[英]Knight's Tour code runs into infinite loop, does not reach a solution
我對“騎士之旅”的遞歸回溯方法遇到了一個無限循環。 起初,我認為問題可能會花很多時間,但是有些解決方案可以立即解決。 請告訴我代碼有什么問題。
package io.github.thegeekybaniya.InterviewPrep.TopTopics.Backtracking;
import java.util.Arrays;
public class KnightsTour {
private static int counter=0;
public static void main(String[] args) {
knightsTour(8);
}
private static void knightsTour(int i) {
int[][] board = new int[i][i];
for (int[] arr :
board) {
Arrays.fill(arr, -1);
}
board[0][0] = 0;
knightsTour(board,0,1);
}
private static boolean knightsTour(int[][] board, int cellno, int stepno) {
if (stepno == board.length * board.length) {
printBoard(board);
return true;
}
int[][] dirs = {
{1, 2}, {1, -2}, {-1, 2}, {-1, -2}, {2, 1}, {2, -1}, {-2, 1}, {-2, -1}
};
int row = cellno / board.length, col = cellno % board.length;
for (int i = 0; i < dirs.length; i++) {
int r = dirs[i][0] + row;
int c = dirs[i][1] + col;
if (isSafe(board, r, c)&&board[r][c]==-1) {
int ncell = r * board.length + c;
board[r][c] = stepno;
if (knightsTour(board, ncell, stepno + 1)) {
return true;
} else {
board[r][c] = -1;
}
}
}
return false;
}
private static boolean isSafe(int[][] board, int r, int c) {
return r >= 0 && c >= 0 && r < board.length && c < board.length;
}
private static void printBoard(int[][] board) {
System.out.println(++counter);
for (int i = 0; i < board.length; i++) {
for (int j = 0; j < board.length; j++) {
System.out.print(board[i][j]+" ");
}
System.out.println();
}
}
}
您的代碼中沒有錯誤,只是蠻力方法很慢,因為搜索空間很大。 您可以通過實施Warnsdorf規則來加快搜索速度。 這是選擇下一個動作的一種試探法,您總是嘗試在該動作之后導致下一個動作的可用動作最少的動作。 可以通過幾個簡單的循環來完成:
int row = cellno / board.length, col = cellno % board.length;
// find move with fewest moves available for the next move:
int minMovesAvailable = 8;
int minMovesDir = 0;
for (int i = 0; i < dirs.length; i++) {
int r = dirs[i][0] + row;
int c = dirs[i][1] + col;
if (isSafe(board, r, c)&&board[r][c]==-1)
{
board[r][c] = stepno;
int movesAvailable = 0;
for (int j = 0; j < dirs.length; j++) {
int r2 = dirs[j][0] + r;
int c2 = dirs[j][1] + c;
if (isSafe(board, r2, c2)&&board[r2][c2]==-1)
{
movesAvailable++;
}
}
board[r][c] = -1;
if(movesAvailable < minMovesAvailable)
{
minMovesAvailable = movesAvailable;
minMovesDir = i;
}
}
}
// now recurse this move first:
// int r = dirs[minMovesDir][0] + row;
// int c = dirs[minMovesDir][1] + col;
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