B-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
给一个n1*n2的棋盘,从(0,0)出发,每次走日字形,能否不重复的遍历所有的点.从A1这个格子开始搜索,就能保证字典序是小的;除了这个条件,我们还要控制好马每次移动的方向,控制方向时保证字典序最小(即按照下图中格子的序号搜索)。控制好这两个条件,直接从A1开始深搜就行了。
#include<cstdio> #include<cstring> #include<algorithm> using namespace std; int path[88][88], vis[88][88], p, q, cnt; bool flag; int dx[8] = {-1, 1, -2, 2, -2, 2, -1, 1}; int dy[8] = {-2, -2, -1, -1, 1, 1, 2, 2}; bool judge(int x, int y) { if(x >= 1 && x <= p && y >= 1 && y <= q && !vis[x][y] && !flag) return true; return false; } void DFS(int r, int c, int step) { path[step][0] = r; path[step][1] = c; if(step == p * q) { flag = true; return ; } for(int i = 0; i < 8; i++) { int nx = r + dx[i]; int ny = c + dy[i]; if(judge(nx,ny)) { vis[nx][ny] = 1; DFS(nx,ny,step+1); vis[nx][ny] = 0; } } } int main() { int i, j, n, cas = 0; scanf("%d",&n); while(n--) { flag = 0; scanf("%d%d",&p,&q); memset(vis,0,sizeof(vis)); vis[1][1] = 1; DFS(1,1,1); printf("Scenario #%d:\n",++cas); if(flag) { for(i = 1; i <= p * q; i++) printf("%c%d",path[i][1] - 1 + 'A',path[i][0]); } else printf("impossible"); printf("\n"); //if(n != 0) printf("\n"); } return 0; }
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