Ponds

Time Limit: 1500/1000 MS (Java/Others) Memory Limit: 131072/131072 K (Java/Others)
Total Submission(s): 1308 Accepted Submission(s): 439

Problem Description

Betty owns a lot of ponds, some of them are connected with other ponds by pipes, and there will not be more than one pipe between two ponds. Each pond has a value v .

Now Betty wants to remove some ponds because she does not have enough money. But each time when she removes a pond, she can only remove the ponds which are connected with less than two ponds, or the pond will explode.

Note that Betty should keep removing ponds until no more ponds can be removed. After that, please help her calculate the sum of the value for each connected component consisting of a odd number of ponds

Input

The first line of input will contain a number T(1≤T≤30) which is the number of test cases.

For each test case, the first line contains two number separated by a blank. One is the number p(1≤p≤104) which represents the number of ponds she owns, and the other is the number m(1≤m≤105) which represents the number of pipes.

The next line contains p numbers v1,...,vp , where vi(1≤vi≤108) indicating the value of pond i .

Each of the last m lines contain two numbers a and b , which indicates that pond a and pond b are connected by a pipe.

Output

For each test case, output the sum of the value of all connected components consisting of odd number of ponds after removing all the ponds connected with less than two pipes.

Sample Input

1 7 7 1 2 3 4 5 6 7 1 4 1 5 4 5 2 3 2 6 3 6 2 7

Sample Output

Source

2015 ACM/ICPC Asia Regional Changchun Online

题目大意：

给定一些池塘，池塘之间连有一些管道。要求将不连管道或者只连一根管道的池塘消去，问最后剩下连在一起且池塘个数为奇数的池塘权值总和。

解题：

比赛的时候，以为是什么奇环，后来发现又不是，思路整体跑偏了。正确的解法是，通过bfs或者dfs不断消去度数为1的点，消完之后，再用dfs找联通块即可。以下提供两种解法，实际上没什么实质差别，复杂度都为O(m),因为每条边最多遍历一次。

解法一：

dfs+dfs

代码：

#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cstring>
#include <string>
#include <queue>
using namespace std;
#define LL long long
int pond[10010];
//邻接表
struct edge
{int next,to,vis;//下一条边序号，到哪个点，边是否被断开
}store[200010];
int head[10010],cnt,degree[10010],num;//head存储每个点连向的第一条边的存储下标，-1代表该点当前已经没有边了
//cnt加边的下标，degree度数，num联通块中的块数
bool vist[10010];//数联通块时的标记
LL sum;//存储联通块的总和
//加边
void addedge(int a,int b)
{store[cnt].to=b;store[cnt].next=head[a];store[cnt].vis=false;head[a]=cnt++;
}
//消去池塘
void dfs(int x)
{int tmp;tmp=head[x];degree[x]=0;//还未到最后一条边while(tmp!=-1){if(degree[store[tmp].to]){//tmp和tmp^1代表相邻两条边store[tmp].vis=store[tmp^1].vis=true;degree[store[tmp].to]--;//如果度数为1，继续搜索if(degree[store[tmp].to]==1)dfs(store[tmp].to);}//移向下一条边tmp=store[tmp].next;}return;
}
void dfs2(int x)
{int tmp,v;vist[x]=1;tmp=head[x];while(tmp!=-1){//如果这条边还没断开if(!store[tmp].vis){v=store[tmp].to;if(!vist[v]&°ree[v]){num++;sum+=pond[v];dfs2(v);}}tmp=store[tmp].next;}
}
int main()
{int t,p,m,u,v,tmp,cas=1;LL ans;scanf("%d",&t);while(t--){scanf("%d%d",&p,&m);memset(head,-1,sizeof(head));memset(degree,0,sizeof(degree));memset(vist,0,sizeof(vist));cnt=ans=0;for(int i=1;i<=p;i++)scanf("%d",&pond[i]);for(int i=1;i<=m;i++){scanf("%d%d",&u,&v);addedge(u,v);addedge(v,u);degree[u]++;degree[v]++;}//搜索度数为1的池塘for(int i=1;i<=p;i++)if(degree[i]==1)dfs(i);//统计结果for(int i=1;i<=p;i++){if(degree[i]&&!vist[i]){sum=pond[i];num=1;dfs2(i);if(num%2)ans+=sum;}}printf("%lld\n",ans);}return 0;
}

解法二：

bfs+dfs

代码：

#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cstring>
#include <string>
#include <queue>
using namespace std;
int pond[10010];
struct edge
{int next,to;
}store[200010];
int head[10010],cnt,degree[10010];
bool vist[10010],cut_off[200010];
long long sum;
int num;
queue <int> qe;
inline void addedge(int a,int b)
{store[cnt].to=b;store[cnt].next=head[a];head[a]=cnt++;
}
void bfs()
{int tmp,cur,v;while(!qe.empty()){cur=qe.front();qe.pop();tmp=head[cur];while(~tmp){v=store[tmp].to;if(degree[v]){cut_off[tmp]=cut_off[tmp^1]=1;degree[v]--;if(degree[v]==1){qe.push(v);degree[v]=0;}}tmp=store[tmp].next;}}
}
void dfs(int x)
{int tmp,v;vist[x]=1;tmp=head[x];while(tmp!=-1){if(!cut_off[tmp]){v=store[tmp].to;if(!vist[v]){num++;sum+=pond[v];dfs(v);}}tmp=store[tmp].next;}
}
int main()
{int t,p,m,u,v;long long  ans;scanf("%d",&t);while(t--){scanf("%d%d",&p,&m);memset(head,-1,sizeof(head));memset(degree,0,sizeof(degree));memset(vist,0,sizeof(vist));memset(cut_off,0,sizeof(cut_off));cnt=0,ans=0;for(int i=1;i<=p;i++)scanf("%d",&pond[i]);for(int i=1;i<=m;i++){scanf("%d%d",&u,&v);addedge(u,v);addedge(v,u);degree[u]++;degree[v]++;}for(int i=1;i<=p;i++)if(degree[i]==1)qe.push(i),degree[i]=0;bfs();for(int i=1;i<=p;i++){if(degree[i]&&!vist[i]){sum=pond[i];num=1;dfs(i);if(num%2)ans+=sum;}}printf("%lld\n",ans);}return 0;
}

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