A Knight's Journey_DFS

Description

Background
The knight is getting bored of seeing the same black and white squares again and again and has decided to make a journey
around the world. Whenever a knight moves, it is two squares in one direction and one square perpendicular to this. The world of a knight is the chessboard he is living on. Our knight lives on a chessboard that has a smaller area than a regular 8 * 8 board, but it is still rectangular. Can you help this adventurous knight to make travel plans?

Problem
Find a path such that the knight visits every square once. The knight can start and end on any square of the board.

Input

The input begins with a positive integer n in the first line. The following lines contain n test cases. Each test case consists of a single line with two positive integers p and q, such that 1 <= p * q <= 26. This represents a p * q chessboard, where p describes how many different square numbers 1, . . . , p exist, q describes how many different square letters exist. These are the first q letters of the Latin alphabet: A, . . .

Output

The output for every scenario begins with a line containing "Scenario #i:", where i is the number of the scenario starting at 1. Then print a single line containing the lexicographically first path that visits all squares of the chessboard with knight moves followed by an empty line. The path should be given on a single line by concatenating the names of the visited squares. Each square name consists of a capital letter followed by a number.
If no such path exist, you should output impossible on a single line.

Sample Input

Sample Output

Scenario #1:

A1

Scenario #2:

impossible

Scenario #3:

A1B3C1A2B4C2A3B1C3A4B2C4

【题意】给出m*n的方阵（但输入时先输入的是n，再输入m），问马是否能走遍棋盘，输出字典序的第一种路径。

【思路】用mp[i][0]表示第i步所在那个格子的横坐标，用mp[i][1]表示第i步所在那个格子的纵坐标。

字典序的话，注意di数组的顺序。用一个dfs就好啦。

#include <iostream>

#include<stdio.h>

#include<string.h>

using namespace std;

const int N=;

int vis[N][N];

int mp[N][];

int n,m;

bool flag;

int di[][]={-,-,-,,-,-,-,,,-,,,,-,,};

bool go(int x,int y)

{

    if(x<||x>=n||y<||y>=m) return false;

    else return true;

}

void dfs(int i,int j,int k)

{

    if(k==n*m)

    {

        for(int i=;i<k;i++)

        {

            printf("%c%d",mp[i][]+'A',mp[i][]+);

        }

        printf("\n");

        flag=true;

       // return ;

    }

    else

    for(int x=;x<;x++)

    {

        int xx=i+di[x][];

        int yy=j+di[x][];

        if(!vis[xx][yy]&&go(xx,yy)&&!flag)

        {

            vis[xx][yy]=;

            mp[k][]=xx;

            mp[k][]=yy;

            dfs(xx,yy,k+);

            vis[xx][yy]=;

        }

    }

}

int main()

{

  int t,cas=;

  scanf("%d",&t);

  while(t--)

  {

      scanf("%d%d",&m,&n);

      memset(vis,,sizeof(vis));

      vis[][]=;

      mp[][]=;

      mp[][]=;

      flag=false;

      printf("Scenario #%d:\n",cas++);

      dfs(,,);

      if(!flag) printf("impossible\n");

    puts("");

  }

    return ;

}

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A Knight's Journey_DFS

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