poj 2488 A Knight's Journey
2012-07-26 22:53
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A Knight's Journey
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
Source
TUD Programming Contest 2005, Darmstadt, Germany
也是一道经典的搜索题,只要注意是按照字典序输出。
Time Limit: 1000MS | Memory Limit: 65536K | |
Total Submissions: 20870 | Accepted: 7050 |
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
3 1 1 2 3 4 3
Sample Output
Scenario #1: A1 Scenario #2: impossible Scenario #3: A1B3C1A2B4C2A3B1C3A4B2C4
Source
TUD Programming Contest 2005, Darmstadt, Germany
也是一道经典的搜索题,只要注意是按照字典序输出。
#include<iostream> #include<string.h> #include<stdio.h> #define N 27 using namespace std; int path [2]; int flag,a,b; int map ; int move[8][2]={-2,-1,-2,1,-1,-2,-1,2,1,-2,1,2,2,-1,2,1};//按照字典序排列 void dfs(int i,int j,int step) { if(step==a*b)//成功条件 { for(int i=0;i<step;i++) printf("%c%d",path[i][0]+'A',path[i][1]+1); printf("\n"); flag=1; } else for(int x=0;x<8;x++) { int n=i+move[x][0]; int m=j+move[x][1]; if(n<b&&m<a&&n>=0&&m>=0&&!map [m]&&!flag)//在边界内且没有被访问 { map [m]=1; path[step][0]=n,path[step][1]=m; // cout<<path[step][0]<<path[step][1]<<endl; dfs(n,m,step+1); map [m]=0;//回溯 } } } int main() { int k=1,n; scanf("%d",&n); while(n--) { flag=0; scanf("%d %d",&a,&b); for(int i=0;i<a;i++) for(int j=0;j<b;j++) map[i][j]=0;//初始化地图 map[0][0]=1; path[0][0]=0,path[0][1]=0;//初始化起点 cout<<"Scenario #"<<k++<<":"<<endl; dfs(0,0,1);//搜索 if(!flag) cout<<"impossible"<<endl; cout<<endl; } return 0; }
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