POJ 2488 A Knight's Journey【DFS + 回溯应用】
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原题链接:http://poj.org/problem?id=2488
我的链接:http://acm.hust.edu.cn/vjudge/contest/view.action?cid=19651#problem/A
A Knight's Journey
Time Limit: 1000MS Memory Limit: 65536KTotal Submissions: 23452 Accepted: 7944
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.
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.
If no such path exist, you should output impossible on a single line.
Sample Input
31 12 34 3
Sample Output
Scenario #1:A1Scenario #2:impossibleScenario #3:A1B3C1A2B4C2A3B1C3A4B2C4
Source
TUD Programming Contest 2005, Darmstadt, Germany
算法:DFS + 回溯
题意:骑士周游列国问题,说白了就是任一给你一个棋盘(当然满足格子数小于26)
让你从第一个格子按照图中所给的马走日的步法
不重复遍历走完整个棋盘。然后按照字典序输出路径即可
思路:按照图中的八个方向dfs即可。
注意: 1.回溯的用法,千万别忘了还原状态。
2.路径的输出,字典序的是列。。。
/******************************************************//AAccepted148 KB0 msC++1259 B题意:骑士周游列国,马走日八个方向走,同时也要注意字典序 最后是按照字典序输出的 注意:先输入列再输入行*******************************************************/#include<stdio.h>#include<string.h>const int maxn = 30;int vis[maxn][maxn];int n,m;int dir[8][2] = {-2,-1, -2,1, -1,-2, -1,2, 1,-2, 1,2, 2,-1, 2,1};//注意方向也要按照字典序来 ,否则WA的好惨。。。struct Path{ int x,y;}p[maxn];int flag;void dfs(int x, int y, int step){ if(flag) return; p[step].x = x; p[step].y = y; if(step == n*m) { flag = 1; return; } Path next; for(int i = 0; i < 8; i++) { next.x = x+dir[i][0]; next.y = y+dir[i][1]; if(next.x >= 1 && next.x <= n && next.y >= 1 && next.y <= m && !vis[next.x][next.y]) { vis[next.x][next.y] = 1; dfs(next.x, next.y, step+1); vis[next.x][next.y] = 0; } } return;}int main(){ int T; scanf("%d", &T); for(int t = 1; t <= T; t++) { scanf("%d%d", &m,&n); //先输入列再输入行 memset(vis,0,sizeof(vis)); memset(p,0,sizeof(p)); flag = 0; vis[1][1] = 1; dfs(1,1,1); printf("Scenario #%d:\n", t); if(flag) { for(int i = 1; i <= n*m; i++) printf("%c%d", p[i].x-1+'A', p[i].y); printf("\n"); } else printf("impossible\n"); if(t != T) printf("\n"); } return 0;}
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