Knight Moves

Problem Description

A friend of
you is doing research on the Traveling Knight Problem (TKP) where
you are to find the shortest closed tour of knight moves that
visits each square of a given set of n squares on a chessboard
exactly once. He thinks that the most difficult part of the problem
is determining the smallest number of knight moves between two
given squares and that, once you have accomplished this, finding
the tour would be easy.

Of course you know that it is vice versa. So you offer him to write
a program that solves the "difficult" part.



Your job is to write a program that takes two squares a and b as
input and then determines the number of knight moves on a shortest
route from a to b.

Input

The input file
will contain one or more test cases. Each test case consists of one
line containing two squares separated by one space. A square is a
string consisting of a letter (a-h) representing the column and a
digit (1-8) representing the row on the chessboard.

Output

For each test
case, print one line saying "To get from xx to yy takes n knight
moves.".

Sample Input

e2 e4

a1 b2

b2 c3

a1 h8

a1 h7

h8 a1

b1 c3

f6 f6

Sample Output

To get from
e2 to e4 takes 2 knight moves.

To get from
a1 to b2 takes 4 knight moves.

To get from
b2 to c3 takes 2 knight moves.

To get from
a1 to h8 takes 6 knight moves.

To get from
a1 to h7 takes 5 knight moves.

To get from
h8 to a1 takes 6 knight moves.

To get from
b1 to c3 takes 1 knight moves.

To get from
f6 to f6 takes 0 knight moves.

题意：给你两个坐标求棋子马过去的最少步数；

解题思路：最短路径问题，有新意的地方就是不再是上下左右走，而是跳马，八个方向用广搜，第一个搜到的就是最短路径；

感悟：一道中规中矩的题；

代码：

#include

#include

#include

#include

#define maxn 10

using namespace std;

int
dir[8][2]={{-2,-1},{-1,-2},{1,-2},{2,-1},{-2,1},{-1,2},{1,2},{2,1}};

int visit[maxn][maxn];

int check(int a,int b)

{

   
if(a<1||a>8||b<1||b>8||visit[a][b])

       
return 1;

    else

       
return 0;

}

struct node

{

    int
x,y;

    int
times;

}start,fr,a;

int bfs(int sx,int sy,int x,int y)

{

   
memset(visit,0,sizeof(visit));

    queue
Q;

   
start.x=sx;

   
start.y=sy;

   
start.times=0;

   
visit[start.x][start.y]=1;

   
Q.push(start);

   
while(!Q.empty())

    {

       
fr=Q.front();

       
Q.pop();

       
//cout<<"x="<<x<<"
"<<"y="<<y<<endl;

       
if(fr.x==x&&fr.y==y)

           
return fr.times;

       
for(int i=0;i<8;i++)

       
{

           
a.x=fr.x+dir[i][0];

           
a.y=fr.y+dir[i][1];

           
if(check(a.x,a.y))

               
continue;

           
a.times=fr.times+1;

           
visit[a.x][a.y]=1;

           
Q.push(a);

       
}

    }

}

int main()

{

   
//freopen("in.txt", "r", stdin);

    char
a,b;

    int
sx,sy,x,y;

   
while(~scanf("%c%d %c%d\n",&a,&sy,&b,&y))

    {

       
//cout<<"sx="<<a<<endl;

       
//cout<<"sy="<<sy<<endl;

       
//cout<<"x="<<b<<endl;

       
//cout<<"y="<<y<<endl;

       
sx=a-'a'+1;

       
x=b-'a'+1;

       
//坐标转化成数字

       
int ans=bfs(sx,sy,x,y);

       
printf("To get from %c%d to %c%d takes %d knight
moves.\n",a,sy,b,y,ans);

    }

    return
0;

}