Sparse Graph
Time Limit: 4000/2000 MS (Java/Others) Memory Limit: 262144/262144 K (Java/Others) Total Submission(s): 1604 Accepted Submission(s): 565
Problem Description
In graph theory, the
complement
of a graph
G
is a graph
H
on the same vertices such that two distinct vertices of
H
are adjacent if and only if they are
not
adjacent in
G
.
Now you are given an undirected graph
G
of
N
nodes and
M
bidirectional edges of
unit
length. Consider the complement of
G
, i.e.,
H
. For a given vertex
S
on
H
, you are required to compute the shortest distances from
S
to all
N−1
other vertices.
Input
There are multiple test cases. The first line of input is an integer
T(1≤T<35)
denoting the number of test cases. For each test case, the first line contains two integers
N(2≤N≤200000)
and
M(0≤M≤20000)
. The following
M
lines each contains two distinct integers
u,v(1≤u,v≤N)
denoting an edge. And
S (1≤S≤N)
is given on the last line.
Output
For each of
T
test cases, print a single line consisting of
N−1
space separated integers, denoting shortest distances of the remaining
N−1
vertices from
S
(if a vertex cannot be reached from S, output ``-1" (without quotes) instead) in ascending order of vertex number.
Sample Input
1
2 0
1
Sample Output
1
Source
2016 ACM/ICPC Asia Regional Dalian Online
思路:
维护一个集合ac,在当前集合中表示可以拓展到点。 维护一个集合nac,在当前集合中表示不可以拓展到点。 bfs搜索,从当前队列中取出一点u,将图G中与u相连的边从ac中删去,并添加到nac中,并拓展ac中到点,添加到队列中,如此反复,直到队列为空。
#include<iostream>
#include<cstdio>
#include<cmath>
#include<cstring>
#include<climits>
#include<string>
#include<queue>
#include<stack>
#include<set>
#include<map>
#include<algorithm>
using namespace std;
#define rep(i,j,k)for(i=j;i<k;i++)
#define per(i,j,k)for(i=j;i>k;i--)
#define MS(x,y)memset(x,y,sizeof(x))
typedef long long LL;
const int INF=0x7ffffff;
const int M=2e5+1;
vector<int>g[M];
int dis[M];
int i,j,k,n,m;
int s;
void solve()
{
set<int>ac,nac;
for(i=1;i<=n;i++){
if(i!=s)ac.insert(i);
}
queue<int>q;
q.push(s);
MS(dis,0);
while(!q.empty())
{
int u=q.front();
q.pop();
for(i=0;i<g[u].size();i++){
int &v=g[u][i];
if(!ac.count(v))continue;
ac.erase(v);
nac.insert(v);
}
for(set<int>::iterator it=ac.begin();it!=ac.end();it++){
dis[*it]=dis[u]+1;
q.push(*it);
}
ac.swap(nac);
nac.clear();
}
int flag=0;
for(i=1;i<=n;i++){
if(i==s)continue;
if(flag)printf(" ");
if(!dis[i])printf("-1");
else printf("%d",dis[i]);
flag=1;
}
printf("\n");
}
int main()
{
int T;
scanf("%d",&T);
while(T--)
{
scanf("%d%d",&n,&m);
for(i=1;i<=n;i++)g[i].clear();
for(i=0;i<m;i++){
int a,b;
scanf("%d%d",&a,&b);
g[a].push_back(b);
g[b].push_back(a);
}
scanf("%d",&s);
solve();
}
return 0;
}
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