuppressWarnings("serial")
private static final class KnightMoveSolvedException extends RuntimeException {
private final int[] solution;
private KnightMoveSolvedException(final int moveCount, final int[] solution) {
/*
* Trim the solution array down to the number of moves...
* (for those performing a partial walk)
*/
this.solution = Arrays.stream(solution).limit(moveCount).toArray();
synchronized (KnightMoveSolvedException.class) { // One Thread (= Solution) at a time please!
final int solution0 = this.solution[0];
final Move initialMove = BOARD_MAP.get(solution0);
final int initialX = initialMove.deltaX;
final int initialY = initialMove.deltaY;
System.out.println(header() + "Solution found for....: x/y: " + initialX + "/" + initialY + " \t" + toBinary(0L) + " \tlength=" + this.solution.length + " \t" + solution0);
this.printSolutionDetail();
}
}
private void printSolutionDetail() {
int x = 0;
int y = 0;
long board = 0;
for (int i=0; i < this.solution.length; i++) {
final int positionOrMove = this.solution[i];
final Move move = i == 0 ? BOARD_MAP.get(positionOrMove) : KNIGHT_MOVE_MAP.get(positionOrMove);
/**/ x = i == 0 ? move.deltaX : x + move.deltaX;
/**/ y = i == 0 ? move.deltaY : y + move.deltaY;
board |= getXYmaskBit(x, y);
System.out.println(header() + "Solution walk.........: x/y: " + x + "/" + y + " \t" + toBinary(board) + " \t" + move.deltaX + "\t" + move.deltaY + "\t" + positionOrMove);
}
}
}
private static final Map<Integer, Move> KNIGHT_MOVE_MAP;
/**/ static {
final Map<Integer, Move> Knight_Move_Map = new TreeMap<>();
IntStream.of(2, -2).forEach(deltaX ->
IntStream.of(1, -1).forEach(deltaY -> {
/*
* Mirror the 4 combinations above to get all 8 possible Knight moves...
*/
{final Move move = new Move(deltaX, deltaY); Knight_Move_Map.put(move.deltaXY, move);}
{final Move move = new Move(deltaY, deltaX); Knight_Move_Map.put(move.deltaXY, move);}
}));
KNIGHT_MOVE_MAP = Collections.unmodifiableMap(Knight_Move_Map);
}
private static final Map<Integer, Move> BOARD_MAP;
/**/ static {
final Map<Integer, Move> Board_Map = new TreeMap<>();
walkBoard((x,y) -> {
final Move move = new Move(x, y);
Board_Map.put(move.deltaXY, move);
});
BOARD_MAP = Collections.unmodifiableMap(Board_Map);
}
private static final Square[][] BOARD = new Square[SIZE_X] [SIZE_Y];
/**/ static {
/*
* Fill the Board with Squares...
*/
walkBoard( (x,y) -> BOARD[x][y] = new Square(x, y));
/**/ System.out.println("Onward Target Count:");
walkBoard( ( y) -> { System.out.print ( y + " : ");},
/**/ (x,y) -> {final Square square = BOARD[x][y]; System.out.print (square.targetMove.length + " ");},
/**/ ( ) -> { System.out.println() ;} );
/*
* So far the Target Moves array is filled with nulls. We MUST fill it...
*/
Arrays.stream(BOARD).flatMap(Arrays::stream).forEach(square -> {
final Move[] targetsSortedByOnwardPointCount = Arrays
.stream(square.targetMove)
.sorted((moveA, moveB) -> {
/*
* We use the Warnsdorff algorithm to sort it by the number of Onward Targets...
*/
final Square targetA = BOARD[square.x + moveA.deltaX] [square.y + moveA.deltaY];
final Square targetB = BOARD[square.x + moveB.deltaX] [square.y + moveB.deltaY];
return Integer.compare(
targetA.targetMove.length, // number of Onward Targets
targetB.targetMove.length); // number of Onward Targets
})
.map(move -> new Move(move, BOARD[square.x + move.deltaX] [square.y + move.deltaY]))
.toArray(Move[]::new);
/*
* Original & sorted arrays should be the same length if we got it right,
* so take max. length as a precaution to force an IndexOutOfBoundsException if we didn't...
*/
final int copyLength = Math.max(square.targetMove.length, targetsSortedByOnwardPointCount.length);
/*
* Overwrite the original Moves with the sorted version...
*/
System.arraycopy(targetsSortedByOnwardPointCount, 0, square.targetMove, 0, copyLength);
});
}
private final int[] SOLUTION = new int[SIZE_X_Y];
private void solve(final int initialX, final int initialY) {
final long initialBoard = getXYmaskBit(initialX, initialY);
System.out.println(header() + "Solve starting at.....: x/y: " + initialX +"/" + initialY + "\t" + toBinary(initialBoard));
try {
SOLUTION [0] = getDeltaXY(initialX, initialY); // First Entry contains Starting-Point
nextMoveToXY(0, BOARD[initialX][initialY], initialBoard);
}
catch (final KnightMoveSolvedException justIgnore_WereDone) {}
}
private void nextMoveToXY(int moveCount, final Square square, final long board) {
moveCount++;
if (moveCount >= SIZE_X_Y) {
final KnightMoveSolvedException solution = new KnightMoveSolvedException(moveCount, SOLUTION);
// return; // (Back up & keep looking for next solution)
/*
* If 1 solution is enough, just throw the Exception...
*/
throw solution;
}
for (final Move move : square.targetMove) {
/*
* Is Target Square vacant? (i.e. Mask Bit not set)...
*/
if ((board & move.target.xyMask) == 0) {
/*
* Yes: try next move recursively with new Position & Board...
*/
SOLUTION [moveCount] = move.deltaXY;
nextMoveToXY(moveCount, move.target, board | move.target.xyMask /* Set Mask Bit on new Board */);
}
}
}
public static void main(final String[] args) throws Exception {
final ExecutorService pool = Executors.newFixedThreadPool(Runtime.getRuntime().availableProcessors());
/*
* We can handle rectangular boards, but for square boards the following holds:
* we only need to solve for 1/8 of the board (a triangle)...
* (the remaining 7/8 are either Mirrors or Rotations of the 1/8)
*/
IntStream .range(0, SIZE_X / 2).forEach(x -> {
IntStream.range(0, x + 1 ).forEach(y -> {
pool.submit(() -> {
try { TimeUnit.SECONDS.sleep(1); } catch (final InterruptedException e) {}
/*
* (Sleep very briefly, so our Thread won't start before the Output below has finished)
*/
new KnightsTourWarnsdorff().solve(x, y);
});
System.out.print("x=" + x + " y=" + y + "\t");
});
System.out.println();
});
pool.shutdown();
}
}
原版：
import java.util.Arrays;
import java.util.concurrent.atomic.AtomicInteger;
import java.util.stream.IntStream;
public class KnightsTour {
@SuppressWarnings("serial")
private static final class KnightMoveSolvedException extends RuntimeException {
private final int[][] solution;
private KnightMoveSolvedException(final int[][] solution) {
this.solution = deepPrimitive2DArrayClone (solution);
}
}
private static final int SIZE_X = 8;
private static final int SIZE_Y = 8;
private static final int SIZE_X_Y = SIZE_X * SIZE_Y;
private static final int[][] SOLUTION = new int[SIZE_X_Y][];
private static final int INDEX_X = 0;
private static final int INDEX_Y = 1;
private static final int KNIGHT_MOVES_LENGTH = 8;
private static final int [][] KNIGHT_MOVES = new int[KNIGHT_MOVES_LENGTH][];
/**/ static {
checkLongSolutionCapacity();
final AtomicInteger moveIndex = new AtomicInteger();
IntStream.of(2, -2).forEach(deltaX ->
IntStream.of(1, -1).forEach(deltaY -> {
/*
* Mirror the 4 combinations above to get all 8 possible Knight moves...
*/
KNIGHT_MOVES[moveIndex.getAndIncrement()] = new int[] {deltaX, deltaY};
KNIGHT_MOVES[moveIndex.getAndIncrement()] = new int[] {deltaY, deltaX};
}));
}
@SuppressWarnings("unused")
private static void checkLongSolutionCapacity() {
if (SIZE_X_Y > Long.SIZE) {
throw new UnsupportedOperationException("Number of squares on board exceeds capacity of long Solution");
}
}
private static long getXYmaskBit(final int x, final int y) {
return Long.MIN_VALUE >>> (x + y * SIZE_X /* Yes, SIZE-X ! */);
}
public static void solve(final int initialX, final int initialY) {
final long initialBoard = getXYmaskBit(initialX, initialY);
System.out.println("Solve starting at X/Y.: " + initialX +"/" + initialY + "\t" + toBinary(initialBoard));
try {
SOLUTION [0] = new int[] {initialX, initialY}; // First Entry contains Starting-Point
nextMoveToXY(0, initialX, initialY, initialBoard);
}
catch (final KnightMoveSolvedException e) {
System.out.println("One possible solution.: " + e.solution);
}
}
private static void nextMoveToXY(int moveCount, final int x, final int y, final long board) {
moveCount++;
if (moveCount >= SIZE_X_Y) {
System.out.println("Solved!...............: count=" + moveCount);
/*
* Print the answer or remember it somewhere...
*/
final int initialX = SOLUTION[0][INDEX_X];
final int initialY = SOLUTION[0][INDEX_Y];
for(final int[] move : SOLUTION) {
final int solutionX = move[INDEX_X];
final int solutionY = move[INDEX_Y];
System.out.println("Move (starting at X/Y): " + initialX +"/" + initialY + "\t" + toBinary(board) + "\t" + solutionX + "\t" + solutionY);
}
// return; // (Back up & keep looking for next solution)
/*
* If 1 solution is enough, just throw the Exception...
*/
throw new KnightMoveSolvedException(SOLUTION);
}
for(final int[] move : KNIGHT_MOVES) {
final int deltaX = move[INDEX_X]; final int newX = x + deltaX; if (newX < 0 || newX >= SIZE_X) {continue;}
final int deltaY = move[INDEX_Y]; final int newY = y + deltaY; if (newY < 0 || newY >= SIZE_Y) {continue;}
/*
* ok: Checks above mean we're on the board, so lets find the new Position Mask...
*/
final long newXYmaskBit = getXYmaskBit(newX, newY);
/*
* Is Target Square vacant (= Mask Bit not set)?...
*/
if ((board & newXYmaskBit) == 0) {
/*
* Yes: try next move recursively with new Position & Board...
*/
SOLUTION [moveCount] = move;
nextMoveToXY(moveCount, newX, newY, board | newXYmaskBit /* Set Mask Bit on new Board */);
}
}
}
public static String toHex (final int value) {
return leftPad(Integer.BYTES * 2, Integer.toHexString (value));
}
public static String toHex (final long value) {
return leftPad(Long .BYTES * 2, Long .toHexString (value));
}
public static String toBinary(final int value) {
return leftPad(Integer.SIZE, Integer.toBinaryString(value));
}
public static String toBinary(final long value) {
return leftPad(Long .SIZE, Long .toBinaryString(value));
}
private static String leftPad (final int paddedLength, final String binaryOrHex) {
final char[] lead = new char[paddedLength - binaryOrHex.length()];
Arrays.fill (lead, '0');
return String.valueOf(lead).concat(binaryOrHex).replace('0', '_');
}
/**
* {@link Object#clone()} can create a Deep Clone of a 1D array of Primitives
* but with 2D will only provide a Shallow Copy (meaning if the content of source
* changes, the content of clone will change!!) so we have to wrap 2D by hand...
*/
private static int[][] deepPrimitive2DArrayClone(final int[][] source) {
final int[][] clone = new int[source.length][];
/**/ int cix = 0;
for (final int[] col : source) {
clone[cix++] = col.clone(); // (ok: 1D, so Deep Clone)
}
return clone;
}
public static void main(final String[] args) throws Exception {
solve(0, 1); // Fast!: 2 Minutes
solve(0, 3); // Fast!: 1 Minute
IntStream.range(0, SIZE_X).forEach(x ->
IntStream.range(0, SIZE_Y).forEach(y -> {
solve(x, y);
}));
}
}
我在网上得到了这个答案。希望对有同样疑问的朋友有所帮助！
public static int knight(String...pos) {
int[][] ab=Stream.of(pos).map(s->new int[]{"abcdefgh".indexOf(s.charAt(0)),s.charAt(1)-48}).toArray(int[][]::new);
int[] dxy=IntStream.range(0,2).map(i->Math.abs(ab[0][i]-ab[1][i])).sorted().toArray();
if(dxy[0]==0&&dxy[1]==1) return 3;
if(dxy[0]==2&&dxy[1]==2||dxy[0]==1&&dxy[1]==1&&(pos[0]+pos[1]).matches(".*?(a1|h1|a8|h8).*")) return 4;
int delta=dxy[1]-dxy[0];
return delta-2*(int)Math.floor(1.0*(delta-dxy[0])/(dxy[0]>delta?3:4));
}
我正在尝试创建一个程序，当给定国际象棋的位置 knight and the destination, all marked in chess notation 时，return 骑士从该位置到达目的地所需的移动次数。在使用该算法计算列表中的 每个 单一可能性之前，我曾尝试过，但它非常慢并且有点问题。这是我的代码：
private static int translateChessNotation(String chess) {
int returned = 8 * (Integer.valueOf(String.valueOf(chess.charAt(1)))- 1);
return returned + (convertAlphabet(chess.charAt(0))); // File
}
public static int knight(String start, String finish) {
int knightPosition = translateChessNotation(start), end = translateChessNotation(finish), i = 0;
ArrayList<Integer> currentPossibleKnightPositions = new ArrayList<>();
currentPossibleKnightPositions.add(knightPosition);
for (; i < 8; i++) {
ArrayList<Integer> newList = new ArrayList<>();
for (int position : currentPossibleKnightPositions) {
newList.add(position + 17);
newList.add(position + 15);
newList.add(position + 10);
newList.add(position + 6);
newList.add(position - 6);
newList.add(position - 10);
newList.add(position - 15);
newList.add(position - 17);
}
ArrayList<Integer> removed = new ArrayList<>();
for (int j : newList) {if (j < 1 || j > 64) {removed.add(j);}}
newList.removeAll(removed);
currentPossibleKnightPositions.clear();
currentPossibleKnightPositions.addAll(newList);
for (int n : currentPossibleKnightPositions) {
if (n == end) {return i + 1;}
}
}
return -1;
}
如有帮助，万分感谢！
这里有一些 Proggy 可以解决所谓的 Knights-Tour 问题，从特定位置开始访问棋盘上的所有方块，因此您可以对其进行调整以将特定的 to-position 设置为结束条件。
这只是蛮力，尝试所有可能的组合，大约需要 50 分钟才能找到每个完整的 Knights-Tour 解决方案。
如果有帮助，我很荣幸收到您的投票。
import java.util.concurrent.atomic.AtomicInteger;
import java.util.stream.IntStream;
public class KnightMove {
@SuppressWarnings("serial")
private static final class KnightMoveSolvedException extends RuntimeException {
private final byte[][] solution;
private KnightMoveSolvedException(final byte[][] solution) {
this.solution = solution;
}
}
private static final int SIZE_X = 8;
private static final int SIZE_Y = 8;
private static final int SIZE_X_Y = SIZE_X * SIZE_Y; // Max 127! (=0x7F)
private static final int [][] KNIGHT_MOVES = new int[8][];
/**/ static {
final AtomicInteger moveIndex = new AtomicInteger();
IntStream.of(2, -2).forEach(deltaX ->
IntStream.of(1, -1).forEach(deltaY -> {
/*
* Mirror the 4 combinations above to get all 8 possible Knight moves...
*/
KNIGHT_MOVES[moveIndex.getAndIncrement()] = new int[] {deltaX, deltaY};
KNIGHT_MOVES[moveIndex.getAndIncrement()] = new int[] {deltaY, deltaX};
}));
}
private static void nextMoveToXY(int moveCount, final int x, final int y, final byte[][] board) {
moveCount++;
board[x][y] = (byte) moveCount;
if (moveCount >= SIZE_X_Y) {
System.out.println("Solved!.....: count=" + moveCount);
for ( final byte[] column : board ) {
for (final byte square : column) {
System.out.print(square + "\t");
}
System.out.println();
}
return; // (Back up & keep looking for next solution)
/*
* If 1 solution is enough, just throw the Exception...
*/
// throw new KnightMoveSolvedException(board);
}
for (final int[] knightMove : KNIGHT_MOVES) {
final int newX = x + knightMove[0]; if (newX < 0 || newX >= SIZE_X) {continue;}
final int newY = y + knightMove[1]; if (newY < 0 || newY >= SIZE_Y) {continue;}
if (board[newX][newY] == 0) {
/*
* Target Square is vacant, so try this move recursively...
*/
nextMoveToXY(moveCount, newX, newY, deepPrimitive2DArrayClone(board));
}
}
}
/**
* {@link Object#clone()} can create a Deep Clone of a 1D array of Primitives
* but will <b>not</b> deliver the desired result with 2D,
* so we have to wrap the rest by hand...
*/
private static byte[][] deepPrimitive2DArrayClone(final byte[][] source) {
final byte[][] clone = new byte[source.length][];
/**/ int cix = 0;
for (final byte[] col : source) {
clone[cix++] = col.clone();
}
return clone;
}
public static void main(final String[] args) throws Exception {
IntStream.range(0, SIZE_X).forEach(x ->
IntStream.range(0, SIZE_Y).forEach(y -> {
try {
System.out.println("Solve starting at X/Y.: " + x +"/" + y);
nextMoveToXY(0, x, y, new byte[SIZE_X][SIZE_Y]);
}
catch (final KnightMoveSolvedException e) {
System.out.println(e.solution);
}
}));
}
}
我已经把上一篇博文中的棋盘数组换成long了。
（64 位，刚好可以代表电路板）
新版本 显着 更快。
根据起始坐标，解决方案需要 1 分钟到 12 小时...
（我先放了几个更快的）
此示例旨在展示基础知识。有多种数学方法（参见维基百科）对其进行优化，但它们会使解决方案更加复杂。
一些要点：
- 如果可以的话，使用基元（byte、short、int、long，...）：它们非常快
- 使用蛮力时避免像 ArrayList 这样的对象：它们非常慢
- 使用递归：它为您保存和恢复状态。它可能会花费一些钱，但它会让生活变得更轻松
- 尽可能使用 final ：它不会更快，但有助于理解
希望你喜欢。 :-)
我现在已经磨练了这个东西。它 大大 比原来的速度更快（一点也不逊色！），使用 Warnsdorff 算法 & 可以解决多个起始位置，运行 同时在所有可用线程上。
大部分工作是正确设置数据结构和初始化。
递归 nextMoveToXY 求解器方法本身非常简单。
Warnsdorff 版本：
import java.time.Instant;
import java.util.Arrays;
import java.util.Collections;
import java.util.Map;
import java.util.TreeMap;
import java.util.concurrent.ExecutorService;
import java.util.concurrent.Executors;
import java.util.concurrent.TimeUnit;
import java.util.function.IntConsumer;
import java.util.stream.IntStream;
public class KnightsTourWarnsdorff {
private interface IntIntConsumer {
void accept(int t, int u);
}
private static final int MAX_INSTANT_TO_STRING_LENGTH = "2020-12-31T23:59:59.123456Z".length();
private static final int SIZE_X = 8;
private static final int SIZE_Y = 8;
private static final int SIZE_X_Y = SIZE_X * SIZE_Y;
/**/ static { check_SIZE_X_Y_withinCapacity();}
/**
* Do this in a Method (we don't want to mark the Class with SuppressWarnings)
*/
@SuppressWarnings("unused")
private static void check_SIZE_X_Y_withinCapacity() {
if (SIZE_X_Y > Long.SIZE) {
throw new UnsupportedOperationException("Number of squares on board exceeds capacity of long Solution");
}
}
/**
* Returns the unique offset corresponding to a Move or our position on the Board.
*/
private static int getDeltaXY(final int deltaX, final int deltaY) {
return deltaX + deltaY * SIZE_X; /* Yes, SIZE_X ! */
}
/**
* Returns a long with a single bit set, corresponding to our position on the Board.
*/
private static long getXYmaskBit(final int x, final int y) {
return 1L << (63 - getDeltaXY(x, y));
}
private static void walkBoard(final IntIntConsumer doXY) {
walkBoard(null, doXY, null);
}
private static void walkBoard(final IntConsumer doRowStart, final IntIntConsumer doXY, final Runnable doRowEnd) {
IntStream .range(0, SIZE_Y).forEach(y -> {if (doRowStart != null) {doRowStart.accept( y);}
IntStream.range(0, SIZE_X).forEach(x -> {if (doXY != null) {doXY .accept(x,y);}
}); if (doRowEnd != null) {doRowEnd .run ( );}
});
}
private static String toBinary(final long value) {
return leftPad(Long.SIZE, Long.toBinaryString(value)).replace('0', '_');
}
private static String leftPad (final int paddedLength, final String value) {
final int padCount = Math.max(0, paddedLength - value.length());
final char[] pad = new char[padCount];
Arrays.fill (pad, '0');
return String.valueOf(pad).concat(value);
}
private static String rightPad (final int paddedLength, final String value) {
final int padCount = Math.max(0, paddedLength - value.length());
final char[] pad = new char[padCount];
Arrays.fill (pad, '0');
return value.concat(String.valueOf(pad));
}
private static String header () {
return rightPad (MAX_INSTANT_TO_STRING_LENGTH, Instant.now().toString()) + " " + Thread.currentThread().getName() + " ";
}
/**
* Square on Board not only knows its x/y location, but also its position as an xyMask<br>
* (for checking whether a square is occupied & marking as occupied).<br>
* <br>
* It knows all possible Moves from this Square within the Board<br>
* (thus obviating the need to check whether we're still on the Board).<br>
* <br>
* Each Specific Move contains a reference to the Target Square, which in turn...<br>
* (these 2 measures speed up Navigation massively)
*/
private static final class Square {
private final int x;
private final int y;
/**
* Used to mark the Square as occupied on the Board
*/
private final long xyMask;
/**
* All possible Moves from this Square.<br>
* (initially all null: filled after all Squares have been instantiated)
*/
private final Move[] targetMove;
private Square(final int x, final int y) {
this.x = x;
this. y = y;
this.xyMask = getXYmaskBit(x, y);
this.targetMove = KNIGHT_MOVE_MAP.values().stream().filter(move -> {
final int newX = x + move.deltaX;
final int newY = y + move.deltaY;
return newX >= 0 && newX < SIZE_X
&& newY >= 0 && newY < SIZE_Y;
}).toArray(Move[]::new);
}
}
/**
* Either a Generic or a Specific Move
*/
private static final class Move {
private final int deltaX;
private final int deltaY;
private final int deltaXY;
private final Square target;
/**
* Create a Generic Move
*/
private Move(final int deltaX, final int deltaY) {
this.deltaX = deltaX;
this.deltaY = deltaY;
this.deltaXY = getDeltaXY(deltaX, deltaY);
this.target = null;
}
/**
* Create a Move to a specific Target Square
*/
private Move(final Move genericMove, final Square target) {
this.deltaX = genericMove.deltaX;
this.deltaY = genericMove.deltaY;
this.deltaXY = genericMove.deltaXY;
this.target = target;
}
}
@SuppressWarnings("serial")
private static final class KnightMoveSolvedException extends RuntimeException {
private final int[] solution;
private KnightMoveSolvedException(final int moveCount, final int[] solution) {
/*
* Trim the solution array down to the number of moves...
* (for those performing a partial walk)
*/
this.solution = Arrays.stream(solution).limit(moveCount).toArray();
synchronized (KnightMoveSolvedException.class) { // One Thread (= Solution) at a time please!
final int solution0 = this.solution[0];
final Move initialMove = BOARD_MAP.get(solution0);
final int initialX = initialMove.deltaX;
final int initialY = initialMove.deltaY;
System.out.println(header() + "Solution found for....: x/y: " + initialX + "/" + initialY + " \t" + toBinary(0L) + " \tlength=" + this.solution.length + " \t" + solution0);
this.printSolutionDetail();
}
}
private void printSolutionDetail() {
int x = 0;
int y = 0;
long board = 0;
for (int i=0; i < this.solution.length; i++) {
final int positionOrMove = this.solution[i];
final Move move = i == 0 ? BOARD_MAP.get(positionOrMove) : KNIGHT_MOVE_MAP.get(positionOrMove);
/**/ x = i == 0 ? move.deltaX : x + move.deltaX;
/**/ y = i == 0 ? move.deltaY : y + move.deltaY;
board |= getXYmaskBit(x, y);
System.out.println(header() + "Solution walk.........: x/y: " + x + "/" + y + " \t" + toBinary(board) + " \t" + move.deltaX + "\t" + move.deltaY + "\t" + positionOrMove);
}
}
}
private static final Map<Integer, Move> KNIGHT_MOVE_MAP;
/**/ static {
final Map<Integer, Move> Knight_Move_Map = new TreeMap<>();
IntStream.of(2, -2).forEach(deltaX ->
IntStream.of(1, -1).forEach(deltaY -> {
/*
* Mirror the 4 combinations above to get all 8 possible Knight moves...
*/
{final Move move = new Move(deltaX, deltaY); Knight_Move_Map.put(move.deltaXY, move);}
{final Move move = new Move(deltaY, deltaX); Knight_Move_Map.put(move.deltaXY, move);}
}));
KNIGHT_MOVE_MAP = Collections.unmodifiableMap(Knight_Move_Map);
}
private static final Map<Integer, Move> BOARD_MAP;
/**/ static {
final Map<Integer, Move> Board_Map = new TreeMap<>();
walkBoard((x,y) -> {
final Move move = new Move(x, y);
Board_Map.put(move.deltaXY, move);
});
BOARD_MAP = Collections.unmodifiableMap(Board_Map);
}
private static final Square[][] BOARD = new Square[SIZE_X] [SIZE_Y];
/**/ static {
/*
* Fill the Board with Squares...
*/
walkBoard( (x,y) -> BOARD[x][y] = new Square(x, y));
/**/ System.out.println("Onward Target Count:");
walkBoard( ( y) -> { System.out.print ( y + " : ");},
/**/ (x,y) -> {final Square square = BOARD[x][y]; System.out.print (square.targetMove.length + " ");},
/**/ ( ) -> { System.out.println() ;} );
/*
* So far the Target Moves array is filled with nulls. We MUST fill it...
*/
Arrays.stream(BOARD).flatMap(Arrays::stream).forEach(square -> {
final Move[] targetsSortedByOnwardPointCount = Arrays
.stream(square.targetMove)
.sorted((moveA, moveB) -> {
/*
* We use the Warnsdorff algorithm to sort it by the number of Onward Targets...
*/
final Square targetA = BOARD[square.x + moveA.deltaX] [square.y + moveA.deltaY];
final Square targetB = BOARD[square.x + moveB.deltaX] [square.y + moveB.deltaY];
return Integer.compare(
targetA.targetMove.length, // number of Onward Targets
targetB.targetMove.length); // number of Onward Targets
})
.map(move -> new Move(move, BOARD[square.x + move.deltaX] [square.y + move.deltaY]))
.toArray(Move[]::new);
/*
* Original & sorted arrays should be the same length if we got it right,
* so take max. length as a precaution to force an IndexOutOfBoundsException if we didn't...
*/
final int copyLength = Math.max(square.targetMove.length, targetsSortedByOnwardPointCount.length);
/*
* Overwrite the original Moves with the sorted version...
*/
System.arraycopy(targetsSortedByOnwardPointCount, 0, square.targetMove, 0, copyLength);
});
}
private final int[] SOLUTION = new int[SIZE_X_Y];
private void solve(final int initialX, final int initialY) {
final long initialBoard = getXYmaskBit(initialX, initialY);
System.out.println(header() + "Solve starting at.....: x/y: " + initialX +"/" + initialY + "\t" + toBinary(initialBoard));
try {
SOLUTION [0] = getDeltaXY(initialX, initialY); // First Entry contains Starting-Point
nextMoveToXY(0, BOARD[initialX][initialY], initialBoard);
}
catch (final KnightMoveSolvedException justIgnore_WereDone) {}
}
private void nextMoveToXY(int moveCount, final Square square, final long board) {
moveCount++;
if (moveCount >= SIZE_X_Y) {
final KnightMoveSolvedException solution = new KnightMoveSolvedException(moveCount, SOLUTION);
// return; // (Back up & keep looking for next solution)
/*
* If 1 solution is enough, just throw the Exception...
*/
throw solution;
}
for (final Move move : square.targetMove) {
/*
* Is Target Square vacant? (i.e. Mask Bit not set)...
*/
if ((board & move.target.xyMask) == 0) {
/*
* Yes: try next move recursively with new Position & Board...
*/
SOLUTION [moveCount] = move.deltaXY;
nextMoveToXY(moveCount, move.target, board | move.target.xyMask /* Set Mask Bit on new Board */);
}
}
}
public static void main(final String[] args) throws Exception {
final ExecutorService pool = Executors.newFixedThreadPool(Runtime.getRuntime().availableProcessors());
/*
* We can handle rectangular boards, but for square boards the following holds:
* we only need to solve for 1/8 of the board (a triangle)...
* (the remaining 7/8 are either Mirrors or Rotations of the 1/8)
*/
IntStream .range(0, SIZE_X / 2).forEach(x -> {
IntStream.range(0, x + 1 ).forEach(y -> {
pool.submit(() -> {
try { TimeUnit.SECONDS.sleep(1); } catch (final InterruptedException e) {}
/*
* (Sleep very briefly, so our Thread won't start before the Output below has finished)
*/
new KnightsTourWarnsdorff().solve(x, y);
});
System.out.print("x=" + x + " y=" + y + "\t");
});
System.out.println();
});
pool.shutdown();
}
}
原版：
import java.util.Arrays;
import java.util.concurrent.atomic.AtomicInteger;
import java.util.stream.IntStream;
public class KnightsTour {
@SuppressWarnings("serial")
private static final class KnightMoveSolvedException extends RuntimeException {
private final int[][] solution;
private KnightMoveSolvedException(final int[][] solution) {
this.solution = deepPrimitive2DArrayClone (solution);
}
}
private static final int SIZE_X = 8;
private static final int SIZE_Y = 8;
private static final int SIZE_X_Y = SIZE_X * SIZE_Y;
private static final int[][] SOLUTION = new int[SIZE_X_Y][];
private static final int INDEX_X = 0;
private static final int INDEX_Y = 1;
private static final int KNIGHT_MOVES_LENGTH = 8;
private static final int [][] KNIGHT_MOVES = new int[KNIGHT_MOVES_LENGTH][];
/**/ static {
checkLongSolutionCapacity();
final AtomicInteger moveIndex = new AtomicInteger();
IntStream.of(2, -2).forEach(deltaX ->
IntStream.of(1, -1).forEach(deltaY -> {
/*
* Mirror the 4 combinations above to get all 8 possible Knight moves...
*/
KNIGHT_MOVES[moveIndex.getAndIncrement()] = new int[] {deltaX, deltaY};
KNIGHT_MOVES[moveIndex.getAndIncrement()] = new int[] {deltaY, deltaX};
}));
}
@SuppressWarnings("unused")
private static void checkLongSolutionCapacity() {
if (SIZE_X_Y > Long.SIZE) {
throw new UnsupportedOperationException("Number of squares on board exceeds capacity of long Solution");
}
}
private static long getXYmaskBit(final int x, final int y) {
return Long.MIN_VALUE >>> (x + y * SIZE_X /* Yes, SIZE-X ! */);
}
public static void solve(final int initialX, final int initialY) {
final long initialBoard = getXYmaskBit(initialX, initialY);
System.out.println("Solve starting at X/Y.: " + initialX +"/" + initialY + "\t" + toBinary(initialBoard));
try {
SOLUTION [0] = new int[] {initialX, initialY}; // First Entry contains Starting-Point
nextMoveToXY(0, initialX, initialY, initialBoard);
}
catch (final KnightMoveSolvedException e) {
System.out.println("One possible solution.: " + e.solution);
}
}
private static void nextMoveToXY(int moveCount, final int x, final int y, final long board) {
moveCount++;
if (moveCount >= SIZE_X_Y) {
System.out.println("Solved!...............: count=" + moveCount);
/*
* Print the answer or remember it somewhere...
*/
final int initialX = SOLUTION[0][INDEX_X];
final int initialY = SOLUTION[0][INDEX_Y];
for(final int[] move : SOLUTION) {
final int solutionX = move[INDEX_X];
final int solutionY = move[INDEX_Y];
System.out.println("Move (starting at X/Y): " + initialX +"/" + initialY + "\t" + toBinary(board) + "\t" + solutionX + "\t" + solutionY);
}
// return; // (Back up & keep looking for next solution)
/*
* If 1 solution is enough, just throw the Exception...
*/
throw new KnightMoveSolvedException(SOLUTION);
}
for(final int[] move : KNIGHT_MOVES) {
final int deltaX = move[INDEX_X]; final int newX = x + deltaX; if (newX < 0 || newX >= SIZE_X) {continue;}
final int deltaY = move[INDEX_Y]; final int newY = y + deltaY; if (newY < 0 || newY >= SIZE_Y) {continue;}
/*
* ok: Checks above mean we're on the board, so lets find the new Position Mask...
*/
final long newXYmaskBit = getXYmaskBit(newX, newY);
/*
* Is Target Square vacant (= Mask Bit not set)?...
*/
if ((board & newXYmaskBit) == 0) {
/*
* Yes: try next move recursively with new Position & Board...
*/
SOLUTION [moveCount] = move;
nextMoveToXY(moveCount, newX, newY, board | newXYmaskBit /* Set Mask Bit on new Board */);
}
}
}
public static String toHex (final int value) {
return leftPad(Integer.BYTES * 2, Integer.toHexString (value));
}
public static String toHex (final long value) {
return leftPad(Long .BYTES * 2, Long .toHexString (value));
}
public static String toBinary(final int value) {
return leftPad(Integer.SIZE, Integer.toBinaryString(value));
}
public static String toBinary(final long value) {
return leftPad(Long .SIZE, Long .toBinaryString(value));
}
private static String leftPad (final int paddedLength, final String binaryOrHex) {
final char[] lead = new char[paddedLength - binaryOrHex.length()];
Arrays.fill (lead, '0');
return String.valueOf(lead).concat(binaryOrHex).replace('0', '_');
}
/**
* {@link Object#clone()} can create a Deep Clone of a 1D array of Primitives
* but with 2D will only provide a Shallow Copy (meaning if the content of source
* changes, the content of clone will change!!) so we have to wrap 2D by hand...
*/
private static int[][] deepPrimitive2DArrayClone(final int[][] source) {
final int[][] clone = new int[source.length][];
/**/ int cix = 0;
for (final int[] col : source) {
clone[cix++] = col.clone(); // (ok: 1D, so Deep Clone)
}
return clone;
}
public static void main(final String[] args) throws Exception {
solve(0, 1); // Fast!: 2 Minutes
solve(0, 3); // Fast!: 1 Minute
IntStream.range(0, SIZE_X).forEach(x ->
IntStream.range(0, SIZE_Y).forEach(y -> {
solve(x, y);
}));
}
}
我在网上得到了这个答案。希望对有同样疑问的朋友有所帮助！
public static int knight(String...pos) {
int[][] ab=Stream.of(pos).map(s->new int[]{"abcdefgh".indexOf(s.charAt(0)),s.charAt(1)-48}).toArray(int[][]::new);
int[] dxy=IntStream.range(0,2).map(i->Math.abs(ab[0][i]-ab[1][i])).sorted().toArray();
if(dxy[0]==0&&dxy[1]==1) return 3;
if(dxy[0]==2&&dxy[1]==2||dxy[0]==1&&dxy[1]==1&&(pos[0]+pos[1]).matches(".*?(a1|h1|a8|h8).*")) return 4;
int delta=dxy[1]-dxy[0];
return delta-2*(int)Math.floor(1.0*(delta-dxy[0])/(dxy[0]>delta?3:4));
}