我正在尝试为the Knight’s Tour编写代码：

A knight’s tour is a sequence of moves of a knight on a chessboard such that the knight visits every square exactly once.

我一直试图改变其他人的代码,但回溯似乎无法正常工作 – 它永远找不到解决方案.当骑士从0,0开始时它完全正常,但如果它从2D网格上的任何其他点开始,程序将永远持续下去.

这段代码中的错误在哪里？

#include <iostream>
#include <ctime>
using namespace std;

const int N = 8;
int map[N][N];

/* A utility function to check if i,j are valid indexes for N*N chessboard */
bool isSafe(int x, int y) {
    return x >= 0 && x < N && y >= 0 && y < N && map[x][y] == -1;
}

/* A utility function to print solution matrix sol[N][N] */
void printSolution() {
    for (int x = 0; x < N; x++) {
        for (int y = 0; y < N; y++)
            cout << map[x][y];
        cout << endl;
    }
}

/* A recursive utility function to solve Knight Tour problem */
bool knightsTourRecursive(int x, int y, int movei, int xMove[N], int yMove[N]) {
    int nextX, nextY;

    if (movei == N*N)
        return true;

    /* Try all next moves from the current coordinate x, y */
    for (int k = 0; k < 8; k++) {
        nextX = x + xMove[k];
        nextY = y + yMove[k];

        if (isSafe(nextX, nextY)) {
            map[nextX][nextY] = movei;

            if (knightsTourRecursive(nextX, nextY, movei+1, xMove, yMove))  // recursion
                return true;
            else
                map[nextX][nextY] = -1;             // backtracking
        }
    }
    return false;
}

bool knightsTour() {
    /* Initialization of solution matrix */
    for (int x = 0; x < N; x++)
        for (int y = 0; y < N; y++)
            map[x][y] = -1;

    /* xMove[] and yMove[] define next move of Knight.
       xMove[] is for next value of x coordinate
       yMove[] is for next value of y coordinate */
    int xMove[8] = {  2, 1, -1, -2, -2, -1,  1,  2 };
    int yMove[8] = {  1, 2,  2,  1, -1, -2, -2, -1 };

    int initX = rand() % N;
    int initY = rand() % N;

    cout << "Starting at " << initX << " " << initY << endl;

    // Since the Knight is initially at the first block
    map[initX][initY]  = 0;

    /* explore all tours using solveKTUtil() */
    if(!knightsTourRecursive(initX, initY, 1, xMove, yMove) ) {
        cout << "Solution does not exist" << endl;
        return false;
    }
    else
        printSolution();

    return true;
}

int main() {
    srand( (unsigned) time(0));
    knightsTour();

    cin.get();
    return 0;
}

解决方法:

这个程序似乎绝对正确,我在这段代码中看不到错误.

然而,骑士之旅是一种高度复杂的算法.实际上,程序需要通过电路板检查最多64个！= 1 * 2 * 3 * … * 64种不同的方式.这是一个有89个零的数字！

在许多情况下,回溯将停留在早期分支,但一些分支将永远上升.

如果从0,0开始的巡回赛如此迅速,那么它可能是纯粹的机会,或者阵列xMove和yMove被巧妙地初始化,这样就可以快速找到(0,0)的解.

所以问题不是你的程序,而是算法.我建议你对这个话题做一些研究.骑士之旅有很多算法,可以在更合理的时间内为您提供解决方案.