poj 1324（BFS+状态压缩）

解题思路：这道题一开始的想法就是状态压缩，即考虑如何判重，由于蛇并非是直线的，所以想到了以每一个点的上下左右共四个

值来表示相对位置。最开始想如何用四进制来表示它，无语。。。。。还是题目做少了，直接用两位来表示一个点即可（两位的二

进制数可以表示0-3）。剩下的关键就是判断蛇头会不会与蛇尾发生碰撞，详细的就看代码吧。。

整体的思路还是比较简单，但是代码很复杂，一般这种复杂点的搜索题代码都挺长的，所以很容易出错，不过可以用A*算法，而且

确实比朴素的算法要快，暂时还没想清楚怎么做。。。

#include <iostream>
#include <cstring>
#include <cstdio>
#include <queue>
using namespace std;

const int MAX_S = (1 << 14) + 100;
const int MAX_N = 20 + 2;
const int INF = (1 << 29);
struct State
{
int x, y, dis, s;
State(int x = 0, int y = 0, int dis = 0, int s = 0) : x(x), y(y), dis(dis), s(s) {};
};
struct Point
{
int x, y;
};
int N, M, res, L;
int vis[MAX_N][MAX_N][MAX_S];
int fx[4] = {-1, 0, 1, 0};
int fy[4] = {0, 1, 0, -1};
bool _map[MAX_N][MAX_N];
Point pos[MAX_N * MAX_N];
queue <State> Q;

int get_start()
{
int dir, dx, dy, s = 0;
for(int i = L - 1; i > 0; i--)
{
dx = pos[i].x - pos[i - 1].x, dy = pos[i].y - pos[i - 1].y;
if(dx == 0 && dy == 1)
dir = 1;
else if(dx == 0 && dy == -1)
dir = 3;
else if(dx == -1 && dy == 0)
dir = 0;
else if(dx == 1 && dy == 0)
dir = 2;
s = s << 2;
s = s | dir;
}
return s;
}
int get_next_state(int i, int s)
{
int dir;
int k = (1 << ((L - 1) << 1)) - 1;
int dx = 0, dy = 0;
dx = dx - fx[i], dy = dy - fy[i];
if(dx == 0 && dy == 1)
dir = 1;
else if(dx == 0 && dy == -1)
dir = 3;
else if(dx == -1 && dy == 0)
dir = 0;
else if(dx == 1 && dy == 0)
dir = 2;
s = s << 2;
s = s | dir;
s = s & k; // 去除高位部分
return s;
}

bool judge_code(int x, int y, int pre_x, int pre_y, int s)
{
int dir;
for(int i = 0; i < L - 1; i++)
{
dir = 3;
dir = dir & s;
s = s >> 2;
if(x == pre_x + fx[dir] && y == pre_y + fy[dir])
return false;
pre_x = pre_x + fx[dir], pre_y = pre_y + fy[dir];
}
return true;
}

void BFS()
{
State a;
int dx, dy, s;
while(!Q.empty())
{
a = Q.front();
Q.pop();
for(int i = 0; i < 4; i++)
{
dx = a.x + fx[i], dy = a.y + fy[i];
s = get_next_state(i, a.s);
if(dx > 0 && dy > 0 && dx <= N && dy <= M && !vis[dx][dy][s] && !_map[dx][dy] && judge_code(dx, dy, a.x, a.y, a.s))
{
if(dx == 1 && dy == 1)
{
res = a.dis + 1;
return ;
}
vis[dx][dy][s] = 1;
Q.push(State(dx, dy, a.dis + 1, s));
}
}
}
}

int main()
{
int s = 0, _case = 0;
State _start;
while(scanf("%d%d%d", &N, &M, &L), N + M + L)
{
res = INF;
memset(_map, 0 , sizeof(_map));
memset(vis, 0 , sizeof(vis));
for(int i = 0; i < L; i++)
scanf("%d%d", &pos[i].x, &pos[i].y);
int K, u, v;
scanf("%d", &K);
for(int i = 0; i < K; i++)
{
scanf("%d%d", &u, &v);
_map[u][v] = 1;
}
if(pos[0].x == 1 && pos[0].y == 1)
{
printf("Case %d: 0\n", ++_case);
continue;
}
s = get_start();
Q.push(State(pos[0].x, pos[0].y, 0, s));
vis[pos[0].x][pos[0].y][s] = 1;
BFS();
if(res == INF)
printf("Case %d: -1\n", ++_case);
else
printf("Case %d: %d\n", ++_case, res);
while(!Q.empty())
Q.pop();
}
return 0;
}