POJ 3592 Instantaneous Transference

wamaker posted @ 2010年10月06日 07:42 in 图论 with tags 强连通分量 , 2042 阅读

起初从boat大牛那里听说了这题,挺有意思的,就做了做。

题意:一辆坦克从N*M矩阵的左上角出发,每次往右或往 下走一格,每格可以是'#'(表示不可以走),'*'表示传送门,或者是数字,表示在该格可以获得的值(只能取一次),传送门可以传送到指定位置,你可以选择被传送或者走相邻的格,问坦克可以获得的值的和最大为多少。

解析:第一次看应该是个DP,(如果无传送门且可以走K轮,可以用网络流),但是矩阵中有传送门的存在,有可能形成环,所以要转化成DAG(有向无环图),可以以格子的相邻关系建边,然后求SCC,缩点再构图,边权为指向的格子的值,后求最长路(可以搜索,可以DP)。

WA了好几次,传送门有可能传到'#'的格子,格子是'#'的时候也要向相邻格子建边,题目求的是坦克可以获得的最大值,而不是到右下角的值(上回做了道类似的网络流,惯性导致想当然了)。

最后贴个代码:

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

struct Edge
{
	int v;
	int next;
}buf[50000];

int head[2000],head2[2000],nE;
bool instack[2200];
int dfn[2020],low[2020],idx,Bcnt;
int stack[2020],top;
int Belong[2020];
int ores[2200];
int Bores[2200];
int N,M;

void addEdge(int u,int v)
{
	buf[nE].v=v;buf[nE].next=head[u];head[u]=nE++;
}

void addEdge2(int u,int v)
{
	buf[nE].v=v;buf[nE].next=head2[u];head2[u]=nE++;
}


void Tarjan(int cur)
{
	dfn[cur]=low[cur]=++idx;
	stack[top++]=cur;
	instack[cur]=true;

	for(int i=head[cur];i!=-1;i=buf[i].next)
	{
		int v=buf[i].v;
		if(!dfn[v])
		{
			Tarjan(v);
			if(low[cur]>low[v])
				low[cur]=low[v];
		}
		else if(instack[v]&&low[cur]>dfn[v])
		{
			low[cur]=dfn[v];
		}
	}
	if(dfn[cur]==low[cur])
	{
		Bcnt++;
		Bores[Bcnt]=0;
		int j;
		do
		{
			j=stack[--top];
			instack[j]=false;
			Belong[j]=Bcnt;
			Bores[Bcnt]+=ores[j];
		}while(j!=cur);
	}
}

void Rebuld()
{
	memset(head2,0xff,sizeof(head2));
	for(int i=0;i<N*M;i++)
		for(int j=head[i];j!=-1;j=buf[j].next)
		{
			int v=buf[j].v;
			if(Belong[i]!=Belong[v])
				addEdge2(Belong[i],Belong[v]);
		}
}

void go()
{
	memset(dfn,0,sizeof(dfn));
	memset(instack,false,sizeof(instack));
	idx=Bcnt=top=0;
	for(int i=0;i<N*M;i++)
		if(!dfn[i])
			Tarjan(i);
	Rebuld();
	int dis[2020];
	memset(dis,0,sizeof(dis));
	dis[Belong[0]]=Bores[Belong[0]];
	queue<int> que;
	que.push(Belong[0]);
	bool inq[2020];
	memset(inq,false,sizeof(inq));
	inq[Belong[0]]=true;
	while(!que.empty())
	{
		int cur=que.front();que.pop();
		inq[cur]=false;
		for(int i=head2[cur];i!=-1;i=buf[i].next)
		{
			int v=buf[i].v;
			if(dis[v]<dis[cur]+Bores[v])
			{
				dis[v]=dis[cur]+Bores[v];
				if(!inq[v])
				{
					inq[v]=true;
					que.push(v);
				}
			}
		}
	}
	int ans=-1;
	for(int i=1;i<=Bcnt;i++)
	   if(dis[i]>ans)
	       ans=dis[i];
	printf("%d\n",ans);
}

char map[45][45];

int main()
{
	int T;
	scanf("%d",&T);
	while(T--)
	{
		memset(head,0xff,sizeof(head));
		nE=0;
		scanf("%d%d",&N,&M);
		for(int i=0;i<N;i++)
			scanf("%s",map[i]);
		memset(ores,0,sizeof(ores));
		for(int i=0,r,c;i<N;i++)
			for(int j=0;j<M;j++)
				if(map[i][j]!='#')
				{	
					if(i+1<N&&map[i+1][j]!='#')addEdge(i*M+j,(i+1)*M+j);
					if(j+1<M&&map[i][j+1]!='#')addEdge(i*M+j,i*M+j+1);
					ores[i*M+j]=map[i][j]-'0';
					if(map[i][j]=='*')
				    {
                       ores[i*M+j]=0;
                       scanf("%d%d",&r,&c);
                       if(map[r][c]!='#')
                            addEdge(i*M+j,r*M+c);
				    }
				}
		go();
	}
	return 0;
}

0MS

  • 无匹配
Avatar_small
my today activity 说:
2023年7月10日 22:39

My Activity today is a piece tracking or recording user activity that collects information whenever users with a Google account use Google services daily such as today, yesterday, weekly, monthly, and yearly for entire activities from the account generation. my today activity These My Activity recording or collection services include YouTube, Google Maps, and other Google apps, as well as your search history when using the Google Chrome browser or doing a Google search.

Avatar_small
CBSE 4th Class Spli 说:
2023年8月21日 19:22

CBSE Curriculum is based on the National Curriculum Framework and Provides Opportunities for Students to Achieve Excellence in Learning, CBSE Provides the Syllabus for 4th Class, This new Syllabus CBSE 4th Class Split up Syllabus 2024 are Designed Strategically by a Team of Subject Experts and are Prescribed by the Ministry of Human Resource Development, formerly Ministry of Education, is Responsible for the Development of Human Resources in India, Primary Level Syllabus for the Children of has been developed with the Supervision of the Central Board of Secondary Education.


登录 *


loading captcha image...
(输入验证码)
or Ctrl+Enter