【USACO3.2.5】魔板 康托展开/BFS

我A*然后错了！  其实我不知道我的A*哪里错了…… 但是不管了，以后再练A*好了。

题目思想： 任何一个全排列数字，可以用康拓展开的知识，来映射到一个数字上去。   http://zh.wikipedia.org/wiki/%E5%BA%B7%E6%89%98%E5%B1%95%E5%BC%80

WIKI有详细的讲解。

当然，用散列函数也可以让全排列数字能有映射效果，MAP什么都可以解决这个问题……

其实就是BFS啦！  核心问题就是，判断这个状态是否进过队列。  把这个8位全排列，用康拓展开映射成数字，或者直接散列函数，或者扔进平衡树，都可以解决问题……

我的程序因为原来想写A*，然后写挂了……所以很丑很长……而且也不快

Compiling...
Compile: OK

Executing...
   Test 1: TEST OK [0.005 secs, 4024 KB]
   Test 2: TEST OK [0.003 secs, 4024 KB]
   Test 3: TEST OK [0.003 secs, 4024 KB]
   Test 4: TEST OK [0.003 secs, 4024 KB]
   Test 5: TEST OK [0.022 secs, 4024 KB]
   Test 6: TEST OK [0.035 secs, 4024 KB]
   Test 7: TEST OK [0.051 secs, 4024 KB]
   Test 8: TEST OK [0.073 secs, 4024 KB]

All tests OK.

/*
TASK:msquare
LANG:C++
*/
#include <iostream>
#include <queue>
#include <cstdio>
#include <cstring>
using namespace std;


int factorial[10]={1,1,2,6,24,120,720,5040,40320,362880};
bool vis[10];
int pnext[10], ppre[10];

inline void clean()
{
	for (int i = 1; i <= 8; ++ i)	
	{
		ppre[i] = i - 1;
		pnext[i] = i + 1;
	}
	pnext[0] = 1;
	ppre[9] = 9;
}

inline void del(int k)
{
	pnext[ppre[k]] = pnext[k];
	ppre[pnext[k]] = ppre[k];
}

inline int cantor_expand(int *r, int n = 8)//r数组(含0下标) 有n位，转化为一个数字
{
	int ans = 0;
	clean();

	for (int i = 0; i != n; ++ i)
	{
		int tmp = -1;
		for (int j = 0; j < r[i]; j = pnext[j], ++ tmp);	
		del(r[i]);
		//cout<<tmp<<" " << n - i - 1 << endl;
		ans += tmp * factorial[n - i - 1];
	}
	return ans;
}

inline void cantor_expand(int k, int *r, int n = 8)//k这个数字，有n位，转化进r数组
{
	clean();
	for (int i = 0; i != n - 1; ++ i)
	{
		int tmp = k / factorial[n - i - 1], count = 0, j;
		for (j = pnext[0]; ; j = pnext[j])	
		{
			++ count;
			if (count == tmp + 1)	break;
		}
		r[i] = j;
		del(j);
		k %= factorial[n - i - 1];
	}
	r[n - 1] = pnext[0];
}

//init 函数：处理最短路径问题

int g[9][9];//保存每个数字到每个地方的距离
void init()
{
	int num[2][4],t=0;
	for (int i = 0; i <= 1; ++ i)
		for (int j = 0; j != 4; ++ j)	num[i][j] = t ++ ;
	memset(g, 40, sizeof(g));
	int inf = g[0][0];
	for (int i = 0; i != 9; ++ i)	g[i][i] = 0;
	g[1][8] = g[2][7] = g[3][6] = g[4][5] = 1;
	g[8][1] = g[7][2] = g[6][3] = g[5][4] = 1;
	g[1][2] = g[2][3] = g[3][4] = g[4][1] = 1;
	g[8][7] = g[7][6] = g[6][5] = g[5][8] = 1;
	g[6][7] = 1;
	for (int k = 0; k != 9; ++ k)
		for (int i = 0; i != 9; ++ i)
			for (int j = 0; j != 9; ++ j)
				if (g[i][k] + g[k][j] < g[i][j])	g[i][j] = g[i][k] + g[k][j];
}

int cantor[10];
struct node
{
	int way;
	int did, willdid;
	int num;
	node(int W, int D, int NUM):way(W),did(D),num(NUM)
	{
		cantor_expand(num, cantor);
		//for (int i = 0; i != 8; ++ i)	cout<<cantor[i]<<" ";cout<<endl;
		willdid = 0;
		for (int i = 0; i != 8; ++ i)
		{
			int tmp = g[cantor[i]][i + 1];
			willdid = max(willdid, tmp);
		}
		willdid = 0;
	}
};

inline bool operator < (node A, node B)
{
	if (A.did + A.willdid == B.did + B.willdid)	return A.way > B.way; //估价步数相同，使用转移
	return A.did + A.willdid > B.did + B.willdid;
}

bool v[41000] = {0};
int pre[41000]={0}, plan[41000];
int cantor_tmp[10];
//priority_queue<node>q;
queue<node>q;

inline int one(int now, int did)
{
	for (int i = 0; i != 8; ++ i)	cantor[i] = cantor_tmp[i];
	swap(cantor[0], cantor[7]);
	swap(cantor[1], cantor[6]);
	swap(cantor[2], cantor[5]);
	swap(cantor[3], cantor[4]);
	int tmp = cantor_expand(cantor);
	if (!v[tmp])
	{
		v[tmp] = 1;	
		pre[tmp] = now;
		plan[tmp] = 1;
		q.push(node(1, did, tmp));
	}
	return tmp;
}

inline int two(int now, int did)
{
	for (int i = 0; i != 8; ++ i)	cantor[i] = cantor_tmp[i];
	int tmp = cantor[3];
	for (int i = 3; i >= 1; -- i)	cantor[i] = cantor[i - 1];
	cantor[0] = tmp;
	tmp = cantor[4];
	for (int i = 4; i <= 7; ++ i)	cantor[i] = cantor[i + 1];
	cantor[7] = tmp;
	tmp = cantor_expand(cantor);
	if (!v[tmp])
	{
		v[tmp] = 1;	
		pre[tmp] = now;
		plan[tmp] = 2;
		q.push(node(2, did, tmp));
	}
	return tmp;
}

inline int three(int now, int did)
{
	for (int i = 0; i != 8; ++ i)	cantor[i] = cantor_tmp[i];
	int tmp = cantor[6];
	cantor[6] = cantor[5];
	cantor[5] = cantor[2];
	cantor[2] = cantor[1];
	cantor[1] = tmp;
	tmp = cantor_expand(cantor);
	if (!v[tmp])
	{
		v[tmp] = 1;
		pre[tmp] = now;
		plan[tmp] = 3;
		q.push(node(3, did, tmp));
	}
	return tmp;
}

int output[41000],ot=0;
void doit()
{
	int aim, tmp, begin(0), a[10];
	for (int i = 0; i != 8; ++ i)	cin >> a[i];
	aim = cantor_expand(a);
	q.push(node(0, 0, begin));
	v[begin] = 1;
	while (1)
	{
		int now = q.front().num;
		int did = q.front().did;
		q.pop();
		cantor_expand(now, cantor_tmp);
		if (one(now, did + 1) == aim)	break;
		if (two(now, did + 1) == aim)	break;
		if (three(now, did + 1) == aim)	break;
	}
	int now = aim;
	while (now != begin)
	{
		output[ot++] = plan[now];
		now = pre[now];
	}
	cout<<ot<<endl;
	for (int i = ot - 1; i >= 0; -- i)	cout<<(char)(output[i]+'A' - 1);
	cout<<endl;
}

int main()
{
	freopen("msquare.in","r",stdin);
	freopen("msquare.out","w",stdout);
	init();
	doit();
	return 0;
}