【POJ】A Knight's Journey
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Problem here
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
31 12 34 3
Sample Output
Scenario #1:A
1Scenario #2:impossible
Scenario #3:A1B3C1A2B4C2A3B1C3A4B2C4
Source
TUD Programming Contest 2005, Darmstadt, Germany
Solution
#include <iostream>#include <memory.h>using namespace std;int dx[8] = {-2, -2, -1, -1, 1, 1, 2, 2};int dy[8] = {-1, 1, -2, 2, -2, 2, -1, 1};int allStep;char ans[100];bool visit[100][100];bool ok;int p, q;void dfs(int cnt, int x, int y){ if(cnt == allStep){ for(int i = 0; i < 2*cnt; i++){ cout << ans[i]; } cout << endl; ok = true; return ; } for(int i = 0; i < 8; i++){ if(ok == false){ int new_x = x+dx[i]; int new_y = y+dy[i]; if(new_x > 0 && new_y > 0 && new_x <= q && new_y <= p){ if(visit[new_x][new_y] == false){ visit[new_x][new_y] = true; ans[2*cnt] = 'A' + new_x-1; ans[2*cnt+1] = '1' + new_y-1; dfs(cnt+1, new_x, new_y); visit[new_x][new_y] = false; } } } }}int main(){ int kase; cin >> kase; for(int ks = 1; ks <= kase; ks++){ cin >> p >> q; allStep = p*q; memset(visit, false, sizeof(visit)); ok = false; visit[1][1] = true; ans[0] = 'A'; ans[1] = '1'; cout << "Scenario #" << ks << ":" << endl; dfs(1, 1, 1); if(ok == false){ cout << "impossible" << endl; } cout << endl; } return 0;}
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