BZOJ 3205 [Apio2013]机器人 ——斯坦纳树

#include <map>
#include <cmath>
#include <queue>
#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
using namespace std;
#define F(i,j,k) for (int i=j;i<=k;++i)
#define D(i,j,k) for (int i=j;i>=k;--i)
#define inf 0x3f3f3f3f
#define maxn 502
#define ll long long
#define mp make_pair

short n,r,c,a[maxn][maxn];
int dp[maxn][maxn][10][10];
char s[maxn][maxn];
short mov[4][2]={{0,1},{1,0},{0,-1},{-1,0}};
short go[maxn][maxn][4][2];

void Readin()
{
	memset(dp,0x3f,sizeof dp);
	cin>>n>>c>>r;
	F(i,1,r)
	{
		scanf("%s",s[i]+1);
		F(j,1,c)
		{
			switch(s[i][j])
			{
				case ‘.‘:a[i][j]=0;break;
				case ‘x‘:a[i][j]=-1;break;
				case ‘A‘:a[i][j]=10;break;
				case ‘C‘:a[i][j]=11;break;
				default: a[i][j]=s[i][j]-‘0‘;dp[i][j][a[i][j]][a[i][j]]=0;break;
			}
		}
	}
	F(i,0,r) a[i][0]=a[i][c+1]=-1;F(i,0,c) a[0][i]=a[r+1][i]=-1; a[r+1][c+1]=-1;
}

int vis[maxn][maxn][4],idx;

void dfs(int nx,int ny,int k)
{
	int tmp=k;
	if (vis[nx][ny][k]==idx)
	{
		go[nx][ny][k][0]=-1;
		go[nx][ny][k][1]=-1;
		return;
	}
	vis[nx][ny][k]=idx;
	if (go[nx][ny][k][0]!=0) return;
	switch(a[nx][ny])
	{
		case 10:tmp=(tmp+3)%4;break;
		case 11:tmp=(tmp+1)%4;break;
	}
	if (a[nx+mov[tmp][0]][ny+mov[tmp][1]]==-1)
	{
		go[nx][ny][k][0]=nx;
		go[nx][ny][k][1]=ny;
		return;
	}
	int tx=nx+mov[tmp][0],ty=ny+mov[tmp][1];
	if (!go[tx][ty][tmp][0]) dfs(tx,ty,tmp);
	go[nx][ny][k][0]=go[tx][ty][tmp][0];
	go[nx][ny][k][1]=go[tx][ty][tmp][1];
}

void init()
{
	F(i,1,r) F(j,1,c)
	F(k,0,3){
		int nx=i,ny=j,flag=1;++idx;
		dfs(nx,ny,k);
	}
}

struct Statement{short x,y,l,r; int v;}sta[maxn*maxn],res[maxn*maxn];
queue <Statement> q,d;
int top=0;

bool Com(Statement a, Statement b)
{return a.v<b.v;}

int cnt[200005],ctop=0;

void Radix_Sort()
{
	memset(cnt,0,sizeof cnt);
	F(i,1,top)
	{
		if (sta[i].v>=200000) continue;
		cnt[sta[i].v]++,ctop=max(ctop,sta[i].v);
	}
	F(i,1,ctop) cnt[i]+=cnt[i-1]; int tmp=cnt[ctop];
	F(i,1,top)
	{
		if (sta[i].v>=200000) continue;
		res[cnt[sta[i].v]--]=sta[i];
	}
	F(i,1,tmp) sta[i]=res[i];
	memcpy(sta,res,(top+1)*sizeof(Statement));
}

void SPFA()
{
//	sort(sta+1,sta+top+1,Com);
	Radix_Sort();
	F(i,1,top) q.push(sta[i]);
	while (!q.empty()||!d.empty())
	{
		int nx,ny,l,r,v;
		if (d.empty()||(!d.empty()&&!q.empty()&&q.front().v<=d.front().v))
		{
			Statement now=q.front(); q.pop();
			nx=now.x,ny=now.y,l=now.l,r=now.r,v=now.v;
		}
		else
		{
			Statement now=d.front(); d.pop();
			nx=now.x,ny=now.y,l=now.l,r=now.r,v=now.v;
		}
		if (dp[nx][ny][l][r]<v) continue;
		for (int k=0;k<4;++k)
			if (go[nx][ny][k][0]!=-1)
			{
				int tx=go[nx][ny][k][0],ty=go[nx][ny][k][1];
				if (dp[tx][ty][l][r]>dp[nx][ny][l][r]+1)
				{
					dp[tx][ty][l][r]=dp[nx][ny][l][r]+1;
					Statement now;
					now.x=tx;now.y=ty;now.l=l;now.r=r;now.v=dp[tx][ty][l][r];
					d.push(now);
				}
			}
	}
}
void DP()
{
	F(i,1,r) F(j,1,c) if (a[i][j]>=1&&a[i][j]<=n)
	{++top;sta[top].x=i;sta[top].y=j;sta[top].l=a[i][j];sta[top].r=a[i][j];sta[top].v=dp[i][j][a[i][j]][a[i][j]];}
	SPFA();
	F(len,2,n)
	{
		F(i,1,n-len+1)
		{
			top=0;
			int j=i+len-1;
			F(x,1,r) F(y,1,c)
			{
				F(z,i,j-1) dp[x][y][i][j]=min(dp[x][y][i][z]+dp[x][y][z+1][j],dp[x][y][i][j]);
				if (dp[x][y][i][j]<inf)
				{
					Statement now;
					now.x=x;now.y=y;now.l=i;now.r=j;now.v=dp[x][y][i][j];
					sta[++top]=now;
				}
			}
			SPFA();
		}
	}
	int ans=inf;
	F(i,1,r) F(j,1,c) ans=min(ans,dp[i][j][1][n]);
	printf("%d\n",ans==inf?-1:ans);
}

int main()
{
	Readin();
	init();
	DP();
}