poj 2488 A Knight's Journey
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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
3
1 1
2 3
4 3
Sample Output
Scenario #1:
A1
Scenario #2:
impossible
Scenario #3:
A1B3C1A2B4C2A3B1C3A4B2C4
【分析】
比较裸的搜索题目了
题意就是给你一个棋盘,然后问一个马(起点未给出)怎么跳能遍历这张棋盘且每个点只能跑一次,如果有多解,输出字典序最小的解,如果无解,输出impossible
其实这道题关键就是字典序问题了,其实只要尽量朝着A1的方向跑就好了,具体顺序详见代码
【代码】
//poj 2488 A Knight's Journey#include<iostream>#include<cstdio>#include<cstring>#define fo(i,j,k) for(i=j;i<=k;i++)#define M(a) memset(a,0,sizeof a)using namespace std;int n,m,t;int u[9]={0,-1,1,-2,2,-2,2,-1,1},v[9]={0,-2,-2,-1,-1,1,1,2,2},r[65][3];bool vis[9][9],flag;void print(){ int i,j; fo(i,1,n*m) printf("%c%d",r[i][2]+'A'-1,r[i][1]);}void dfs(int x,int y,int tot){ r[tot][1]=x; r[tot][2]=y; int i,j; if(flag) return; fo(i,1,8) { int a=x+u[i],b=y+v[i]; if(a>=1 && a<=n && b>=1 && b<=m && !vis[a][b]) { vis[x][y]=1; dfs(a,b,tot+1); vis[x][y]=0; } } if(tot==n*m) { print(); flag=1; }}int main(){ int i,j,k; scanf("%d",&t); fo(k,1,t) { flag=0; scanf("%d%d",&n,&m); printf("Scenario #%d:\n",k); fo(j,1,m) { fo(i,1,n) { M(vis); M(r); dfs(i,j,1); if(flag) break; } if(flag) break; } if(!flag) printf("impossible"); printf("\n\n"); } return 0;}
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